# Double Pendulum Creating Chaotic Motion

**In physics and mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, is a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions.[1] The motion of a double pendulum is governed by a set of coupled ordinary differential equations and is chaotic.**

The double pendulum undergoes chaotic motion, and shows a sensitive dependence on initial conditions. The image to the right shows the amount of elapsed time before the pendulum flips over, as a function of initial position when released at rest. Here, the initial value of *θ*_{1} ranges along the x-direction from −3.14 to 3.14. The initial value *θ*_{2} ranges along the y-direction, from −3.14 to 3.14.

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