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. The motion of a double pendulum is governed by a set of coupled ordinary differential equations and is chaotic.
Long exposure of double pendulum exhibiting chaotic motion (tracked with an LED)
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.
Image: Two Lorenz Orbits
Image: Lorenz Coordinates Small