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A Kater's pendulum is a reversible free swinging pendulum invented by British physicist and army captain Henry Kater in 1817 (made public on 29 January 1818), [1] for use as a gravimeter instrument to measure the local acceleration of gravity.
His first major contribution to science was the comparison of the merits of the Cassegrainian and Gregorian telescopes; Kater determined the latter to be an inferior design. [ 1 ] His most substantial work was the invention of Kater's pendulum , enabling the strength of gravity to be determined, first at London [ 2 ] and subsequently at various ...
Action angles result from a type-2 canonical transformation where the generating function is Hamilton's characteristic function (not Hamilton's principal function ).Since the original Hamiltonian does not depend on time explicitly, the new Hamiltonian (,) is merely the old Hamiltonian (,) expressed in terms of the new canonical coordinates, which we denote as (the action angles, which are the ...
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Plot of the Jacobi hyperbola (x 2 + y 2 /b 2 = 1, b imaginary) and the twelve Jacobi Elliptic functions pq(u,m) for particular values of angle φ and parameter b. The solid curve is the hyperbola, with m = 1 − 1/b 2 and u = F(φ,m) where F(⋅,⋅) is the elliptic integral of the first kind. The dotted curve is the unit circle.
The seconds pendulum (also called the Royal pendulum), 0.994 m (39.1 in) long, in which each swing takes one second, became widely used in quality clocks. The long narrow clocks built around these pendulums, first made by William Clement around 1680, became known as grandfather clocks. The increased accuracy resulting from these developments ...
which differs by only 1% from the 2014 CODATA value of 6.67408 × 10 −11 m 3 kg −1 s −2. [25] Today, physicists often use units where the gravitational constant takes a different form. The Gaussian gravitational constant used in space dynamics is a defined constant and the Cavendish experiment can be considered as a measurement of this ...
In physics and mathematics, in the area of dynamical systems, an elastic pendulum [1] [2] (also called spring pendulum [3] [4] or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of both a simple pendulum and a one-dimensional spring-mass system. [2]