History 291 Fall 2002 History 291Lecture 20 Pendulums and Falling Bodies: Clocking Longitude.
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Transcript of 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
History 291 Fall 2002
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
History 291 Fall 2002
1-sec. pendulum
History 291 Fall 2002
h1h2
h’1h’2
History 291 Fall 2002
Christiaan Huygens(1629-95)
History 291 Fall 2002
History 291 Fall 2002
History 291 Fall 2002
History 291 Fall 2002
History 291 Fall 2002
cycloid
History 291 Fall 2002
History 291 Fall 2002
History 291 Fall 2002
Springs and Other Regulators
• Why the cycloid is tautochronic• Hooke’s law of springs• The spring-balance regulator• Other tautochronic mechanisms
History 291 Fall 2002
History 291 Fall 2002
Huygens’ original sketch of his balance-spring regulator20 January 1675
History 291 Fall 2002
History 291 Fall 2002
History 291 Fall 2002
Pendulums, Gravity, and the Shape of the Earth
• The great voyage of 1687 - correcting for latitude
• Descartes’s vortices or Newton’s gravity?
History 291 Fall 2002
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