VERY nice ppt

1. History 291 Fall 2002
History 291 Lecture 20
Pendulums and Falling Bodies:
Clocking Longitude

2. History 291 Fall 2002
Galileo
math’l mechanics weakly
connected to non-mechanistic
cosmology
Descartes
mechanistic cosmology weakly
connected to math’l mecanics
laws of accelerated motion
esp. v2 h
laws of impact: cons. motion
pendulum
non-tautochronism
(Mersenne et al.)
determination of [g]
as measured by
incorrect as tested by

3. History 291 Fall 2002
1-sec. pendulum

4. History 291 Fall 2002
h1
h2
h’1
h’2

5. History 291 Fall 2002
Christiaan Huygens
(1629-95)

6. History 291 Fall 2002

7. History 291 Fall 2002

8. History 291 Fall 2002

9. History 291 Fall 2002

10. History 291 Fall 2002
cycloid

11. History 291 Fall 2002

12. History 291 Fall 2002

13. 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

14. History 291 Fall 2002

15. History 291 Fall 2002
Huygens’ original sketch of his balance-spring regulator
20 January 1675

16. History 291 Fall 2002

17. History 291 Fall 2002

18. 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?

19. History 291 Fall 2002

20. 12/16/56
pendulum clock
1658
Horologium
1673
Horologium
oscillatorium
1657 first efforts at
using leaves to temper
swing of pendulum
12/1/1659 tautochronism of cycloid
12/20/1659 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. wedges
by 1664 complete theory of Cosc
& sliding weight
1673-74 relation of vibrating
string to cycloid
1675-76 spring as source of
incitation parfaite
2/1675 art. in Journal des Sçavans
on 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 of
period of conical pendulum
1671 triangular suspension
1675 anchor escapement
1663 Holmes to Lisbon
1664 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 cylindricum
trichordon - abandoned 1685
1685 application of triangular
suspension to spring-driven marine
clock
1-2/1693 balancier marin parfait
1694 studies on marine clock
6/1658 Pascal’s challenge problems
re: cycloid sent to H. via Boulliau
late 1659 challenge of priority by Italians
(Leopoldo de’ Medici)
Sea Trials

21. Laws of fall Vortex theory
cycloid
astronomy
Pendulum
clock
1657
Tautochrone
1659
Cycloidal
pendulum
1659
Center of
oscillation
1661-4
Marine clock
method of longitude
equation of time
1662
Spring
balance
1675
Tautochronic
oscillators
1683-93
Constrained
motion along
arbitrary curve
Isochrone,
brachistochrone
Newton
Bernoulli
Varignon
calculus of
variations
Harmonic oscillation
theory of springs
Bernoulli
Dynamics of rigid bodies
moment of inertia
“potential ascent. = actual descent”
Daniel Bernoulli (Hydrodynamica, 1738)
Theory of evolutes
higher differentials
Analytical dynamics
on variously described
orbits, e.g. polar coords.
Varignon, 1700ff.
Analytic kinematics
Centrifugal force
Conical pendulum
pendulum
Evolute of circle
Evolute of cycloid
impact
center of
percussion
Torricelli’s Principle
Evolute of parabola
Period of pendulum
Galileo Descartes
Huygens and the Pendulum Clock, 1657-93
msm 98

22. History 291 Fall 2002