Double pendulum

Pendulum with another pendulum attached to its end 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 complex physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. The motion of a double pendulum is governed by a pair of coupled ordinary differential equations and is chaotic. Analysis and interpretation Several variants of the double pendulum may be considered; the two limbs may be of equal or unequal lengths and masses, they may be simple pendulums or compound pendulums (also called complex pendulums) and the motion may be in three dimensions or restricted to one vertical plane. In the following analysis, the limbs are taken to be identical compound pendulums of length ℓ and mass m, and the motion is restricted to two dimensions. Double compound pendulum Motion of the double compound pendulum (from numerical integration of the equations of motion) In a compound pendulum, the mass is distributed along its length. If the double pendulum mass