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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.
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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 ...
Symmetry breaking in pitchfork bifurcation as the parameter ε is varied. ε = 0 is the case of symmetric pitchfork bifurcation.. In a dynamical system such as ¨ + (;) + =, which is structurally stable when , if a bifurcation diagram is plotted, treating as the bifurcation parameter, but for different values of , the case = is the symmetric pitchfork bifurcation.
For a simple pendulum, this definition yields a formula for the moment of inertia I in terms of the mass m of the pendulum and its distance r from the pivot point as, =. Thus, the moment of inertia of the pendulum depends on both the mass m of a body and its geometry, or shape, as defined by the distance r to the axis of rotation.
These curves correspond to the pendulum swinging periodically from side to side. If < then the curve is open, and this corresponds to the pendulum forever swinging through complete circles. In this system the separatrix is the curve that corresponds to =. It separates — hence the name — the phase space into two distinct areas, each with a ...
For a free, rigid beam, an impulse is applied at right angle at a point of impact, defined as a distance from the center of mass (CM). The force results in the change in velocity of the CM, i.e. d v c m {\displaystyle dv_{cm}} :