Continental Drift / Displacement of Continents excerpt from Core Publishing ISBN 0-9690-4410-0 1980

Michael ( Miklos) Csuzdi, P. Eng. ( Electrical) Oct 8, 1929 - July 23, 1995

Michael Csuzdi devoted a great deal of his life in private research studying weather and geophysical phenomena. He applied electrical engineering theory to explain super nova storms; cyclones and anticyclones; earth currents, geomagnetic fields and their reversal; and finally displacement of the continents.

These physical phenomena he concluded were all based on the well observed flow of electrons from the earth’s molten magma core out to space. This thermionic emission he fully modeled with the well established equations related to electrostatic charge and vacuum tube technology. He concluded it is the immense volume of the earth’s combined oceans and continents that makes these small electrical forces of nature grow exponentially into the force of nature of our planet. In later years he applied the same mathematical modeling to explain the continental positions on the earth’s moon and the planet Mars based on observed data of the time.

His body of work based on thermionic emission is best understood by the pure physics community rather than the geophysics community that has consistently applied mechanically oriented explanations to observations on Earth. This has limited it’s understanding and acceptance. This need not be the case as the concepts and equations are straight forward and easily understood with an open scientific mind.

You have entered this web page based on a key word search that is tied to a subject and explained by Michael Csuzdi’s theories. It is hoped that the following chapter taken from this published work with spark interest in the proposed explanation and drive curiosity in reading the complete document. Only then can the wholeness of his thermionic emission theory be fully realized as complete and scientifically accurate.

The goal of this website is to drive further independent review and scientific debate on the theories proposed by Michael Csuzdi. If they can be corroborated then the potential for better weather prediction, earthquake prediction and an unlimited source of clean energy harvesting could be realized.

Please feel free to share any of these documents and links with others as you see fit. The more review and dialogue the better.

8. Displacement of the Continents.

Electrically charged bodies exhibit a force between themselves. This force is described by Coulomb's equation:

F == (8-1)

where £0

is the permittivity of free space, 8.85 x 10-12

coulomb2 /newton, Q1 and Q2 are the electric charges of the bodies, in coulombs, R is the distance between the bodies, in metres, F is the force, in newtons. The force is an attraction if the signs of the charges are different, and it is a repulsion if they are identical. Since the Earth's crust is infused with negative charges, large blocks of the crust, the continents, should repel one another. In this chapter I investigate the numerical values of this repulsion force.

Coulomb's force results in the displacement of bodies infused with free electrons if at least one of the bodies is free to move. The Absolute Electrometer, a standard laboratory equipment, utilizes this relationship to convert electric force into a mechanical displacement of a metal plate (Figure 8-1). This instrument is a parallel plate

a,;\

Figure 8-1

capacitor in an equal-arm balance which measures the force between the plates. The word "absolute" in the name of the balance arises because it may be calibrated without reference to other electric meters. It is a direct link between electrical and mechanical units. If we could place one coulomb charge (6.25 x 1018 electrons) on each plate while the plates are one metre apart, there would develop a repulsion force of 9 x 109 newtons (916,000 metric tons force) between the plates. But a very large voltage gradient accompanies such large charges when the charged object is small. This experiment could be done only with very large plates. In laboratory practice 10-6 coulomb ( 6. 25 x 10 12

electrons) is used where the force is 10-12 part (0.916 milligram-force) of the above figure.

A gold leaf electroscope (Figure 8-2) is a similar instrument to the absolute electrometer in respect of displaying the electric force by the repulsion between its leaves. The two leaves (a,b) are joined to the same metal rod (c) which ends in a metal ball (d). These parts form a single metal structure and it constitutes one of the plates of a

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capacitor, where the other plate is the ground. The mechanical force on the leaves is their own weight which tends to keep them together. When an electric charge is placed on the ball, the flexible gold leaves separate, indicating a repulsion force within the very same plate of the capacitor. It is important to realize that this displacement is not between the two plates of the capacitor, but within the same plate, where the flexible construction allows this movement when a small charge is applied on them. If the charge was greatly increased, at a certain value the entire metal structure would split apart along the axis E-E, and the two halves would fly apart.

E I

i a I b

i E

Figure 8-2

3 S

//

Figure 8-J

A charged metal carries all the electric charges on its surface, but an insulator can be infused with charges in the form of free electrons in its entire volume. A non-metal equivalent to the gold leaf electroscope is the pith-ball electroscope (Figure 8-3), with which the repulsion force can be demonstrated. The silk threads (s) and the pith or plastic foam balls (p) constitute the electroscope. The balls can be infused with free electrons if they are placed in a stream of electrons flowing in their environment. This can be a charged open capacitor which is discharging in the air, or a glass rod which has been rubbed with cat hair, and is also discharging. The balls separate from one another on account of their free electron content which repel one another. One important feature of an insulator is that the charges occupy its volume, as opposed to a metal where they are on its surface only. Thus, an insulator can carry more electrons than a metal before the voltage gradient reaches the breakdown (arclng) level because the electrons are farther apart.

In a larger scale experiment the pith balls can be replaced by rock material, granite, for example. With the 9.25 x 1015 electrons per metre 3 charge density calculated for the crust in Chapter 6, two blocks of granite of one metre edge-lengths at touching distance apart, would

repel one another with 19,714 newtons, or 2010 kg-force. However, the state of electron infusion must be maintained during this test, This infusion is maintained by the magma cathode of the Earth while the rock is an integral part of the cathode's crustal envelope. But when a rock block is exc _avated from the crustal envelope, its electron content escapes like from a charged capacitor disconnected from the charger. When laboratory experiments are intended with the rock blocks to demonstrate the existence of this force, the original electron density must be restored by some means. Even the pith balls of the electroscope are not displaced unless they are properly infused first by free electrons. Furthermore, the calculated charge density of the crust is an average value. The crust is open to the atmosphere at its upper surface, thus in the very top layer this density is very low. Correspondingly, at its bottom surface it is greater than the average. The granite electroscope should be charged to the average value.

edge length force, F weight, w W/F (kg-force) (kg)

0.01 m 2 X 10- 5 3 X 10- 3 1.5 X 102

0.1 m 2 X 10- 1 3 X 10° 1.5 X 101

1 m 2 X 10 3 3 X 10 3 1.5 X 10° 10 m 2 X 10 7 3 X 10 6 1.5 X 10-

1

100 m 2 X 1011 3 X 10 9 1.5 X 10·2

1 km 2 X 101s 3 X 1012 1.5 X 10· 3

10 km 2 X 1019 3 X 1015 1.5 X 10· 4

100 km 2 X 1023 3 X 1018 1.5 X 10· 5

1000 km 2 X 1021 3 X 1021 1.5 X 10-s

1.5 m 1.01 X 104 1.01 X 10 4 1.00

.Table 8-1

Table 8-1 shows the calculations for pairs of granite blocks, where each block is of a cubic shape. The blocks are at touching distance apart, thus the distance between their centres is equal to the edge-length of · a block, The force F is in kilogram-force, and the weight Wis in kilograms. The weight/force ratio is also calculated. The force rapidly increases with the edge-length: it increases with the 4th power. As the weight of a block increases with the 3rd power only, the weight/force ratio decreases with the size. It is a most

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edge

interesting conclusion that a granite block would float in the air above another similar block if their sizes are large enough. This size is 1.5 metres edge-length. Above this size the upper block accelerates upward. However, the repulsion force decreases with the inverse square of the distance, thus the weight/force ratio becomes unity again at some vertical distance. For example, a 10 m size block would float at 816 m above the other block. (In the spherical geometry of the Earth this flotation of the crust is manifested by the Bouguer gravi tional anomaly, where large blocks of the crust, the mountains, are all above the height calculated from rock densities, and the anomaly is greater with larger mountains. In general, all isostatic anomalies are caused by the electric repulsion forces in the crust which have vertical components in the spherical geometry).

F (kg-:force)

D I s T A N C E length 1 m 10 m 100 m 1 km 10 km 100 km 1000 km 10000 km

0.01

0.1

1

10

100

1

10

100

1000

m 2 X 10"9 2 X 10·11 2 X 10"13 2 X 10·15 2 X 10"17 2 X 10·19 2 X 10·21 2

m 2 X 10·3 2 X 10"5 2 X 10"7 2 X 10"9 2 X 10"11 2 X 10·13 2 X 10·15 2

m 2 X 10 3 2 X 10 1 2 X 10·1 2 X 10"3 2 X 10"5 2 X 10· 1 2 X 10"9 2 m - 2 X 10 7 2 X 10 5 2 X 10 3 2 X 10 1 2 X 10"1 2 X 10"3 2 m - - 2 X 1011 2 X 10 9 2 X 107 2 X 10 5 2 X 10 3 2 km - - - 2 X 1015 2 X 1013 2 X 1011 2 X 10 9 2 km - - - - 2 X 1019 2 X 1011 2 X 1015 2 km - - - - - 2 X 1023 2 X 1021 2 km - - - - - - 2 X 1027 2

Table 8-2

The electric force decreases with the distance. Table 8-2 shows this effect. The force decreases with the 2nd power of the distance. When the same two blocks move apart 10 times their initial distance, the force drops to the one-percent value. However, the magnitude of the force at greater block sizes is very large, thus even atlarge distances the driving force remains significant. Two blocks of 1 km edge-length each, at a distance of 1000 km, have a driving force of 2 x lOi kilogram-force (2 million metric-tons of thrust). The force increases with the 6th power of the edge-length (when their distance is kept constant). At the same distance of 1000 km, two blocks ten times as

X 10·23

X 10· 11

X 10·11

X 10"5

X 10 1

X 10 7

X 1013

X 1019

X 1025

edge

large (10 km), have a repulsion thrust of a million times as large (2 x 1015 kg-force). A real continent, Africa for example, with its 3 x 10 7 km2 surface area and 30 km thickness, has a volume of 9 x 108 km3 , equivalent to a cubic block of 1000 km edge-length. The repulsion force between two such blocks at 10,000 km distance is 2 x la25

kg-force on an imaginary flat surface. (On the Earth's spherical surface these numbers will be different).

However, the real measure of the effect of the force on mass is acceleration, a• F/m, where Fis the force in newtons, mis the mass, in kilograms, and a is the acceleration, in metre/second 2 • Table 8-3 shows the values of acceleration for a wide range of block sizes and distances. The same numbers are illustrated in a graphic form in Figure 8-4. This is a log-log graph with the distance R on the horizontal axis, and log a/7 on the vertical. (This latter one is the exponent of the ten-multiplier of the a-values in Table 8-3. For reference, the acceleration of free fall, 9.81 m/sec2 , log 9,81/7 =-0.15, and the acceleration of the bullet in a shotgun, 200,000 m/sec 2 , log 200,000/7 ~ 4.46, are represented by dot-dash lines).

A C C E L E R A T I O N a (metre/sec 2 )

D I s T A N C E R

107

length 1 m 10 m 100 m 1 km 10 km 100 km 1000 km 10000 km

0.01

0.1

1

10

100

1

10

100

1000

m 7 X 10"6 7 X 10"8 7 X 10·10 7 X 10·12 7 X 10"14 7 X 10·16 7 X 10·18 7 X

m 7 X 10· 3 7 X 10·5 7 X 10·1 7 X 10-9 7 X · 10·11 7 X 10·13 7 X 10"15 7 X

m 7 X 10° 7 X 10· 2 7 X 10·4 7 X 10·5

7 X 10·5

7 X 10·10 7 X 10·12 7 X

m - 7 X 10 1 7 X 10· 1 7 X 10·3 7 X 10·5 7 X 10· 1 7 X 10· 9 7 X m - - 7 X 10 2 7 X 10° 7 X 10"2 7 X 10· 4 7 X 10"6 7 X km - - - 7 X 103 7 X 101 7 X 10·1 7 X 10·3 7 X km - - - - 7 X 104 7 X 10 2 7 X 10° 7 X km - - - - - 7 X 105 7 X 10 3 7 X km - - - - - - 7 X 106 7 X

Table 8-J The above calculated floating granite blocks of 1,5 m size are on the graph where the "free fall" line and the "blocks touching" lines meet, The acceleration can be enormous if the blocks are large enough. When two blocks of 1000 km size, side by side, are charged to the electron density of the Earth's crust, and are free to move, they move apart at

10·20

10"17

10·14

10·11

10"8

10· 5

10·2

10 1

104

108

an acceleration greater than that of a bullet shot. At the 7 x 106

m/sec 2 acceleration they would travel 7 x 106 m (7000 km) in the first second. ( On the Earth's spherical surface the continents, as blocks, are not always free to move. Electric repulsion forces from all other continents strongly control these movements).

IQ 1 ..... (!} 0 ..J

1m 10m 100m 1km 10km 100km 1000km 10000km

DISTANCE R

Figure 8-4

Continents moving on the Earth's spherical surface can be best visualized when we imagine an all-ocean planet. Place two cork-ships on the water side-by-side, and give them same-polarity electric charges. They will exert a repulsion force on one another, and will start moving apart. Assume that the repulsion force acts also through the body of water and through the mass of the solid Earth, thus the repulsion force remains active when the ships are beyond the horizon. (This assumption is correct as long as the medium between the charged bodies is non-conductive, that is, dielectric, or it is a non-perfect conductor. If it is only partially conducting, the repulsion force still acts through at some attenuation). The ships will move until they are exactly at 180° angular distance apart, at the opposite points of the globe. Figure 8-Sa shows this geometry with ships M and N which move from A to Band C.

---A-MIN

I I i i i i I

8 •------~-------• C

(a) Figure 8-5 . (.b)

The dual movements of the ships can be simplified into a single movement if we anchor one of them at point A. Figure 8-Sb shows this, when ship N is fixed at the top of the globe, and ship M moves from A to D. The movements of the ship is independent on the rotation of the planet. Therefore, the top of the globe in these representations is not the north pole, it can be anywhere on the surface. It is only a computational and displaying convenience to keep one of the ships at or near to the top of the display.

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Figure 8-5b also illustrates the force vectors of the moving ship at intermediate points. As an example, Bis at 45°, and C is at 135° from A. If each ship carries 1.48 x 10 15 coulombs charge, as the Africa-size 1000 km edge-length block, and they are on an Earth-size planet with 6370 km radius, then at B, at 4900 km distance apart, the absolute value of the force, F "' 8. 21 x 10 26 newtons. Because of the curvature of the Earth, the force in the local horizontal direction is less, it is 7. 62 x 10 26 newtons, 93% of the absolute value. For the same reason a vertial force component also develops: 3.19 x 1026

newtons, 39% of the absolute value. When the ship arrives at point C, at 11,800 km distance, the absolute value drops to 1. 42 x 10 26 · .newtons because of the distance. The curvature causes a much greater effect here: the vertical force is 1.31 x 10 26 newtons, 92% of the absolute value, while the horizontal one is 0.60 x 10 26 newtons, only 42%. Finally, when the ship .arrives, at D, the horizontal force component drops to zero, and the total repulsion force acts in the local vertical direction, 1.21 x 10 26 newtons. The most important conclusion is that however great the repulsion force is on the ship, it will stay at this 180° angular distance position. Since the ship's movement is confined to the surface, only a local horizontal force component could drive it. When this force component becomes zero, we can say that the ship is at a "zero force" position, or at a "null", meaning only the local horizontal force. The vertical force can still be of a very great value. This can even have an observable effect: it can lift the ship above its normal position. This is observable if the force is comparable to the weight of the ship since this force acts against gravity here. The ship appears to lose density.

An object floating in liquid is particularly suitable for the observation of this apparent weight reduction. A floating object continually fallows this force by rising or sinking about its normal water-line. In contrast, an object on a solid surface does not move vertically until its total weight is compensated. The continents of the Earth are floating in the liquid magma, thus they should manifest the proportional rising or sinking as a response to the electric repulsion force. They do: the force increases by the 6th power of the block size (Table 8-2), thus the larger the body the more it should rise above the average position. Geophysicists observe this phenomenon, but they give a false explanation: ·

" ••• gravity is less than average in high areas and greater than average over oceanic areas, which indicates that rocks beneath high areas have relatively low density compared to rocks beneath oceanic areas."[42]

The "Airy-Pratt isostasy compensation" as well as the "Bouguer gravitational anomaly" are caused by the electric repulsion forces through the bulk of the Earth, in the locally vertical direction where

the larger the mass the greater its rise over the geoid. are the mountains whose mass is much greater than the floor.

High areas thin ocean

With only two ships it is easy to see their final positions on the globe. However, for many more ships their interaction becomes more and more complicated, but can be followed by a computer. I prepared such a program which handles up to 7, or more ships (Appendix). For completenesa I use this program also for the two-ship case. Figure 8-6 shows the computer displays, the top and the side views of a model globe on which the ships move. I use the same coordinate grids as the

K

Figure 8-6 ones for geographic globes. However, the poles of the grid do not refer to north or south poles, because this electric force and the related displacements of charged bodies are independent of the rotation of the planet. The grids are convenient means to convey the spherical shape of the globe beside identifying the positions of the ships. Also, it will be convenient to place one of the ships to the top of the globe as a reference for comparing the final positions of different number of ships.

In Figure 8-6 the two ships are placed initially at Mand N. The ship at M is fixed, and the one at N is allowed to move in response to the

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repulsion force. The computer allows its movement for a short distance, then recalculates the direction of the force at this position, and allows another short move. The dots on the illustration represent these intermediate positions. The ship moves in the direction of the arrow. On the top view, at P, it moves below the horizon, but this globe is transparent, thus it can be seen moving in the bottom hemisphere until it arrives at its final position at K. A heavy solid line is drawn between the ships at Mand K. This straight line is a geometrical symbol for the final positions of the two ships. In this example the fixed ship is offset by 10° from the pole to allow the projected view of the solid straight line in the top view.

Figure 8-7 Figure 8-8 Figure 8-9

Three ships on the globe move 120° apart on a great circle (Figure 8-7). Here the fixed ship is at the top, T, of the globe. One of the moving ships moves from D to S, the other from B to R. The final positions of the ships are interconnected again by straight lines which show an equilateral triangle.

Four ships can take up two possible configurations at their final positons. If they were on the same great circle before displacement,

they remain on this circle during their movements, and form a square at their final positions (Figure 8-8). If they were at any other arbitrary positions, they form a triangular pyramid (Figure 8-9).

For five ships there are three possible solutions: 8-10) , a rectangular pyramid ( Figure 8-11) , or a pyramid (Figure 8-12), depending on the initial ships.

a pentagon (Figure double triangular positions of the

For six ships there are again three poss! ble solutions: (Figure 8-13), a pentagonal pyramid (Figure 8-14), or

a hexagon a double

T T

B

Figure 8.-10 Figure 8-11 Figure 8-12

rectangular -pyramid (Figure 8-15). On this latter one I display the paths of the ships which indicate their intricate movements. Five of the six ships are positioned initially within 20° of the equator, and the sixth one at the top. Each ship carries 4.8 x 108 coulombs charge. The computer calculates the direction of the local horizontal force-vector on the first ship, from the other five, and lets it move for 50 seconds. After this time the new coordinates of the ship is calculated, and a dot is placed on the display at this position. Then the force-vector is calculated for the second ship from the momentary positions of the other five ships, and it moves for 50 seconds, etc.

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114

Since the ships move on a spherical surface, after each step the direction of the force on each ship changes significantly, and influences the force direction on the next ship to move. These rather large steps are slight deviation from the real process where the continents move continually, and their influence on the other continents is also continual, but delayed by the propagation velocity of the effect. However, I noticed that if at least 100 steps are taken between the initial and the final positions, the course of the paths do not differ significantly from those with 1000 steps or more. But the most important observation is that the final geometry, the double rectangular pyramid, is the same under all conditions.

J K

M

T T

B

Figure 8-13 Figure 8-14 Figure 8-15

I should also not that the "final - positions" are actually arbitrary limitations on successive approximations. As the ships move closer and closer to the zero-force positions, the magnitude of the forces continuously decreases, and so does the resulting displacement. While during the first step the ships move hundreds of kilometres during the allotted 50 seconds, after hundred steps the stepsize is down by 3 or 4 magnitudes, to a few metres. Therefore, in order to save computation time, I set the parameters in such a way that after 100 steps no discernible further movements were observable on the graphics display, and I declared these as final positions.

The pentagonal pyramid of Figure 8-14 is comparable to the positions of the Earth's real continents. Figure 8-16 is a six-view projection of the terrestrial globe where each view is rotated 90° with respect to its neighbor. Lines drawn from the centre of Africa to the centres of all other continents constitute a near perfect five-pointed star whose divisions differ from the perfect 72° only by a few degrees. However, while .the five-pointed star is a clear clue for placing Africa to the top of the pyramid, the pyramid's base line continents do not line up straight along the base line. This zig-zagging requires further investigations of the mathematical model.

Figure 8-16

The first step towards the solution of this problem is to review the physics behind the charged state of the continents. The Earth's continents float on the liquid molten magma cathode. Through thermionic charge emission this cathode pumps free electrons into the mass of the continents as the crust is a near perfectly closed envelope of the cathode. However, the continents are only part of the crust, the rest is ocean floor which also must be in a charged state. From this point of view the only difference between the floor and a continent is their thickness. Thus, each plate of the floor should

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also be treated in the same way as each continent: in the mathematical model each plate should be represented by a "ship". But most plates are small in volume, therefore their electric forces on the continents are negligible, especially since this force is proportional to the 6th power of the volume's equivalent cubic edge-length. For example, the volume of the North Atlantic ocean floor is 75% of the volume of the smallest continent, Australia, thus its force on a continent is only 18% that of Australia. However, the volume of the largest ocean floor, the Pacific, is not negligible. According to Table 8-4 the Pacific Floor qualifies as the 2nd largest continent. As a consequence, the Earth's continents are a seven-ship system. Figures 8-17, 18, and 19 illustrate the three basic configurations of the seven-ship model: a heptagon, a hexagonal pyramid, and a double pentagonal pyramid. This latter one is the case of the terrestrial continents where the Pacific Floor is at the bottom tip of the pyramid.

surface thickness volume

107 km2 km 101a m3 A B

Eurasia 5.42 40 2.17 7 4

Pacific Floor 18 .05 7 1. 26 4 4

Africa 2.98 40 1.19 4 3 North America 2.42 JO 0.73 2 3 South America 1.80 35 0.63 2 2

Antarctica 1. 31 35 o.46 1 2

Australia 0.90 35 0.32 1 1·

Table 8-4

The reason for the zig-zagging of the Earth's base line continents can be found in the mathematical model in two steps. The first is that the equal charges of the ships are replaced by unequal ones. The effect of unequal charges can be studied on the three-ship system of Figure 8-7. If unequal charges are introduced, the equilateral ,, 3 x 120° triangle becomes distorted. For example, if charge ratios of 1.5, 1.2, and 1.0 are used, the angular distances between the ships change to 127. 71 °, 111.66°, and 120.63°, the largest angle being between the largest charges. This system defaults to a two-ship system when the smallest charge decreases to · zero, and the angular distances between the two remaining ships increases to 2 x 180°. Column A of Table 8-4 shows the volume ratios of the Earth's continents, normalized to the volumes of the smallest one, Australia, and rounded to the nearest integers. Column Bis an adjustment of these values to meet certain limitations of the given computer. Thus the results are expected to be a typical, _not an exact case, of the Earth. These values are used as charge

ratios in a seven-ship system to see their effects on the final positions of the ships. Figure 8-20 illustrates the graphics display of the result, and 8-21 is a redraw of the same positions in a six-view plot. In order to make this illustration directly comparable to the real continental configuration of Figure 8-16, I did not connect the bottom ship, B, with the base line ships. The result of the unequal charge ratios is that the exact 72° star-divisions get distorted, the plane of the base line ships get tilted, and the bottom ship moves out from the bottom pole of the coordinate grid.

H H

N L

T

Figure 8-17 Figure 8-18 Figure 8-19 - -

The second step is to give a finite area to the ships (without changing their electric charge). This is justified on the basis that the electric force varies with the square of the distance, thus for any ship the effective charge centre of an other ship is not at its geometric centre, but at a point closer to the first ship. Thus, assigning an area to the ships non-linearly increases the force between them. Figure 8-22 is the graphics display of the result. Here the base line connections are represented by dashed lines in order to make them distinguishable from the other lines. Figure 8-23 is its six-view representation. In this the shape of the mathematical ships are also illustrated (ship P should still be a point, and ships L, N should be lines). It is noticeable that zig-zagging of the base line ships does take place.

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118

My · computer program is equipped with the equations to calculate the rotation of the ships with finite area, on which torque develops as a result of their shape. However, I have only preliminary results. These indicate that such rotation takes place in all cases when the shape of the ship differs from a perfect circle. There is also a final position in the rotation. The ship takes up a final angular position in which the torque is zero, that is, when the torque from all other ships cancel out. This zero-torque position is a function of the geometric shape of the ships, and their spherical positions with respect to all other ships. By placing two such ships side by side at their initial place, their rotations start simultaneoulsy with their

p

T

Figure 8-20

displacements, and it continues during their travel. The projection of the shape of one ship on the other continuously changes while moving on the spherical surface, thus there is a new angular position at each new surface position. However, the total rotation even over large distances rarely exceeds one complete turn. The program does not take into account inertia, thus at each step the ship is rotated to its zero torque angular position, and is held there until the next step. Nevertheless, it is easy to visualize that continents with inertial mass, large force, and with small friction may over-rotate, or even ~pin, before settling down at the zero force and zero torque positons.

From the above described mechanism of the displacement . of the continents I attempt to reconstruct the geological history of the continents. In the early age of the Earth, before the development of the magma, the Earth had one unbroken surface. The thermal energy of the internal radioactive decay eventually generated magma at certain places of the interior. Beta and gamma decays generate high velocity free electrons whose collisions with atoms of the Earth's material supply the thermal energy. These collisions eventually break the velocity of these electrons, but the electrons are not annihilated.

p

p

Figure 8-21

Although their original kinetic energy is lost in the repeated collisions, a new force develops on them, keeping them in motion. This force is Coulomb's repulsion force which acts between each and all free electrons in the Earth's interior. If radioactive elements are more or less evenly distributed in this mass, then the direction of the electric force on each of these free electrons is radially outward from the Earth.

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120

The magnitude of the repulsion force is zero at the centre of the Earth, where all the force-vectors cancel out, and it is maximum at the surface, where the forces add vectorially. Thus, the electrons of the radioactive decay, after transfering their decay energies to the neutral rock-matter of the Earth, continue to move by increasingly accelerating outward. They continue to transfer their newly developing kinetic energy to the rock-matter, heating it up. The heating effect rapidly increases with the radius of the Earth, and if there was no cooling at the surface, this surface would melt first. The temperature of the centre does not increase over its original value. However, there is cooling at the surface, thus the maximum temperature develops

T

Figure 8-22

slightly below. (At present the magma surface is at 99.2% of the radius). Thus the Earth's magma is only a spherical layer whose thickness is probably less than 100 km, or 1.5% of the radius. The temperature decreases below this layer, and probably drops to absolute zero (0 kelvin) at the centre. The interior liquid shown by seizmic measurements is water, and the solid core is water ice.

When the temperature reached the melting point of rock in the maximum temperature layer, the developed magam separated a 50 to 100 km thick

solid rock shell, the crust, from the bulk of the Earth. This crust is floating partially submerged in the magma. However, at the elevated temperature the magma layer acts as a thermionic emitter, and this significantly increases the free electron content of the crust. Since the propagation velocity of free electrons in the crust is slow, the repulsion force between the crustal electrons develops a mechanical stress in the crust in the direction of the force. Non-homogenity in the crust and in the crustal electron density resulted in the asymmetrical melting of the crust, and eventually more than half of the

p

Figure 8-2J p

crust melted and sunk in the magma. Water flooded this area, and the first ocean floor developed. The remaining part of the crust became the first continent. However, the mechanical stress in this continent lost its balance, and the electric force broke up the hemisphere size crust into two halves. Two continents side by side are moved 180° apart by the electric repulsion force. This type of displacement is cataclysmic, and it is completed in a few hours.

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122

Eventually mechanical stress started developing also in these two continents. The simplest form of this stress results from the fact that a large and very brittle plate floats on liquid, and at the same time its thickness unevenly changes by melting and erosion. For example, the present day North America is 5000 km wide, but its thickness is only 50 km, or 1% of its width. If one of its ends melts faster than the other, then it sinks faster than the other. This develops a bending moment, or torque, somewhere inland. When this stress exceeds the strength, the plate breaks into two. At this instant the plate becomes two continents sitting side by side, but this is not a zero force position for them, and their internal repulsion force starts acting on them.

For one or two continents the displacement can only be cataclysmic. But for three or more continents there is also a drift-type displacement. For example, three equal size continents are in zero force positions when they are at 120° angular distances apart. If only one of them melts, slowly but completely, over a length of time, eventuAlly only two continents remain, and they should be at 180° angular distance apart by this time. Consequently, those two non-melting continents will "drift" towards their 180° positions during th entire melting of the third continent.

This is, however, a special drift. The Earth's continents, as long as there are oceans, are embedded in the ocean floor like real ships in a frozen lake. When the third continent loses volume to melting, a force arises on the other two as their zero force positions move away. But the rigid ocean floor does not allow an immediate drift of the continents when the force first arises. The force must increase in magnitude to a value where the stress on the floor becomes greater than its strength. Then the floor suddenly gives way, and the out-of position continent jumps to the new zero force position. When this jump is at least several millimetres, it is observed as an earthquake. All earthquakes are jumps to new zero force positions. The manifestat .ion that the jump is to a pre-determined position is, that there is an oscillation around it by the land mass. The large force accelerates the mass at the moment of break toward the zero force position, but the frictions are very small, and the inertia carries the mass beyond this point. At the other side of the zero position the direction of the force is opposite, and the reverse force (not friction) breaks the velocity, stops the mass as fast as it accelerated before, and starts accelerating it now backward. Hundreds of such cycles take place during the few minutes of the earthquake before friction eventually absorbs the kinetic energies. In the meantime the water of the ocean cools the magma at the broken floor, and the re-solidified floor keeps the continent fixed until the force adequately arises on it again. In my calculations the force on large masses are great enough to break the ocean floor when the shift of the zero force position is less than one millimetre, and the resonant

frequency of a large continent is much less than one herz. Thus most of the drift-steps are not observed individually, but only when the accumulated drift becomes geologically significant over millions of years. Observable earthquakes are limited to sub-continents, like the area west of the San Andrean fault. Sub-continents . have their own zero-force positions within their large main-continent.

There are geological evidences that there were five cataclysmic incidents in the Earth's history when conditions for life, especially for the higher forms of life, were interrupted for a length of time, and most of the related species involved became extinct. Simultaneously, several inches thick mud covered most part of the Earth, which are now embedded in the rock formations of that age. In my view these five events coincided with the births of five of the six physical continents. Before the last cataclysm the Earth showed a rectangular pyramid configuration of the continents, North America was still attached to Eurasia. Alaska and Siberia were the same land in the subtropical zone, and the mammoth lived on it. Then an inland fault developed, and a large area suddenly separated from the eastern end of Eurasia, and this became North America. The two land masses immediately started to move to their new zero force positions in the pentagonal pyramid system, but because of their non-circular geometry a torque also developed on both, and caused their rotations. North America rotated clockwise, Eurasia counterclockwise, thus both Alaska and Siberia moved to the north in a few hours. The mammoth died out in the jerks of the land, and their carcasses with their broken bones got quickly frozen. After a quick thaw their flesh is still edible, and there is undigested tropical food in their stomach. They still can be found in this state both in Alaska and in Siberia.

Simultaneously, the last prehistoric man, the Cro-Magnon man also died out, even though his land moved southward, from the latitudes of present day Scandinavia to the present day Southern France, according to the counterclockwise rotation of Eurasia, 20,000 years ago. Another birth of a continent, 60 million years ago killed out the dinosaur. Suffocation was another possible cause for death during these periods, since millions of square kilometres of the magma surface became exposed to the ocean water as a continent quickly traveled thousands of kilometres and broke up the ocean floor along its way. Most of the ocean's water evaporated and saturated the atmosphere for an extended length of time which prevented breathing. When the water eventually returned, it deposited the still observable mud layers what the water dragged from the magma surface when it boiled away.

During the sudden moves of continents some of them may move in the north-south direction, radically changing its own climate when moving in or out of the arctic. Ice ages are old and unsolved problems by present theories, because ice ages do not appear simultaneously on all continents, and on some continents none has taken place. The ice ages are direct consequences of the electric displacement of continents.

123

124

The characteristic electric-force organization of continental masses can be recognized on those planets where global topographic maps are available. Venus and Mars are these planets. During its geological life a planet increases the number of its continents. However, when its radioactive decay energy is exhausted and its magma cools and solidifies, the momentary geometric configuration of its continents becomes frozen into its surface. But the surface elevations remain observable, and it is possible to delineate the continents even in the absence of the ocean's water.

U)

::s "C II] ... C II]

Cl>

E 0 -

5

4

3

2

1

0

I Wenu.s

5

7 T

7

I find that the land masses, represented by their peaks, are positioned according to the 3-ship configuration (Figure 8-7) with the restriction that the masses are un-equal. According to the rules the two smaller masses should be closest to one another, and the two largest ones should be the farthest. With volume figures of V, = 3.0, V2= 2.4, and V3 = 2.0, the angular distance between V1 and V2 is 127. 71 °, and between V2 and V3 is 120.63°, according to the computer model. Their longitudes in the scale of Figure 8-24 are 1 2 = 197. 7 °, and L3 = 309. 4 °. These longitudes are in a close agreement with the observed values of Figure 8-24. Consequently, Venus is at least a triangular system. However, there can be a fourth continent at one of the poles, but a radar from the Earth can not observe this. In this case the system would be a triangular pyramid as in Figure 8-9. But a fifth continent at the other pole, to form a double triangular pyramid, is unlikely, because one hemisphere should be entirely an ocean floor, a Venusian Pacific •

120

\ . . g~:f .. :· . '

. ! ,q, .• J 33() ':), • . , 300

180 150 210

Figure 8-25

A detailed global topographic map of Mars in the + 60° latitude is available [45], Figure 8-25. There is a total of 13 km elevation variation on Mars, of which the lower half can be considered as ocean bed, and the top half as continental area. (For the Earth this is 22 km, of which 55% of ocean and 45% is land). On the top 6500 metres martian land three continents can be delineated. (At the 280° long., -10° lat., and at the 195° long., -40° lat. broken passages have to be assumed similarly to the one between North America and South America). These three continents are organized in the same way as those of Venus:

125

1110

126

there is one large continent, "A" at 120° latitude, and two smaller ones, "B" at 330° longitude, and "C" at 230° longitude. The centres of these continents are separated from one another according to the electric repulsion forces: the angular distance between the two smallest ones, "B" and "C", is the shortest, 100°, and it is the longest, 170°, between the two largest ones, "A" and "B".

The geometric centres of all three continents are in the same plane, as it should be for a triangular configuration. This plane is titled to the equator (by 9.5°), and it is also shifted southward. This indicates that the configuration is actually a triangular pyramid, and there should be another continent in the northern hemisphere whose centre is 9.5° from the north pole. Electrically a large ocean floor qualifies for this purpose. Indeed, it has been established [46] that the entire northern hemisphere of Mars lies several kilometres below the mean surface of the planet. It appears that at the geological death of Mars, lava flooded the southern hemisphere first, and the last ocean had been the Martian Pacific in .the northern hemisphere.

9. Bibliography

(1] Supernovas: Quickie tropical storms. (Science News, Vol. 107, p. 152, 1975)

[2] Characteristics of Heso-(3-Scale Deep Convection Over the Eastern Tropical Atlantic, by Lee R. Hoxit. (NOAA Technical Report ERL 366-APCL 38, 1976)

[3] 1bunderstonns. (Encyclopaedia Britannica, 15th ed. Vol. 18, 1974)

[4] Electronic Engineering Principles, by John D. Ryder. (Prentice Hall, Inc. New York, 1949)

(5] On The Structure and Organization of Clouds in the GATE Area, by J. Simpson and R.H. Simpson. (GATE Report No. 14, January 1975).

[6] Rapid Structural Changes in an Asymmetrical Tropical Depression, by Edward J. Zisper. (GATE Report No. 14, January 1975).

[7] Cyclones and Anticyclones. (Encyclopaedia Britannica, 15th ed. Vol. S, P• 392, 1974).

[8] Physics of the Earth, by Frank D. Stacey. (John Wiley & Sons, Inc. New York, 1969).

[9] Physics of the Earth and Planets, by A.H. Cook. (John Wiley & Sons, Inc. New York, 1973).

(10] Squall line. (McGraw-Hill Encyclopedia of Science and Technology, Vol. 13, P• 20, 1977)

[11] Hurricanes and Typhoons. (Encyclopaedia Britannica, 15th ed. Vol 9, P• 58, 1974)

(12] Astronomy and Cosmology; a m:xlern course, by Fred Hoyle. (W. H. Freeman and Company, San Francisco, 1975).

(13] Space Physics, by D. P. LeGalley and Allan Rosen, editors. (John Wiley & Sons, Inc. 1964).

[14] Concise Encyclopedia of Astronomy, by Paul Muller. (Wm. Collins Sons and Co., and Follett Publishing Co. 1968).

(15] Atmosphere. (Encyclopaedia Britannica, 15th ed. Vol. 2, 1974).

[16] A Negative Experiment Relating to Magnetism am the Earth's Rotation, by P. Blackett. (Phil. Trans. A 245, 1952).

127

128

[17] Magnetohydrodynamic Devices. (Encyclopaedia Britannica, 15th ed. Vol. 11, P• 329, 1974).

(18] MHD's target: payoff by 2000, by Enrico Levi. (IEEE Spectrum, May, 1978).

(19] Rowland, H. A. (Encyclopaedia Britannica, 15th ed. Vol. VIII, p. 696, 1974)

(20) On the Electromagnetic Effect of Convection Currents, by H. A. Rowland. (Philosophical Magazine and Journal of Science, June, 1889).

(21] Electric Engineering Principles, by John D. Ryder. (Prentice-Hall, Inc. New York, 1949).

(22] Atmospheric Electric Field. (Van Nostrand's Scientific Encyclopedia, 4th edition, p. 137, 1968).

[23] 'lbe Nature of Violent Storms, by Louis J. Battan. (Anchor Books, 1961).

(24] 'lbe Redshift Controversy, by Halton Arp and J. N. Bahcall. (W. A. Benjamin, Inc. Reading, Mass. 1973)

(25) Electrostatic motors are powered by the electric field of the earth. (Scientific American, p. 126, October 1974).

(26) A Treatise on Electricity and Magnetism, by James Clerk Maxwell. (Dover Publications, Inc. 1954).

(27] Jet Streams. (Encyclopaedia Britannica, 15th ed. Vol. 10, 1974)

[28] Terrestrial Electricity. (McGraw-Hill Encyclopedia of Science and Technology, Vol. 13, p. 524, 1977).

(29] Geomagnetism, bys. Chapman and J. Bartels. (Oxford, 1940).

[30) Earth-Current Results at Tucson Magnetic Observatory, 1932-1942, by w. J. Rooney. (Carnegie Institution of Washington, 1949).

[31] Piezoelectricity. (McGraw-Hill Encyclopedia of Science and Technology, Vol. 10, P• 426, 1977).

[32) Electrostrictive Transducers. (McGraw-llill Encyclopedia of Science and Technology, Vol. 8, p. 426, 1977).

(33] (Proposed Vol. 15 and 16, Publication 175, of the Carnegie Institution of Washington).

[34] Electricity and Magnetism, by M. Nelkon. (Edward Arnold Publication, London).

[35] A possible cause of the Earth's magnetism and a theory of its variations,by William Sutherland. (Terrestrial Magnetism and Atmospheric Electricity,Vol. 5, 1900).

[36) Reversals of the Earth's Magnetic Field. (Scientific American, February 1967).

[37] Paleomagnetism of the Stormberg Lavas of South Africa, by J. s. v. van Zijlet al. (J. R. Astr. Soc., Vol. 7, 23, and 169, 1962).

(38] Lineation of magnetic anomalies in the northeast Pacific observed near the ocean floor, by B. P. wyendik et al. (J. Geophys. Res., Vol. 73, 5951-5957, 1968).

[39] The Solar System. (Scientific American, September 1975).

[40) The Odyssey, by Homer. (Book XII).

[41) An Ancient Greek Computer. (Scientific American, June 1975).

[42] The Dynamic Earth, by Peter J. Wyllie. (John Wiley & Sons, Inc. 1971).

[43] Anatomy of the Earth, by Andre Cailleux. (Weidenfeld and NicholsonPublishers, London, 1968).

[44] Ve1U1s: Topography revealed by radar data, by D. B. Campbell et. al.(Science, Vol. 175, 514-516, 1972).

[45] Martian topography derived from occultation, radar, spectral, andoptical measurements, by E. J. Christensen. (J. Geophys. Res.,Vol. 80, 2909-2913, 1975).

[46) Evidence for convection in planetary interiors from first order topography, by R. E. Lingenfelter and G. Schubert. (The Moon, Vol. 7, 172-180).

[47] Magnetic survey off the west coast of North America, by R. G. Masonand A. D. Raff. (Bull. Geol. Soc. Am., Vol. 72, 1259-1266, 1961).

[48] Variations of the Kinetic Energy of Large Scale Eddy Qirrents inRelation to the Jet Stream, by s.-K. Kao and w. P. Hurley. {J. Geophys.Res., Vol. 67, 4233-4242, 1962).

129

1)0

10. Acknowledgements

1llanks are due to David c. Gilmore, a vehicle dynamics engineer, for valuable assistance in the translation of various physical concepts into mathematical models. 1hese included the repulsive forces causing continental movement; the derivation of spherical coordinates fran the vectored forces and displacements. He also provided DJ.JCh useful discussions, proof read a part of the manuscript, and contributed the watercolor which appears on the cover.

Quoted; cited, or otherwise referenced material is listed in the Bibliography, and identified in the text by the same nwnber (in square brackets).

[l] is reprinted with permission of "Science News, the weekly news magazine of science, copyright 1975 by Science Service, Inc."

[3],[7],(27], and Figure 3-10 (11] are reprinted with permission from Encyclopaedia Britannica, 15th edition (1974).

[4] is copyright 1974 by Prentice Hall, Inc. Reprinted with permission.

(22] is copyright 1968 by D. van Nostrand Company, Inc. Reprinted with permission.

(28],[31],[32], and Figure 2-13 [10] are copyright 1977 by McGraw-Hill Book Company. Reprinted with permission.

Figure 7-5 [37] is reprinted with permission of Blackwell Scientific Publications Ltd. (1be diagram is redrawn to metric scales).

Figure 4-8 (a simplified version of Figure 1 of [48]), and Figure 7-6 [38] are reprinted with permission of the Journal of Geophysical Research.

Figure 7-7 [47] is reprinted with permission of the Geological Society of America.

[42] is copyright 1971, and Figure 4-5 (13] is copyright 1964 by Jolm Wiley & Sons, Inc. Reprinted with permission.

Figure 8-24 [44] is copyright 1972 by the American Association for the Advancement of Science. Reprinted with permission. (11le three arrows are additions to the original illustration).

Figure 8-25 [45] is reprinted with permission of the Journal of Geophysical Research. (The delineations, shading, and the dot-dash line are additions to the original illustration).

131

11. Appendix

1.32

0001 PROGRAM MAZO 0002 REAL*4 INC,M,IN,MO,MOl,HLM,ILM 0003 INTEGER*2 H 0004 REAL*8 SYR,SXR,SZR,SSR 0005 COMMON Q,TH(20),PH(lO),R,N,IP,M,PI,DRC,

)G(lO),XC(l0,10),YC(l0,10),NC(lO),DELT 0006 DIMENSION T1(7),P1(7),P2(7),FT1(7),A(7),T2(7),

)FT2(7),T(7),P(7),M0(7),M01(7),MLM(7),ILM(7), )FlX(7),FlY(7),FlZ(7),F2X(7),F2Y(7),F2Z(7), )T3(7),P3(7),PH1(7),TH1(7),PH2(7),TH2(7),IDA(5),ITI(4), )IX(7),IY(7),NAME1(5),ITY(7),H(7),TY(7),TX(7)

0007 DIMENSION X( 4, 7), Y( 4, 7), Z( 4, 7), XP( 4, 7, 6), YP( 4, 7, 6), INS( 4, 7, 6) 0008 CALL INIT (6000) 0009 PI=3.1415926535897932384626 0010 DRC=PI/180. 0011 IA=2 0012 IB=5 0013 IC=6 0014 IE=7 0015 IS=2 0016 WRITE (5,104) 0017 104 FORMAT(/////////,' N=2,3,4.',//,' USE THE 220.D, 320.D, OR

> 420.D SERIES',//) 0018 WRITE (5,103) 0019 103 FORMAT(/,' ENTER INPUT FILE NAME : '$) 0020 READ (5,11) (NAMEl(I), I=l,5) 0021 ·11 FORMAT (5A2) 0022 CALL ASSIGN (4,NAMEl,9,'RDO') 0023 CALL IN2 (TLIM,B,CD,IN) 0024 207 WRITE (5,100) 0025 100 FORMAT (/,' ENTER "1" FOR SIDE VIEW, "5" FOR TOP VIEW '$) 0026 READ (5,204) IP 0027 IF (IP .EQ. 1 .QR. IP .EQ. 5) GOTO 206 0028 GOTO 207 0029 206 WRITE (5,201) 0030 201 FORMAT(/,' FOR NO VERTEX ENTER 2',/,

) 'FOR SINGLE VERTEX ENTER 3',/,' FOR DOUBLE VERTEX ENTER 4',/, ) T26,': ',$)

0031 READ (5,204) ID 0032 IF (IP .EQ. 5) GOTO 5 0033 CALL RSTR ('A201.GR') 0034 GOTO 7 0035 5 CALL RSTR ('A205.GR') 0036 7 CALL MENU (970,60,1,101,'##') 0037 ILIM=TLIM 0038 CALL SUBP (345) 0039 CALL OFF (345) 0040 CALL APNT (0,1020,,-8) 0041 CALL TEXT ('A2= ') 0042 CALL NMBRR (72 ,A(2),8,'(1PE8.2)') 0043 CALL TEXT(' M/SEC** 2' ) 0044 CALL APNT (0, 1000,,-8) 0045 CALL TEXT ( 'A3 = ') 0046 CALL NMBRR (7 3, A( 3) , 8, '(1PE8. 2)') 0047 CALL APNT (0,980,,-8) 0048 CALL TEXT ('A4= ')

0049 0050 0051 0052 0053 0054 0055 0056 0057 0058 0059 0060 0061 0062 0063 0064 0065 0066 0067 0068 0069 0070 0071 0072 0073 0074 0075 0076 0077 0078 0079 0080 0081 0082 0083 0084 0085 0086 0087 0088 0089 0090 0091 0092 0093 0094 0095 0096 0097 0098 0099 0100 0101 0102 0103 0104

10

12

14

16

CALL NMBRR (74,A(4),8,'(1PE8 . 2)') CALL ESUB (345) CALL SUBP (344) CALL OFF (344) CALL APNT (0,1020,,-8) CALL TEXT ('H2= ') CALL NMBRR (92,FT1(2),8,'(1PE8.2)') CALL TEXT(' N') CALL APNT (0,1000,,-8) CALL TEXT ('H3= ') CALL NMBRR (93,FT1(3),8,'(1PE8.2)') CALL APNT (0,980,,-8) CALL TEXT ('H4= ') CALL NMBRR (94,FT1(4),8,'(1PE8.2)') CALL ESUB (344)

ICOUNT=O DO 10 I=l,N Tl (I) =TH(I) Pl(I)=PH(I) T2(I)=Tl(I) P2(I)=Pl(I) M=B**3*3000. Q=M*CD*l. 61E-19 DO 12 I=l,N MLM(I)=O. ILM(I)=O. LL=NC(I) DO 12 J=l,LL MLM( I) =MUI( I )+M ILM(I)=ILM(I)+M*(XC(J,I)**2+YC(J,I)**2)+ 1.

CALL SUBP (342) CALL OFF (342) CALL APNT (800,1020,,-8) CALL TEXT ('Ml=') CALL NMBRR ( 80,MLM(l), 8, '(1PE8. 2)') CALL TEXT(' KG') CALL APNT (800,1000,, -8) CALL TEXT ('M2= ') CALL NMBRR (81,MLM(2),8,'(1PE8.2)') CALL APNT (800,980,,-8) CALL TEXT ('M3= ') CALL NMBRR (82,MLM(3),8,'(1PE8. 2)' ) CALL APNT (800,960,, -8 ) CALL TEXT ('M4= ') CALL NMBRR (83,MLM(4),8,'(1PE8.2)') CALL ESUB (342)

CALL SH2 (Tl,Pl,FlX,FlY,FlZ,MOl,FTl,WTl) DO 14 1=2 ,N A( l)=FTl( I )/MLM(I) F2X( I )=FlX(I) F2Y(I)=FlY(I) F2Z(I)=F1Z(I)

CALL SUBP (46) IF (ICOUNT .EQ. O) DT=l.OE-10 IF (ICOUNT .EQ. 1) DT=DELT DT=DT*IN START NEXT ITERATION

133

1.34

0105 ICOUNT=ICOUNT+l 0106 WRITE (5,19) ICOUNT 0107 19 FORMAT ('+',13,' ')

0108 0109 OllO 0111 0112 0113 Oll4 0115 Oll6 0117 0118 0119 0120 0121 0122 0123

0124

0125 0126 0127 0128

0129 0130 0131 0132 0133 0134 0135 0136 0137 0138 0139 0140 0141 0142 0143 0144 0145 0146 0147 0148 0149 0150 0151 0152 0153

0154 0155

C CALCULATES LATEST POSITIONS OF ALL CONTINENTS BUT FIRST ONE

20 C

C

22 C

25

23

241

242

243

244

245 C 21 301

DO 20 1=2,N SXl=F2X(I)/MLM(I)*DT*DT/2. SYl=F2Y(I)/MLM(I)*DT*DT/2. SZl=F2Z(I)/MLM(I)*DT*DT/2. PHD=Pl(I)*DRC THD=Tl(I)*DRC RX=R*COS(PHD)*COS(THD) RY=R*COS(PHD)*SIN(THD) RZ=R*SIN(PHD) SXR=RX+SXl SYR=RY+SYl SZR=RZ+SZl

F2X,F2Y,F2Z ARE THE X,Y,Z COMPONENTS OF TOTAL SURFACE FORCE ACTING ON I-TH CONT. Pl, Tl = CURRENT CO-ORDINATES OF I-IB CONT.

t "

RX,RY, RZ = COMPONENTS OF CUl~RENT POSITIONS OF I-TH CONT.

NEW X,Y,Z COMPONENTS OF I-TH CONT.

T2(I)=DATAN2 (SYR,SXR)/DRC ! POLAR COMPONENTS OF NEW POSITIONS SSR=SQRT(SXR**2+SYR**2) P2(I)=DATAN2(SZR,SSR)/DRC G(I)=G(I)+MOl(I)/ILM(I)*DT*DT/2./DRC G = NEW ROTATIONAL POSITION

EVALUATE NEW SURFACE FORCES CALL SH2 (T2,P2,F2X,F2Y,F2Z,M01,FT2,WT2)

CALCULATE NEW SURFACE ACCELERATION DO 22 1=2,N A(I)=FT2(I)/MLM(I)

CALL NMBRR (90+I,FT2(I)) CALL NMBRR (70+1,A(I))

REDEFINE Tl,Pl, AS P2,T2 DO 25 1=2 ,N Tl(I)=T2(I) Pl(I )=P2(I) Wfl=WT2

CALL LPEN (IH,IT) IF (IH .EQ. 0) GOTO 21 IF (IT .EQ. 101) GOTO 23 GOTO (241,242,243,244,245) IT-240 IF (~WL .EQ. 1) GOTO 21 CALL MENU (970,40,50,241,'0FF','MA','VF','HF','AC') MFL=l CALL OFF (101) GOTO 21 CALL OFF (342) CALL OFF ( 343) CALL OFF (344) CALL OFF (345) GOTO 21 CALL ON (342) GOTO 21 CONTINUE GOTO 21 CALL ON (344) GOTO 21 CALL ON (345)

PLANES IF (KF .EQ. O) GOTO 320 WRITE (5,303)

0156 303 FORMAT(' ENTER "3" FOR ROTATE '$) 0157 READ (5,204) IR 0158 IF (IR .NE. 3) STOP 0159 300 DO 310 I=l ,N 0160 310 T2(I) =T2(I)+l.5 0161 CALL OFF (46) 0162 CALL OFF (342) 0163 CALL OFF (343) 0164 CALL OFF (3 44 ) 0165 CALL OFF ( 345) 0166 ICN=ICN+l 0167 WRI TE ( 5 ,19) ICN 0168 CALL OFF (4 6) 016 9 320 CONTINUE 0170 DO 42 I=l , N 0171 I L=NC( I ) 0172 DO 42 I I =l,I L 0173 CALL LA2 ( P2 , T2, I , II ,XT, YT,ZT, 0 ) 0174 X( II , I)=XT 017 5 Y( II , I ) =YT 0176 42 Z( II ,l) =ZT

C THE PLANES 0177 DO 43 II=l , N 0178 IL=NC( II ) 0179 DO 43 I=l , IL 0180 DO 43 III=l,6 0181 XP(I,II , III)=R 0182 YP(I,II,III ) =R 0183 INS(I,II,III)=4 0184 IF (III .EQ. 5) GOTO 48 0185 44 IF(Y(I,II) .LE . 0) INS(I,II,1)=4 0186 XP(I , II,l)=X(I , II) 0187 YP(I,II,l)=Z(I,II) 0188 GO TO 43 0189 48 IF(Z(I,II) .LE . 0) INS(I,II,5)=4 0190 XP(I,II,5)= X(I,II) 0191 YP(I,II , 5)=-Y(I,II) 0192 43 CONTINUE

C CONV TO RECTANGULAR COORD 0193 DO 200 J=l,N 0194 DO 200 I=l,NC(J) 0195 IX(J)=XP(I,J , IP)*500./R+500. 0196 IY(J)=YP(I , J,IP)*500./R+500. 0197 IF (IR .EQ. 3) GOTO 200 0198 CALL APNT (IX(J),IY(J),,INS(I,J,IP)) 0199 200 CONTINUE 0200 IF (ICOUNT .GE. !LIM) GOTO 205 020 1 GOTO 16 0202 205 IF (KF .EQ. O) CALL ESUB (46) 0203 KF=l

0204

0205 0206 0207

C

C 72

GOTO (72,72,73,74) N

IF ( IR . NE . 3 ) GOTO 1 72 CALL OFF (46) CALL POINTR (4,47)

CHORDS

N=2

1.35

0208 0209 0210 0211

0212 0213 0214 0215 0216

0217 0218 0219 0220 0221 0222 0223 0224 0225 0226 0227 0228 0229 0230 0231 0232 0233 0234 0235 0236 0237 0238 0239

0240 0241 0242 0243 0244 0245 0246 0247 0248

0249 0250 0251 0252 0253 0254 0255 0256 0257 0258 0259

136

C 172

C 73

197

198

192

187

188

C 173

C 74

457

458

467

CALL CHANGE (4,IX(l),IY(l),,-8) CALL ADVANC (4) CALL CHANGE (4,IX(2)-IX(l),IY(2)-IY(l)) GOTO 300

CALL SUBP (47) CALL APNT (IX(l),IY(l),,-8) CALL VECT (IX(2)-IX(l),IY(2)-IY(l)) CALL ESUB (47) GOTO 301

IF (IR .NE. 3) GOTO 173 GOTO (197,198) IS CALL POINTR (4,47) CALL OFF (47) GOTO 192 CALL POINTR (4,48) CALL OFF (48)

N=3

CALL CHANGE (4,IX(l),IY(l),,-8) CALL ADVANC (4) CALL CHANGE (4,IX(2)-IX(l),IY(2)-IY(l)) CALL ADVANC (4) CALL CHANGE (4,IX(3)-IX(2),IY(3) - IY(2)) CALL ADVANC (4) CALL CHANGE (4,IX(l)-IX(3),IY(l)-IY(3)) GOTO (187,188) IS CALL OFF (48) CALL ON ( 47) IS=2 GOTO 300 CALL OFF (47) CALL ON ( 48) IS=l GOTO 300

CALL SUBP (47) CALL APNT (IX(l),IY(l),,-8) CALL VECT (IX(2)-IX(l),IY(2)-IY(l)) CALL VECT (IX(3)-IX(2),IY(3)-IY(2)) CALL VECT (IX(l)-IX(3),IY(l)-IY(3)) CALL ESUB (47) CALL COPY (48,47) CALL ON ( 47) GOTO 301

IF (IR .NE. 3) GOTO 174 GOTO (457,458) IS CALL POINTR (4,47) CALL OFF (47) GOTO 467 CALL POINTR (4,48) CALL OFF ( 48)

N=4

CALL CHANGE (4,IX(H(l)),IY(H(l)),,-8) CALL ADVANC (4) CALL CHANGE (4,IX(H(2))-IX(H(l)),IY(H(2))-IY(H(l))) CALL ADVANC (4)

0260 0261 0262 0263 0264 0265 0266 0267 0268 0269 0270 0271 0272 0273 0274 0275 0276 0277 0278 0279 0280

0281 0282 0283 0284 0285 0286 0287 0 288 0289 0 29 0 0291 0292 0293 0294 0295 0296 0297 0298 0299 0300 0301 0302 0303 0304 0305 0306 0307 0308

176 587

588

C 174 78

79

81

204 999

CALL CHANGE (4 , IX(H(3)) - IX(H(2)) , IY(H(J)) - f Y(ll(2 ) )) CALL ADVANC (4) CALL CHANGE ( !1 , IX ( H ( 4 ) ) - I X ( l I ( 3 ) ) , I Y ( fl ( 4 ) )- r Y ( 11 ( 3 ) ) ) CALL ADVANC (4) CALL C!IANGE (4,IX(H(l))-1X(IJ(4)) , 1Y(ll(l ))-IY( ii(L1)) ) CALL ALJVANC (4) IF (I D .EQ. 2) GOTO 176 CALL CIIANCE (4 ,IX( H( J) ) - IX(H (l) ) ,IY(H(J))-IY(l l(l))) CALL ADVM/C ( Lf) CALL CHAtJGE (4,TX(H(2)),IY(ll(2))) CALL ADVANC (4) CALL CHANGE (4,TX(H(4)) -IX (ll(2)),JY(ll(4))-IY(l1( 2) )) GOTO (587,588) IS CALL OFF ( 48) CALL ON ( 47) IS=2 GOTO 30 0 CALL OFF ( Lf 7) CALL ON ( 48) IS=l GOTO 300

DO 78 I=l,4 TX(I)=T 2(I) +l 80, DO 79 J=l ,4 XMA=AMAXl (TX( 1), TX(2), TX(3), TX(4)) DO 79 I=l, 4 IF (TX(I) .L T . - 900. ) GOTO 79 IF ( TX(I) • NE. XMA) GOTO 79 H(J)=I TX(I) ==-999. 99 CONTINUE CALL SUBP ( 4 7) CALL APNT (IX(H(l)),IY(H(l)), ,-8) CALL VECT (IX( H( 2) )-IX( H(l)), IY( H( 2) )-IY( H(l))) CALL VECT (IX(H(3))-IX(H(2)) , IY(H(3))-IY(H(2))) CALL VECT (IX( H( 4) )-IX(H(3)), IY( H( 4) )-IY( H( 3))) CALL VECT (IX(H(l))-IX(H(4)),IY(H(l))-IY(H(4))) IF (ID .EQ. 2) GOTO 81 CALL VECT (IX(H(3))-IX(H(l)),IY(H(3))-IY(H(l))) CALL APNT (IX(H(2)),IY(H(2)),,-8) CALL VECT (IX(H(4)) - I X( H(2)),IY(H(4))-IY(H(2))) CALL ESUB (47) CALL COPY (48 , 47) CALL ON ( 47) IF (ID .EQ. 5) GOTO 999 DUMMY GOTO 301 FOR1'1.AT (12) STOP END

137

138

0001 PROGRAM MA25 0002 REAL*4 INC,M,IN,MO,MOl,MLM,ILM 0003 INTEGER*2 H 0004 REAL*8 SYR,SXR,SZR,SSR 0005 COMMON Q,Tll(20),PH(l0),R,N,IP,M,PI,DRC,

)G(lO) ,XC( 10, 10), YC( 10, 10), NC( 10), DELT 0006 DIMENSION Tl(7),Pl(7),P2(7),FT1(7),A(7),T2(7),

)FT2(7), T(7), P(7) ,MO( 7) ,M01(7) ,MLM(7), ILM(7), )FlX(7),FlY(7),FlZ(7),F2X(7),F2Y(7),F2Z(7), )T3( 7) ,P3( 7), PHl( 7), THl( 7), PH2( 7), TH2( 7), IDA( 5), ITI( 4), )IX(7),IY(7),NAHE1(5),ITY(7),H(7),TY(7),TX(7)

0007 DIMENSION X( 4, 7), Y( 4, 7), Z( 4, 7), XP( 4, 7, 6), YP( 4, 7, 6), INS( 4, 7, 6) 0008 CALL INIT (6000) 0009 PI=3.1415926535897932384626 0010 DRC=PI/180. 0011 IA=2 0012 IB=5 0013 IC=6 0014 IE=7 0015 IS=2 0016 WRITE (5,104) 0017 104 FORMAT(/////////, ' N=5' ,//,' USE THE 520.D SERIES') 0018 WRITE (5,103) 0019 103 FORMAT(/,' ENTER INPUT FILE NAME : '$) 0020 READ (5,11) (NAMEl(I), I=l,5) 0021 11 FORMAT (5A2) 0022 CALL ASSIGN (3, 'LP:') 0023 CALL ASSIGN (4,NAMEl,9,'RDO') 0024 CALL IN2 (TLIM,B,CD,IN) 0025 207 WRITE (5,100) 0026 100 FORMAT ( /,' ENTER "l" FOR SIDE VIEW, "5" FOR TOP VIEW '$) 0027 READ (5,204) IP 0028 IF (IP .EQ. 1 .OR. IP .EQ. 5) GOTO 206 0029 GOTO 207 0030 206 WRITE (5,201) 0031 201 FORMAT ( /,' FOR NO VERTEX ENTER 2', /,

) 'FOR SINGLE VERTEX ENTER 3',/,' FOR DOUBLE VERTEX ENTER 4',/, ) T26,': ',$)

0032 READ (5,204) ID 0033 IF (IP .EQ. 5) GOTO 5 0034 CALL RSTR ('A201.GR') 0035 GOTO 7 0036 5 CALL RSTR ('A205.GR') 0037 7 CALL MENU (970,60,1,101,'/tl/') 0038 ILIM=TLIM 0039 CALL SUBP (345) 0040 CALL OFF (345) 0041 CALL APNT (0,1020,,-8) 0042 CALL TEXT ('A2= ' ) 0043 CALL NMBRR (72,A(2),8,'(1PE8.2)') 0044 CALL TEXT(' M/SEC**2') 0045 CALL APNT (0,1000,,-8) 0046 CALL TEXT ('A3= ') 0047 CALL NMBRR (73,A(3),8,'(1PE8.2)') 0048 CALL APNT (0,980,,-8) 0049 CALL TEXT ('A4= ')

0050 0051 0052 0053 0054 0055 0056 0057 0058 0059 0060 0061 0062 0063 0064 0065 0066 0067 0068 0069 0070 0071 0072 0073 0074 0075 0076 0077 0078 0079 0080 0081 0082 0083 0084 0085 0086 0087 0088 0089 0090 0091 0092 0093 0094 0095 0096 0097 0098 0099 0100 0101 0102 0103 0104 0105

10

12

CALL NMBRR (74,A(4),8,"'(1PE8.2)') CALL APNT (0,960,,-~) CALL TEXT ('AS="') CALL NMBRR (75,A(5),8,"'(1PE8.2)') CALL ESUB (345) CALL SUBP (344) CALL OFF (344) CALL APNT (0,1020,,-8) CALL TEXT ("'H2= ') CALL NMBRR (92,FT1(2),8,'(1PE8.2)') CALL TEXT (' N"') CALL APNT (0,1000,,-8) CALL TEXT ('H3= ') CALL NMBRR (93, FT1(3),8,"'(1P E8.2)"') CALL APNT (0,980,,-8) CALL TEXT ("'H4= ') CALL NMBRR (94,FT1(4),8,"'(1PE8.2)') CALL APNT (0,960,,~8) CALL TEXT ('HS="') CALL NMBRR (95,FT1(5),8,"'(1PE8.2)') CALL ESUB (344)

ICOUNT•O DO 10 I=-1,N Tl(I)=-TH(I) Pl(I)=PH(I) T2(I)•Tl(I) P2(I)=Pl(I) M=B**3*3000. Q•M*CD*l.61E-19 DO 12 I:;l ,N MLM( I )=O. ILM(I)=O. LLsNC(I) DO 12 J=l,LL MLM(I)=MLM(I)+M ILM( I)=ILM( I)+M*(XC(J, I)**2+YC(J, 1)**2)+1.

CALL SUBP ( 342) CALL OFF (342) CALL APNT (800,1020,,-8) CALL TEXT ('Ml=') CALL NMBRR (80,MLM(l),8,"'(1PE 8.2) "') CALL TEXT("' KG') CALL APNT (800,1000,,-8) CALL TEXT ("'M2= "') CALL NMBRR (81,MLM(2),8,"'(1PE8.2)"') CALL APNT (800,980,,-8) . CALL TEXT ("'M3= ') CALL NMBRR (82,MLM(3),8,"'(1PE8.2)') CALL APNT (800,960,,~8) CALL TEXT ('M49 "') CALL NMBRR (83,~LM(4),8,"'(1PE8.2) ' ) CALL APNT (800,940,, - 8) CALL TEXT ('MS•') CA.LL NMBRR (84,MLM(5),8,""(1PE8.2)"') CALL ESUB (342)

CALL SH2 (Tl, Pl, FlX, FlY ,F lZ ,MOl, FTl, WTl)

139

140

0106 DO 14 1=2,N 0107 A(I)=FTl(I)/MLM(I) 0108 F2X(I)=FlX(I) 0109 F2Y(I)=FlY(I) 0110 14 F2Z(I)=FlZ(l) 0111 CALL SUBP (46) 0112 16 IF (ICOUNT .EQ. 0) DT=l.OE-10 OU3 IF ( ICOUNT .EQ. 1) DT=DELT 0114 DT=DT*IN START NEXT ITERATION 0115 ICOUNT=ICOUNT+l 0116 WRITE (5,19) ICOUNT 0117 19 FORMAT ('+',13,' ')

Oll8 Oll9 0120 0121 0122 0123 0124 0125 0126 0127 0128 0129 0130 0131 0132

0133

0134 0135 0136 0137

0138 0139 0140 0141 0142 0143 0144 0145 0146 0147 0148 0149 0150 0151 0152 0153 0154 0155 0156 0157

C CALCULATES LATEST POSITIONS OF ALL CONTINENTS BUT FIRST ONE

20 C

C

22 C

25

23

241

242

DO 20 I=2,N SXl=F2X(I)/MLM(I)*DT*DT/2. SYl=F2Y(I)/MLM(I)*DT*DT/2. SZl=F2Z(I)/MLM(I)*DT*DT/2. PHD=Pl(I)*DRC THD=Tl(I)*DRC RX=R*COS(PHD)*COS(THD) RY=R*COS(PHD)*SIN(THD) RZ=R*SIN(PHD) SXR=RX+SXl SYR=RY+SYl SZR=RZ+SZl

F2X,F2Y,F2Z ARE THE X,Y,Z COMPONENTS OF TOTAL SURF ACE FORCE ACTING ON I-TH CONT. Pl, Tl = CURRENT CO-ORDINATES OF I-TH CONT

! " RX,RY,RZ = COMPONENTS OF CURRENT

POSITIONS OF I-TH CONT.

NEW X,Y,Z COMPONENTS OF I-TH CONT.

T2(I)=DATAN2 (SYR,SXR)/DRC POLAR COMPONENTS OF NEW POSITIONS SSR=SQRT(SXR**2+SYR**2) P2(I)=DATAN2(SZR,SSR)/DRC

EVALUATE NEW SURFACE FORCES CALL SH2 (T2,P2,F2X,F2Y,F2Z,M01,FT2,WT2)

CALCULATE NEW SURFACE ACCELERATION DO 22 1=2,N A(I)=FT2(I)/MLM(I)

CALL NMBRR (90+I,FT2(I)) CALL NMBRR (70+1,A(I))

REDEFINE Tl,Pl, AS P2,T2 DO 25 1=2,N Tl(I)=T2(1) Pl(I)=P2(I) WTl=WT2

CALL LPEN (IH,IT) IF (IH .EQ. O) GOTO 21 IF (IT .EQ. 101) GOTO 23 GOTO (241,242,243,244,245) IT-240 IF (MFL .EQ. 1) GOTO 21 CALL MENU (970,40,50,241,'0FF', ' MA','VF','HF','AC') MFL=l CALL OFF (101) GOTO 21 CALL OFF (342) CALL OFF (343) CALL OFF (344) CALL OFF. ( 345) GOTO 21 CALL ON ( 342) GOTO 21

0158 0159 0160 0161 0162

243

244

245

CONTINUE GOTO 21 CALL ON (344) GOTO 21 CALL ON (345)

C PLANES 0163 21 IF (KF .EQ. 0) GOTO 320 0164 301 WRITE (5,303) 0165 303 FORMAT(' ENTER "3" FOR ROTATE '$) 0166 READ (5,204) IR 0167 IF (IR .NE. 3) STOP 0168 300 DO 310 I=l,N 0169 310 T2(I)=T2(I)+l. 0170 CALL OFF (46) 0171 CALL OFF (342) 0172 CALL OFF (343) 0173 CALL OFF (344) 0174 CALL OFF (345) 0175 ICN=ICN+l 0176 WRITE (5,19) ICN 0177 320 CONTINUE 0178 DO 42 I=l,N 0179 IL•NC(I) 0180 DO 42 II=l,IL 0181 CALL LA2 (P2,T2,I,II,XT,YT,ZT,O) 0182 X(II,I)•XT 0183 Y(II,I)•YT 0184 42 Z(II,I)=ZT

C THE PLANES 0185 DO 43 II=l,N 0186 IL=NC(II) 0187 DO 43 I=l,IL 0188 DO 43 III=l,6 0189 XP(I,II,III)=R 0190 YP(I,II,III)=R 0191 INS(I,II,III)=8 0192 IF (III .EQ. 5) GOTO 48 0193 44 IF(Y(I,II) .LE. O) INS(I,II,1)=4 0194 XP(I,II,l)=X(I,II) 0195 YP(I,II,l)•Z(I,II) 0196 GO TO 43 0197 48 IF(Z(I,II) .LE. O) INS(I,II,5)=4 0198 XP(I,II,5)• X(I,II) 0199 YP(I,II,5)•-Y(I,II) 0200 43 CONTINUE

0201 0202 0203 0204 0205 0206 0207 0208 0209 0210

C

200

205

CONV TO RECTANGULAR COORD DO 200 Jsl ,N DO 200 I•l,NC(J) IX(J)=XP(I,J,IP)*500./R+500. IY(J)•YP(I,J,IP)*500./R+500. IF (IR .EQ. 3) GOTO 200 CALL APNT (IX(J),IY(J),,INS(I,J,IP)) CONTINUE IF (!COUNT .GE. ILIM) GOTO 205 GOTO 16 IF (KF .EQ. O) CALL ESUB (46)

141

142

0211 C C

0212 75 0213 0214 151 0215 0216 0217 0218 0219 131 0220 0221 0222 0223 130 0224 0225 0226 138 0227 0228 0~29 0230 0231 0232 0233 0234 0235 0236 132 0237 0238 0239 887 0240 0241 0242 888 0243 0244 860 0245 0246 0247 0248 0249 0250 0251 0252 0253 0254 0255 0256 0257 0258 0259 0260 169 0261 0262 0263 0264

KF=l

DO 151 1=1,5 TY( l)=P2( I )+90. TX(I)=T2(1)+180. YMA=O. YMI=999. DO 131 I=l,5 YMA=AMAXl (YMA,TY(I)) YMI=AMINl (YMI,TY(I)) IF (ID .EQ. 2) GOTO 138 DO 130 1=1,5

CHORDS N=5

IF (YMA .EQ. TY(I)) H(l)=I IF (YMI .EQ. TY(I)) H(5)=1 TX(H(l))=-999. IF (ID .EQ. 4) TX(H(5))=-999. IF (ID .EQ. 2) IA=l IF (ID .EQ. 3 .QR. ID .EQ. 4) IA=2 IF (ID .EQ. 4) IB=4 DO 132 J=IA,IB XMA=AMAXl (TX(l),TX(2),TX(3),TX(4),TX(5)) DO 132 1=1,5 IF (TX(I) .LT. -900.) GOTO 132 IF (TX(I) .NE. XMA) GOTO 132 H(J)=I TX(!) =-999.99 CONTINUE IF (IR .NE. 3) GOTO 163 GOTO (887,888) IS CALL POINTR (4,47) CALL OFF ( 4 7) GOTO 860 CALL POINTR (4,48) CALL OFF ( 48) CALL CHANGE (4,IX(H(2)),IY(H(2)),,-8) CALL ADVANC ( 4) CALL CHANGE (4,IX(H(3))-IX(H(2)),IY(H(3))-IY(H(2))) CALL ADVANC (4) CALL CHANGE (4,IX(H(4))-IX(H(3)),IY(H(4))-IY(H(3))) CALL ADVANC (4) IF(ID.EQ.4) CALL CHANGE (4,IX(H(2))-IX(H(4)),IY(H(2))-IY(H(4))) IF(ID.EQ.4) CALL ADVANC (4) IF (ID .EQ. 4) GOTO 169 CALL CHANGE (4,IX(H(5))-IX(H(4)),IY(H(5))-IY(H(4))) CALL ADVANC (4) CALL CHANGE (4,IX(H(l))-IX(H(5)),IY(H(l))-IY(H(5))) CALL ADVANC (4) CALL CHANGE (4,IX(H(2))-IX(H(l)),IY(H(2))-lY(H(l))) CALL ADVANC (4) IF (ID .EQ. 2) GOTO 168 CALL CHANGE (4,IX(H(5))-IX(H(2)),IY(H(5))-IY(H(2))) CALL ADVANC (4) CALL CHANGE (4,IX(H(3)),IY(H(3)),,-8) CALL ADVANC (4) CALL CHANGE (4,IX(H(l))-IX(H(3)),IY(H(l))-IY(H(3)))

\,

0265 0266 0267 0268 0269 0270 0271 0272 0273 0274 0275 0276 0277 0278 0279 0280 0281 0282 0283 0284

0285 0286 0287 0288 0289 0290 0291 0292 0293 0294 0295 0296 0297 0298 0299 0300 0301 0302 0303 0304 0305 0306 0307 0308 0309 0310 0311

168 947

948

C 163

166

164

204 999

CALL ADVANC (4) CALL CHANGE (4,IX{1:J(4))-IX(H(l)),IY(H(4))-IY(H(l))) CALL ADV.ANC (4) IF (ID .NE. 4) GOTO 168 CALL CHANGE (4,IX(H(5))-IX(H(4)),IY(H(5))-IY(H(4))) CALL ADVANC (4) CALL CHANGE (4,IX(H(3))-IX{H(S)),IY(H(3))-IY(H(S))) CALL ADVANC (4) CALL CHANGE (4,IX(H(l)),IY(H(l)),,-8) CALL ADVANC ( 4) CALL CHANGE (4,IX(H(2))-IX{H{l)),IY(H(2))-IY(H(l))) GOTO (947,948) IS CALL OFF { 48) CALL ON ( 47) IS=2 GOTO 300 CALL OFF (47) CALL ON (48) IS•l GOTO 300

CALL SUBP (47) CALL APNT (IX(H(2)),IY(H(2)), ,8) CALL VECT (IX(H(3))-IX(H(2)),IY(H(3))-IY(H(2))) CALL VECT (IX(H(4))-IX(H(3)),IY(H(4))-IY(H(3))) IF(ID .EQ. 4) CALL LVECT (IX(H(2))-IX(H(4)),IY(H(2))-IY(H(4))) IF (ID .EQ, 4) GOTO 166 CALL VECT (IX(H(5))-IX(H(4)),IY(H(S))-IY(H(4))) CALL VECT (IX(H(l))-IX{H(5)),JY(H(l))-IY(H(S))) CALL VECT (IX(H(2) )-IX(H(l)), IY(H(2) )-IY(H(l))) IF (ID .EQ. 2) GOTO 164 CALL VECT (IX(H(5))-IX(H(Z)),IY(H(5))-IY(H(2))) CALL APNT (IX(H(3)),IY(H(3)),,-8) CALL VECT (IX(H{l))-IX(H(3)),IY(H(l))-IY(H(3))) GALL VECT (IX(H(4))-IX(H(l)),IY(H(4))-IY(H(l))) IF (ID .NE. 4) GOTO 164 CALL VECT (IX(H(5))-IX(H(4)),IY(H(S))-IY(H(4))) CALL VECT (IX(H(3))-IX(H(5)),lY(H(3))-IY(H(5))) CALL APNT (IX(H(l)),IY(H(l)),,-8) CALL VECT (IX(H(2))-IX(H{l)),IY(H(2))-IY(H(l))) CALL ESUB (47) CALL COPY (48,47) CALL ON (47) IF (ID .EQ. 5) GOTO 999 DUMMY GOTO 301 FORMAT (l2) STOP END

14J

144

0001 PROGRAM MA26 0002 REAL*4 INC,M,IN,MO,MOl,MLM,ILM 0003 INTEGER*2 H 0004 REAL*8 SYR,SXR,SZR,SSR 0005 COMMON Q, TH(20) ,PH( 10) ,R, N, IP ,M, PI , DRC,

)G(lO),XC(l0,10),YC(l0,10),NC(lO) , DELT 0006 DIMENSION Tl(7),Pl(7),P2(7),fT1(7 ) , A(7),T2(7),

)FT2(7),T(7),P(7),M0(7),M01(7),MLM (7 ),ILM(7), )FlX(7),FlY(7),FlZ(7),F2X(7),F2Y(7 ) ,F2Z(7), )T3(7),P3(7),PH1(7),TH1(7),PH2(7),TH2(7),IDA(5),ITI(4), )IX(7) ,IY(7) ,NAMEl( 5), ITY( 7) ,H( 7), TY( 7), TX(7)

0007 DIMENSION X(4,7),Y(4,7),Z(4,7),XP(4,7,6),YP(4,7,6),INS(4,7,6) 0008 CALL INIT (6000) 0009 PI=3.1415926535897932384626 0010 DRC=PI/180. 0011 IA=2 0012 IB=5 0013 IC=6 0014 IE=7 0015 IS=2 0016 WRITE (5,104) 0017 104 FORMAT(/////////,' N=6',//,' USE THE 620.D SERIES') 0018 WRITE (5,103) 0019 103 FORMAT (/,' ENTER INPUT FILE NAME : ' $) 0020 READ (5,11) (NAMEl(I), I=l,5) 0021 11 FORMAT (5A2) 0022 CALL ASSIGN (3 ,' LP:') 0023 CALL ASSIGN (4,NAMEl,9,'RDO ' ) 0024 CALL IN2 (TLIM,B , CD,IN) 0025 207 WRITE (5,100) 0026 100 FORMAT (/,' ENTER "l" FOR SIDE VIEW, "5" FOR TOP VIEW '$) 0027 READ (5,204) IP 0028 IF (IP .EQ. 1 .OR. IP .EQ. 5) GOTO 206 0029 GOTO 207 0030 206 WRITE (5,201) 0031 201 FORMAT(/,' FOR NO VERTEX ENTER 2' ,/,

> 'FOR SINGLE VERTEX ENTER 3' ,/ ,' FOR DOUBLE VERTEX ENTER 4',/, > T26, ' : ' ,$)

0032 READ (5,204) ID 0033 WRITE (5,141) 0034 141 FORMAT(' ENTER POINT REDUCTION FACTOR (12): '$) 0035 READ (5,204) IPR 0036 WRITE (5,105) 0037 105 FORMAT(' ') 0038 IF (IPR .EQ. O) IPR=l 0039 IF (IP .EQ. 5) GOTO 5 0040 CALL RSTR ('A201.GR') 0041 GOTO 7 0042 5 CALL RSTR ('A205.GR') 0043 7 CALL MENU (970,60,1,101,'## ' ) 0044 ILIM=TLIM 0045 CALL SUBP (345) 0046 CALL OFF (345) 0047 CALL APNT (0,1020,,-8) 0048 CALL TEXT ( 'A2= ') 0049 CALL NMBRR (72,A(2),8,'(1PE8.2) ' )

0050 0051 0052 0053 0054 0055 0056 0057 0058 0059 0060 0061 0062 0063 0064 0065 0066 0067 0068 0069 0070 0071 0072 0073 0074 0075 0076 0077 0078 0079 0080 0081 0082 0083 0084 0085 0086 0087 0088 0089 0090 0091 0092 0093 0094 0095 0096 0097 0098 0099 0100 0101 0102 0103 0104 0105

10

12

CALL TEXT(' M/SEC**2') CALL APNT (0,1000,,-8) CALL TEXT ('A3= ') CALL NMBRR (73,A(3),8,'(1PE8,2)') CALL APNT (0,980,,-8) CALL TEXT ('A4= ') CALL NMBRR (74,A(4),8,'(1PE8,2)') CALL APNT (0,960,,-8) CALL TEXT ('AS=') CALL NMBRR (75,A(5),8,'(1PE8,i)') CALL APNT (0,940,,-8) CALL TEXT ('A6= ') CALL NMBRR (76,A(6),8,'(1PE8,2)') CALL ESUB (345) CALL SUBP (344) CALL OFF (344) CALL APNT (0,1020,,-8) CALL TEXT ('H2= ') CALL NMBRR (92,FT1(2),8,'(1PE8,2)') CALL TEXT(' N') CALL APNT (0,1000,,-8) CALL TEXT ('H3= ') CALL NMBRR (93,FT1(3),8,'(1PE8,2)') CALL APNT (0,980,,-8) CALL TEXT ('H4= ') CALL NMBRR (94,FT1(4),8,'(1PE8,2)') CALL APNT (0,960,,-8) CALL TEXT ('HS=') CALL NMBRR (95,FT1(5),8,'(1PE8,2)') CALL APNT (0,940,,-8) CALL TEXT ('H6= ') CALL NMBRR (96,FT1(6),8,'(1PE8,2)') CALL ESUB (344)

ICOUNT=O DO 10 I=l,N Tl(I)=TH(I) Pl(I)=PH(I) T2(I )=Tl(I) P2(I)=Pl(I) M=B**3*30000, Q=M*CD*l.61E-19 DO 12 I=l ,N MLM(I)=O, ILM(I)=O, LL=NC(I) DO 12 J=l ,LL MLM(I)=MLM(I)+M ILM(I)=ILM(I)+M*(XC(J,1)**2+YC(J,I)**2)+1.

CALL SUBP (342) CALL OFF (342) CALL APNT (800,1020,,-8) CALL TEXT ('Ml=') CALL NMBRR (80,MLM(l),8,'(1PE8,2)') CALL TEXT(' KG') CALL APNT (800,1000,,-8) CALL TEXT ('M2= ')

145

0106 0107 0108 0109 0110 0111 0112 0113 0114 ous 0116 0117 0118 0119 0120 0121 0122 0123 0124 0125 0126 0127 0128 0129 0130 0131 0132

146

0133 0134 0135 0136 0137 0138 0139 0140 0141 0142 0143 0144 0145 0146 . 0147

0148

0149 0150 0151 0152

0153 0154 0155 0156 0157

~ALL NMBRR (81,MLM(2),8,'(1PE8.2)') CALL APNT (800,980,,-8) CALL TEXT ('M3= ') CALL NMBRR (82,MLM(3),8,'(1PE8.2)') CALL APNT (800,960,,-8) CALL TEXT ('M4= ') CALL NMBRR (83,MLM(4),8,'(1PE8.2)') CALL APNT (800,940,,-8) CALL TEXT ('MS=') CALL NMBRR (84,MLM(S),8,'(1PE8.2)') CALL APNT (800,920,,-8) CALL TEXT ('M6= ') CALL NMBRR (85,MLM(6),8,'(1PE8.2)') CALL ESUB (342) CALL SUBP (46)

CALL SH2 (Tl,Pl,FlX,FlY,FlZ,MOl,FTl,WTl) DO 14 1=2,N A(I)=FTl(I)/MLM(I) F2X(I)=FlX(I) F2Y( I)=Fl Y(I)

14 F2Z(I)=FlZ(I) 16 IF (ICOUNT .EQ. O) DT=l.OE-10

IF (ICOUNT .EQ. 1) DT=DELT DT=DT*IN START NEXT ITERATION ICOUNT=ICOUNT+l

WRITE (5,19) ICOUNT 19 FORMAT ('+',13,' ') C CALCULATES LATEST POSITIONS OF ALL CONTINENTS BUT FIRST ONE

DO 20 1=2 ,N SXl=F2X(I)/MLM(I)*DT*DT/2. F2X,F2Y,F2Z ARE THE X,Y,Z COMPONENTS SYl=F2Y(I)/MLM(I)*DT*DT/2. OF TOTAL SURFACE FORCE ACTING SZl=F2Z(I)/MLM(I)*DT*DT/2. ON I-TH CONT. PHD=Pl(I)*DRC Pl,Tl = CURRENT CO-ORDINATES OF I-TH CONT. THD=Tl(I)*DRC ! " RX=R*COS(PHD)*COS(THD) RX,RY,RZ = COMPONENTS OF CURRENT RY=R*COS(PHD)*SIN(THD) POSITIONS OF I-TH CONT. RZ=R*SIN(PHD) SXR=RX+SXl NEW X,Y,Z COMPONENTS OF I-TH CONT. SYR=RY+SYl SZR=RZ+SZl T2(I)=DATAN2 (SYR,SXR)/DRC POLAR COMPONENTS OF NEW POSITIONS SSR=SQRT(SXR**2+SYR**2)

20 P2(I)=DATAN2(SZR,SSR)/DRC C EVALUATE NEW SURFACE FORCES

CALL SH2 (T2,P2,F2X,F2Y,F2Z,M01,FT2,WT2) C CALCULATE NEW SURFACE ACCELERATION

DO 22 1=2,N A(I)=FT2(I)/MLM(I)

CALL NMBRR (90+I,FT2(I)) 22 CALL NMBRR (70+I,A(I)) C REDEFINE· Tl,Pl, AS P2,T2

DO 25 1=2,N Tl(I)=T2(I)

25 Pl(I)=P2(I) WTl=WT2

CALL LPEN (IH,IT)

0158 0159 0160 0161 0162 0163 0164 0165 0166 0167 0168 0169 0170 0171 0172 0173 0174 0175 0176 0177

23

241

242

243

244

245

IF (IH .EQ. O) GOTO 21 IF (IT .EQ. 101) GOTO 23 GOTO (241,242,243,244,245) IT-240 IF (MFL .EQ. 1) GOTO 21 CALL MENU ( 970, 40, 50,241, 'OFF', 'MA', 'VF', 'HF',' AC') MFL=l CALL OFF (101) GOTO 21 CALL OFF (342) CALL OFF (343) CALL OFF (344) CALL OFF (345) GOTO 21 CALL ON (342) GOTO 21 CONTINUE GOTO 21 CALL ON (344) GOTO 21 CALL ON (345)

C PLANES 0178 21 IF (KF .EQ. O) GOTO 320 0179 301 WRITE (5,303) 0180 303 FORMAT(' ENTER "3" FOR ROTATE '$) 0181 READ (5,204) IR 0182 IF (IR • NE. 3) STOP 0183 300 DO 310 I=l,N 0184 310 T2(I)=T2(I)+l.5 0185 CALL OFF (46) 0186 CALL OFF (342) 0187 CALL OFF (343) 0188 CALL OFF (344) 0189 CALL OFF (345) 0190 ICN=ICN+l 0191 WRITE (5,19) ICN 0192 320 CONTINUE 0193 DO 42 I=l,N 0194 IL=NC(I) 0195 DO 42 II=l,IL 0196 CALL LA2 (P2,T2,I,II,XT,YT,ZT,0) 0197 X(II,I)=XT 0198 Y(II,I)=YT 0199 42 Z(II,I)=ZT

C THE PLANES 0200 DO 43 II=l,N 0201 IL=NC(II) 0202 DO 43 I=l,IL 0203 DO 43 III=l,6 0204 XP(I,II,III)=R 0205 YP(I,II,III)=R 0206 INS(I,II,III)=8 0207 IF (III .EQ. 5) GOTO 48 0208 44 IF(Y(I,II) .LE. O) INS(I,II,1)~4 0209 XP(I,II,l)=X(I,II) 0210 YP(I,II,l)=Z(l,II) 0211 GO TO 43

147

0212 0213 0214 0215

0216 0217 0218 0219 0220 0221 0222 0223 0224 0225 0226

0227 0228 0229 0230 0231 0232 0233 0234 0235 0236 0237 0238 0239 0240 0241 0242 0243 0244 0245 0246 0247 0248 0249 0250 0251

0252 0253 0254 0255 0256 0257 0258 0259 0260 0261 0262 0263

148

48

43 C

200

205 C C 76

51

31

30

38

32 C

647

648

660

IF(Z(I,II) .LE. O) INS(I,II,5)=4 XP(I,II,5)= X(I,II) YP(I,II,5)=-Y(I,II)

CONTINUE CONV TO RECTANGULAR COORD

DO 200 J=l ,N DO 200 I=l,NC(J) IX(J)=XP(I,J,IP)*SOO./R+SOO. IY(J)=YP(I,J,IP)*SOO./R+SOO. IF (IR .EQ. 3) GOTO 200 IF ((ICOUNT-(ICOUNT/IPR)*IPR) .NE. 0) GOTO 200 CALL APNT (IX(J),IY(J),,INS(I,J,IP)) CONTINUE IF (ICOUNT .GE. ILIM) GOTO 205 GOTO 16 KF=l

DO 51 I=l,6 TY(I)=P2(I)+90. TX(I)=T2(I)+l80. YMA=O. YMI=999. DO 31 I=l,6 YMA=AMAXl (YMA,TY(I)) YMI=AMINl (YMI,TY(I)) IF (ID .EQ. 2) GOTO 38 DO 30 I=l ,6

CHORDS N=6

IF (YMA .EQ. TY(I)) H(l)=I IF (YMI .EQ. TY(I)) H(6)=I TX( H(l ))=-999. IF (ID .EQ. 4) TX(H(6))=-999. IF (ID .EQ. 2) IA=l IF (ID .EQ. 3 .OR. ID .EQ. 4) IA=2 IF (ID .EQ. 4) IC=5 DO 32 J=IA, IC XMA=AMAXl (TX(l),TX(2),TX(3),TX(4),TX(5),TX(6)) DO 32 I=l,6 IF (TX(I) .LT. -900.) GOTO 32 IF (TX(I) .NE. XMA) GOTO 32 H(J)=I TX(I) =-999.99 CONTINUE

IF (IR .NE. 3) GOTO 63 GOTO (647,648) IS CALL POINTR (4,47) CALL OFF ( 47) GOTO 660 CALL POINTR (4,48) CALL OFF ( 48) CALL CHANGE (4,IX(H(l)),IY(H(l)),,-8) CALL ADV ANC (4 ) CALL CHANGE (4,IX(H(2))-IX(H(l)),IY(H(2))-IY(H(l))) CALL ADVANC (4) CALL CHANGE ( 4, IX( H(3 ))-IX( H( 2)), IY( H( 3 ))-IY( H( 2)))

149

0264 CALL ADVANC (4) 0265 CALL CHANGE (4,IX(H(4))-IX(H(3)),IY(H(4))-IY(H(3))) 0266 CALL ADVANC (4) 0267 CALL CHANGE (4,IX(H(5))-IX(H(4)),IY(H(5))-IY(H(4))) 0268 CALL ADVANC (4) 0269 CALL CHANGE (4,IX(H(6))-IX(H(5)),IY(H(6))-IY(H(5))) 0270 CALL ADVANC (4) 0271 IF (ID .EQ. 2 .QR. ID .EQ. 3)

) CALL CHANGE (4,IX(H(l))-IX(H(6)),IY(H(l))-IY(H(6))) 0272 IF (ID ·.EQ. 2 .OR. ID .EQ. 3) CALL ADVANC (4) 0273 IF (ID .EQ. 2) GOTO 261 0274 CALL CHANGE (4,IX(H(3) ),IY( H(3))) 0275 CALL ADVANC (4) 0276 CALL CHANGE ( 4, IX(H(l) )-IX(H(3)), IY(H(l) )-IY(H( 3))) 0277 CALL ADVANC (4) 0278 CALL CHANGE (4,IX(H(4))-IX(H(l)),IY(H(4))-IY(H(l))) 0279 CALL ADVANC (4) 0280 CALL CHANGE (4,IX(H(l)),IY(H(l))) 0281 CALL ADVANC (4) 0282 CALL CHANGE (4,IX(li{5))-IX(H(l)),IY(H(5))-IY(H(l))) 0283 CALL ADVANC (4) 0284 CALL CHANGE (4,IX(H(2)),IY(H(2))) 0285 CALL ADVANC (4) 0286 CALL CHANGE (4,IX(H(6))-IX(H(2)),IY(H(6))-IY(H(2))) 0287 CALL ADVANC (4) 0288 IF (ID .EQ. 3) GOTO 261 0289 CALL CHANGE (4,IX(H(2)),IY(H(2))) 0290 CALL ADVANC (4) 0291 CALL CHANGE (4,IX(H(5))-IX(H(2)),IY(H(5))-IY(H(2))) 0292 CALL ADVANC (4) 0293 CALL CHANGE (4,IX(H(3)),IY(H(3))) 0294 CAJ;..L ADVANC (4) 0295 CALL CHANGE (4,IX(H(6))-IX(H(3)),IY(H(6))-IY(H(3))) 0296 CALL ADVANC (4) 0297 CALL CHANGE (4,IX(H(4))-IX(H(6)),IY(H(4))-IY(H(6))) 0298 261 GOTO (747,748) IS 0299 747 · CALL OFF (48) 0300 CALL ON (47) 0301 IS•2 0302 GOTO 300 0303 748 CALL OFF (47) 0304 CALL ON (48) 0305 IS•l 0306 GOTO 300 0307 63 CALL ESUB (46) 0308 CALL SUBP (47) 0309 CALL APNT ( IX( H(l)), IY( H(l)), , -8) 0310 CALL VECT (IX(H(2))-IX(H(l)),IY(H(2))-IY(H(l))) 0311 CALL VECT (IX(H(3))-IX(H(2)),IY(H(3))-IY(H(2))) 0312 CALL VECT (IX(H(4))-IX(H(3)),IY(H(4))-IY(H(3))) 0313 CALL VECT (IX(H(5))-IX(H(4)),IY(H(5))-IY(H(4))) 0314 CALL VECT (IX(H(6))-IX(H(5)),IY(H(6))-IY(H(5))) 0315 IF (ID .EQ. 2 .OR. ID .EQ. 3)

> CALL VECT (IX(H(l))-IX(H(6)),IY(H(l))-IY(H(6))) 0316 IF (lD .EQ. 2) GOTO 230 0317 CALL APNT (IX(H(3)),IY(H(3)),,-8)

0318 0319 0320 0321 0322 0323 0324 0325 0326 0327 0328 0329 0330 0331 0332 0333 0334 0335 0336 0337

150

230

204 999

CALL VECT (IX(H(l))-IX(H(3)),IY(H(l))-IY(H(3))) CALL VECT (IX(H(4))~IX(H(l)),IY(H(4))-IY(H(l))) CALL APNT (IX(H(l)),IY(H(l)),,-8) CALL VECT (IX(H(5))-IX(H(l)),IY(H(5))-IY(H(l))) CALL APNT (IX(H(2)),IY(H(2)),,-8) CALL VECT (IX(H(6))-IX(H(2)),IY(H(6))-IY(H(2))) IF (ID .EQ. 3) GOTO 230 CALL APNT (IX(H(2)),IY(H(2)),,-8) CALL VECT (IX(H(5))-IX(H(2)),IY(H(5))-IY(H(2))) CALL APNT (IX(H(3)),IY(H(3)),,-8) CALL VECT (IX(H(6))-IX(H(3)),IY(H(6))-IY(H(3))) CALL VECT (IX(H(4))-IX(H(6)),IY(H(4))-IY(H(6))) CALL ESUB (47) CALL COPY (48,47) CALL ON ( 47) IF (ID .EQ. 5) GOTO 999 DUMMY GOTO 301 FORMAT (12) STOP END

0001 PROGRAM MA27 0002 REAL*4 INC,M,IN,MO,MOl,MLM,ILM 0003 INTEGER*2 H 0004 INTEGER*4 ICC(7) 0005 REAL*8 SYR,SXR,SZR,SSR 0006 COMMON Q,TH(20),PH(l0),R,N,IP,M,PI,DRC,

)G(lO),XC(l0,10),YC(l0,10),NC(lO),DELT 0007 DIMENSION Tl(7),Pl(7),P2(7),FT1(7),A(7),T2(7),

) FT2(7),T(7),P(7),M0(7),M01(7),MLM(7),ILM(7), )FlX(7),FlY(7),FlZ(7),F2X(7),F2Y(7),F2Z(7), )T3(7),P3(7),PH1(7),TH1(7),PH2(7),TH2(7),IDA(5),ITI(4), )IX(7),IY(7),NAME1(5),ITY(7),H(7),TY(7),TX(7)

0008 DIMENSION X(9,7),Y(9,7),Z(9,7),XP(9,7,6),YP(9,7,6),INS(9,7,6), )XCG(7), YCG(7), ZCG(7) ,XCP(7), YCP(7) , INSC(7, 6 ), JX(7) ,J Y(7 )

0009 CALL INIT (6000) 0010 PI=3.1415926535897932384626 OOll DRC=PI/180. 0012 IA=2 0013 I B=S 0014 IC=6 0015 IE=7 0016 IS=2 0017 WRITE (5,104) 0018 104 FORMAT(///////// ,"' N=7"', //,"' USE THE 720.D SERIES') 0019 WRITE (5,103) 0020 103 FORMAT(/,"' ENTER INPUT FILE NAME : "'$) 0021 READ (5,11) (NAMEl(I), I=l,5) 0022 11 FORMAT (5A2) 0023 CALL ASSIGN (3,"'LP:"') 0024 CALL ASSIGN (4,NAMEl,9,'RDO') 0025 CALL IN2 (TLIM,B,CD,IN) 0026 207 WRITE (5,100) 0027 100 FORMAT(/,"' ENTER "l" FOR SIDE VIEW, "5 " FOR TOP VIEW "'$) 0028 READ (5,204) IP 0029 IF (IP .EQ. 1 .QR. IP .EQ. 5) GOTO 206 0030 GOTO 207 0031 206 WRITE (5,201) 0032 201 FORMAT(/,"' FOR NO VERTEX ENTER 2', /,

> "'FOR SINGLE VERTEX ENTER 3',/,"' FOR DOUBLE VERTEX ENTER 4"',/, > T26,"': ', $)

0033 READ (5,204) ID 0034 IF (ID .EQ. 2) GOTO 220 0035 WRITE (5,210) 0036 210 FORMAT(/,"' TO DRAW UPPER HALF, ENTER 6 :'$) 0037 READ (5,204) JUP 0038 IF (ID .NE. 4) GOTO 220 0039 WRITE (5,212) 0040 212 FORMAT("' TO DRAW LOWER HALF, ENTER 6 : '$) 0041 READ (5,204) JLP 0042 WRITE (5,141) 0043 141 FORMAT(' ENTER POINT REDUCTION FACTOR ( 12): ' $) 0044 READ (5,204) IPR 0045 IF (IPR .EQ. 0) IPR=l 0046 220 CALL SUBP (45) 0047 IF (IP .EQ. 5) GOTO 5 0048 CALL RSTR ('A201.GR"')

151

152

0049 0050 5 0051 7 0052

C C

0053 0054 0055 0056 0057 0058 0059 10 0060 0061 0062 0063 0064 0065 0066 0067 0068 12 0069 0070 0071 0072 0073 0074 14 0075 16 0076 0077 0078 0079

C 0080 0081 0082 0083 0084 0085 0086 0087 0088 0089 0090 0091 0092 0093 0094 20

C 0095

C 0096 0097 22

C 0098

GOTO 7 CALL RSTR ('A205 . GR') ILIM=TLIM CALL ESUB (45)

CALL SUBP (.46) ICOUNT=O DO 10 I=l,N Tl(I)=TH(I) Pl(I)=PH(I) T2(I)=Tl(I) P2(I)=Pl(I) M=B**2*30000.*3000 . Q=B**2*30000. *CD*l . 61E-19 DO 12 I=l ,N MLM(I)=O. ILM(I)=O. LL=NC(I) DO 12 J=l,LL MLM(I)=MLM(I)+M ILM(I)=ILM(I)+M*(XC(J,I)**2+YC(J,I)**2)+1. CALL SH2 (Tl,Pl,FlX,FlY,FlZ,MOl , FTl,WTl) DO 14 I=2,N A(I)=FTl(I)/MLM(I) F2X(I)=FlX(I) F2Y(I)=F1Y(I) F2Z(I)=FlZ(I) IF (ICOUNT .EQ. O) DT=l.OE-10 IF (ICOUNT .EQ. 1) DT=DELT DT=DT*IN START NEXT ITERATION ICOUNT=ICOUNT+l

WRITE (5,19) ICOUNT CALCULATES LATEST POSITIONS OF ALL CONTINENTS BUT FIRST ONE

DO 20 1=2,N SXl=F2X(I)/MLM(I)*DT*DT/2. F2X,F2Y,F2Z ARE THE X,Y,Z COMPONENTS SYl=F2Y(I)/MLM(I)*DT*DT/2. OF TOTAL SURFACE FORCE ACTING SZl=F2Z(I)/MLM(I) *DT*DT/2. ON I-TH CONT. PHD=Pl(I)*DRC Pl,Tl = CURRENT CO-ORDINATES OF I-TH CONT. THD=Tl(I)*DRC ! " RX=R*COS(PHD)*COS(THD) RX,RY,RZ = COMPONENTS OF CURRENT RY=R*COS(PHD)*SIN(THD) POSITIONS OF I-TH CONT. RZ=R*SIN(PHD) SXR=RX+SXl ! NEW X,Y,Z COMPONENTS OF I-TH CONT. SYR=RY+SYl SZR=RZ+SZl T2(I)=DATAN2 (SYR,SXR)/DRC POLAR COMPONENTS OF NEW POSITIONS SSR=SQRT(SXR**2+SYR**2) P2(I)=DATAN2(SZR,SSR)/DRC

EVALUATE NEW SURFACE FORCES CALL SH2 (T2,P2,F2X,F2Y,F2Z,M01,FT2,WT2)

CALCULATE NEW SURFACE ACCELERATION DO 22 I=2,N A(I)=FT2(I)/MLM(I)

REDEFINE Tl,Pl, AS P2,T2 DO 25 I=2,N

0099 0100 0101

25 Tl(I )=T2(1) Pl(I)=P 2(I ) WTl=WT2

C PLANES 0 102 IF (KF .EQ. O) GOTO 320 0103 301 WRITE (5,303) 0104 303 FORMAT( ' ENTER "3" FOR ROTATE '$) 0105 READ (5,204) IR 0106 IF (IR .NE. 3) STOP 0107 300 DO 310 I=l,N 0108 310 T2(I)=T2(1)+1.5 0109 ICN=ICN+l OllO WRITE (5,19) ICN 0111 19 FORMAT ('+',13,' ') 0112 320 CONTINUE 0113 DO 42 I=l,N 0114 IL=NC(I) 0115 CALL LA2 (P2,T2,I,l,XK,YK,ZK,l) 0116 XCG(I)=XK 0117 YCG(I)=YK 0118 ZCG(I)=ZK 0119 DO 42 II=l,IL 0120 CALL LA2 (P2,T2,I,II,XT,YT,ZT,0) 0121 X(II,I)=XT 0122 Y(II,I)=YT 0123 42 Z(II,I)=ZT

C THE PLANES 0124 DO 43 11=1,N 0125 IL=NC(II) 0126 DO 43 I= l ,IL 01 27 XP(I,II,IP)=R 0128 YP(I ,II ,IP)=R 0129 INS(I,II,I P)=8 0130 IF (IP .EQ. 5) GOTO 48 0131 44 IF(Y(I,II) . LE. O) INS(I,II,1)=4 0132 XP(I,II,l)=X(I,I I) 0133 YP(I,II,l)=Z(I,I I) 0134 GO TO 43 0135 48 IF(Z(I,11) .LE. O) INS(I,II,5)=4 0136 XP(I,II,5)= X(I,II) 0137 YP(I,II,5)=-Y(I, II) 0138 43 CONTINUE 0139 DO 45 I=l,N 0140 INSC(I,IP)=8 0141 XCP(I)=R 0142 YCP(I)=R 0143 IF (IP .EQ, 5) GOTO 46 0144 IF (YCG(I) .LE, 0) INSC(I,IP)=4 0145 XCP(I)=XCG(I) 0146 YCP(I)=ZCG(l) 0147 GOTO 45 0148 46 IF (ZCG(I) .LE. O) INSC(I,IP)=4 0149 XCP(I)= XCG(I) 0150 YCP(I)=-YCG(I) 0151 45 CONTINUE

C CONV TO RECTANGULAR COORD

153

154

0152 0153 0154 0155 0156 0157 0158 208 0159 0160 0161 0162 0163 0164 200 0165 0166 0167 205 0168 0169 0170 203 0171 0172 0173 0174 228 0175 0176 230 0177 232

C C

0178 202 0179 0180 451 0181 0182 0183 0184 0185 431 0186 0187 0188 0189 440 0190 0191 0192 438 0193 0194 0195 0196 0197 0198 0199 0200 0201 0202 432

C 0203 0204

DO 200 J=l,N IF ((ICOUNT-(ICOUNT/IPR)*IPR) .NE. 0) GOTO 208 JX(J)=XCP(J)*500./R+500. JY(J)=YCP(J)*500./R+500. IF (IR . EQ. 3) GOTO 208 CALL APNT (JX(J),JY(J),,INSC(J,IP)) DO 200 I=l,NC(J) IX(J)=XP(I,J,IP)*500./R+500. IY(J)=YP(I,J,IP)*SOO./R+SOO. IF (IR .EQ. 3) GOTO 200 IF ((ICOUNT-(ICOUNT/IPR)*IPR) .NE. 0) GOTO 200 CALL APNT (IX(J),IY(J),,INS(I,J,IP)) CONTINUE IF (ICOUNT .GE. ILIM) GOTO 205 GOTO 16 KF=l IF (IR .EQ. 3) GOTO 202 WRITE (5,203) FORMAT(/,' ENTER 1 FOR PRINTOUT OF POSITIONS: '$) READ (5