CYCLOID

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History 291 Lecture 20Pendulums and Falling
BodiesClocking Longitude
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Galileo mathl mechanics weakly connected to
non-mechanistic cosmology
Descartes mechanistic cosmology weakly connected
to mathl mecanics
laws of accelerated motion esp. v2 h
laws of impact cons. motion
determination of g as measured by
incorrect as tested by
pendulum
non-tautochronism (Mersenne et al.)
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1-sec. pendulum
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Christiaan Huygens (1629-95)
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cycloid
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Springs and Other Regulators

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

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Huygens original sketch of his balance-spring
regulator 20 January 1675
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Pendulums, Gravity, and the Shape of the Earth

• The great voyage of 1687 - correcting for
  latitude
• Descartess vortices or Newtons gravity?

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12/16/56 pendulum clock
1657 first efforts at using leaves to
temper swing of pendulum
6/1658 Pascals challenge problems re cycloid
sent to H. via Boulliau
1658 Horologium
late 1659 challenge of priority by
Italians (Leopoldo de Medici)
12/1/1659 tautochronism of cycloid 12/20/1659
cycloidal leaves
10/5/1659 sketch of conical pendulum clock
1/13/1660 tested cycloidal clock against sun
10/21/59 ms. on centrifugal force
Sea Trials
1661 first efforts with sliding weight to adjust
Cosc
1662-65 marine clocks
1661-65 Cosc, CG for various solid, esp. wedges
1663 Holmes to Lisbon 1664 Holmes to Guinea
by 1664 complete theory of Cosc sliding weight
1667-68 calculation of period of conical pendulum
1673 Horologium oscillatorium
1669 Duc de Beaufort, de la Voye
1671 triangular suspension
1672-3 Richer to Cayenne
1673-74 relation of vibrating string to cycloid
1675 anchor escapement
2/1675 art. in Journal des Sçavans on
spring-balance watch
1675-76 spring as source of incitation parfaite
1683-4 first sketch of balancier marin parfait
1683 pendulum cylindricum trichordon - abandoned
1685
1686-7 Helder and de Graaf
1685 application of triangular suspension to
spring-driven marine clock
1690-2 de Graaf
1-2/1693 balancier marin parfait 1694 studies on
marine clock
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Huygens and the Pendulum Clock, 1657-93
Galileo
Descartes
astronomy
Torricellis Principle
cycloid
Laws of fall
Vortex theory
pendulum
Centrifugal force
impact
Evolute of circle
Conical pendulum
center of percussion
Evolute of parabola
Period of pendulum
Evolute of cycloid
Marine clock method of longitude equation of
time 1662
Spring balance 1675
Pendulum clock 1657
Cycloidal pendulum 1659
Center of oscillation 1661-4
Tautochronic oscillators 1683-93
Tautochrone 1659
Constrained motion along arbitrary curve
Theory of evolutes higher differentials
Harmonic oscillation theory of springs Bernoulli
Analytical dynamics on variously
described orbits, e.g. polar coords. Varignon,
1700ff.
Isochrone, brachistochrone
Newton Bernoulli Varignon
Dynamics of rigid bodies moment of
inertia potential ascent. actual
descent Daniel Bernoulli (Hydrodynamica, 1738)
calculus of variations
Analytic kinematics
msm 98
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