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The Mathematical Analysis of Pendulum Motion


Dutch mathematician, astronomer, physicist and horologist Christiaan Huygens published Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstationes geometricae in Paris in 1673. Depite the reference to time-measurement in its title, this work is a general treatise on dynamics of bodies in motion, with an emphasis on the motion of the pendulum. It contains the first mathematical analysis of pendulum motion, including the formula for the relation between the period and the time of free fall from rest, the rule for deriving the center of oscillation for both simple and compound pendulums, and proof of the tautochronism of the cycloid (the arc traced by a point on a circle when the circle is rolled along a flat plane), which made possible Huygens's invention of the first reliable pendulum clock in 1656. Also included are Huygens's theories of the evolutes of curves, descriptions of his marine clocks and their trials, the first value for the force of gravity (which he derived using a simple pendulum), and the most important of his studies of centrifugal force; these last were used by Newton in his determination of universal gravitation.

Hook & Norman, The Haskell F. Norman Library of Science and Medicine (1991) no. 1137.

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