history 291 fall 2002 history 291lecture 20 pendulums and falling bodies: clocking longitude

History 291 Fall 2002

History 291 Lecture 20

Pendulums and Falling Bodies:

Clocking Longitude


Galileomath’l mechanics weakly

connected to non-mechanisticcosmology

Descartesmechanistic cosmology weaklyconnected to math’l mecanics

laws of accelerated motionesp. v2 h

laws of impact: cons. motion

pendulum

non-tautochronism(Mersenne et al.)

determination of [g] as measured by

incorrect as tested by


1-sec. pendulum


h1h2

h’1h’2


Christiaan Huygens(1629-95)


cycloid


Springs and Other Regulators

• Why the cycloid is tautochronic• Hooke’s law of springs• The spring-balance regulator• Other tautochronic mechanisms


Huygens’ original sketch of his balance-spring regulator20 January 1675


Pendulums, Gravity, and the Shape of the Earth

• The great voyage of 1687 - correcting for latitude

• Descartes’s vortices or Newton’s gravity?

12/16/56pendulum clock

1658Horologium

1673Horologium oscillatorium

1657 first efforts atusing leaves to temper

swing of pendulum

12/1/1659 tautochronism of cycloid12/20/1659 cycloidal leaves

1/13/1660 tested cycloidal clock against sun

1661 first efforts with sliding

weight to adjust Cosc 1661-65 Cosc, CG for various

solid, esp. wedgesby 1664 complete theory of Cosc

& sliding weight

1673-74 relation of vibratingstring to cycloid

1675-76 spring as source ofincitation parfaite

2/1675 art. in Journal des Sçavanson spring-balance watch

10/5/1659 sketch of conical pendulum clock

10/21/59 ms. on centrifugal force

1662-65 marine clocks

1667-68 calculation ofperiod of conical pendulum

1671 triangular suspension

1675 anchor escapement

1663 Holmes to Lisbon1664 Holmes to Guinea

1669 Duc de Beaufort, de la Voye

1672-3 Richer to Cayenne

1686-7 Helder and de Graaf

1690-2 de Graaf

1683-4 first sketch of balancier marin parfait

1683 pendulum cylindricumtrichordon - abandoned 1685

1685 application of triangularsuspension to spring-driven marine clock

1-2/1693 balancier marin parfait1694 studies on marine clock

6/1658 Pascal’s challenge problemsre: cycloid sent to H. via Boulliau

late 1659 challenge of priority by Italians(Leopoldo de’ Medici)

Sea Trials

Laws of fall Vortex theory cycloid

astronomy

Pendulumclock1657

Tautochrone1659

Cycloidalpendulum

1659

Center ofoscillation

1661-4

Marine clockmethod of longitude

equation of time1662

Springbalance

1675

Tautochronicoscillators1683-93

Constrainedmotion alongarbitrary curve

Isochrone,brachistochrone

NewtonBernoulliVarignon

calculus ofvariations

Harmonic oscillationtheory of springs

Bernoulli

Dynamics of rigid bodiesmoment of inertia

“potential ascent. = actual descent”Daniel Bernoulli (Hydrodynamica, 1738)

Theory of evoluteshigher differentials

Analytical dynamicson variously described

orbits, e.g. polar coords.Varignon, 1700ff.

Analytic kinematics

Centrifugal force

Conical pendulum

pendulum

Evolute of circle

Evolute of cycloid

impact

center ofpercussion

Torricelli’s Principle

Evolute of parabola

Period of pendulum

Galileo Descartes

Huygens and the Pendulum Clock, 1657-93

msm 98

history 291 fall 2002 history 291lecture 20 pendulums and falling bodies: clocking longitude

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