One mode of motion for this system was approximated by Chirikov using the Melnikov-Arnoldintegral. T
One mode of motion for this system was approximated by Chirikov using the Melnikov-Arnoldintegral. The Gudermannian can be used to derive its motion near unstable equilibria. A completedescription of this system requires the use of Jacobi elliptic functions. In phase space, this system hasa separatrix at H equals g over l, within which it has closed cycles and outside of which it issinusoidal. These devices' amplitude is independent of their (*) period. The equation of motion for thissystem is often derived using the small-angle approximation, and shows that its period is proportional to thesquare root of the length of the string. For 10 points, name this simple system consisting of a weight on theend of a string.
One mode of motion for this system was approximated by Chirikov using the Melnikov-Arnoldintegral.
pendulum