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Dynamicswhat moves us

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General Dynamics

• Aristotle

• Newton

• Einstein

where

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Aristotle

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384-322 B.C.Everything that is in motion must be moved by something. For if it has not the source of its motion in itself it is evident that it is moved by something other than itself, for there must be something else that moves it. – Physica, Book VII, Part 1.

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Aristotelian Dynamics

In one dimension:We can make it look like a state equation by using the limit definition of the derivative:

The state equation is deterministic and reversible (but wrong). 4

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Aristotelian Dynamics (cont.)

Solution for , a constant:

Integrating over time gives

where is a constant determined by an initial condition on x(t).

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Aristotelian Dynamics (cont.)

implies

a constant, and as a consequence

Predicts:• No orbits.• No pendulums.

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Isaac Newton

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1642-1727

Philosophiæ Naturalis Principia Mathematica

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Newtonian Dynamics

•Deterministic• Reversible• Right

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Newton’s Laws

I. If , is constant.

II.

III. Every action, , has an equal and opposite reaction,

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Body in a Uniform Gravitational Field

The applied force is

and the initial conditions are

and

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Uniform Gravity (cont.)

From Newton (I) we see right away that

For we have

leading to

For position we find

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An Aside on Units

Fundamental units are

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Unit Measured in…

Length meters

Time seconds

Mass kilograms

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Units of Observed Quantities

Quantity Units Measured in…position metersvelocity meters/secondacceleration meters/second2

force kilogram-meters/second2

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