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Rayleigh–Lorentz pendulum (or Lorentz pendulum) is a simple pendulum, but subjected to a slowly varying frequency due to an external action (frequency is varied by varying the pendulum length), named after Lord Rayleigh and Hendrik Lorentz. [1] This problem formed the basis for the concept of adiabatic invariants in mechanics. On account of ...
A pendulum is a body suspended from a fixed support such that it freely swings back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back towards the equilibrium position.
Johann Bernoulli solved the problem in a paper (Acta Eruditorum, 1697). Schematic of a cycloidal pendulum. The tautochrone problem was studied by Huygens more closely when it was realized that a pendulum, which follows a circular path, was not isochronous and thus his pendulum clock would keep different time depending on how far the pendulum ...
One pendulum moves the pen back and forth along one axis, and the other pendulum moves the drawing surface back and forth along a perpendicular axis. By varying the frequency and phase of the pendulums relative to one another, different patterns are created.
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 ...
A simple pendulum. As shown at right, a simple pendulum is a system composed of a weight and a string. The string is attached at the top end to a pivot and at the bottom end to a weight. Being inextensible, the string has a constant length.
The method removes secular terms—terms growing without bound—arising in the straightforward application of perturbation theory to weakly nonlinear problems with finite oscillatory solutions. [1] [2] The method is named after Henri Poincaré, [3] and Anders Lindstedt. [4]
A double pendulum consists of two pendulums attached end to end.. In physics and mathematics, in the area of dynamical systems, a double pendulum, also known as a chaotic pendulum, is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. [1]