Mechanics
Double Pendulum: Deterministic Chaos
Two almost identical starts, completely different futures.
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Theory
A double pendulum obeys Newton’s laws exactly, yet its motion is chaotic: tiny differences in the initial conditions grow exponentially (sensitive dependence, measured by the Lyapunov exponent). Long-term prediction becomes impossible in practice.
What to observe
- Both pendulums start 1° apart and move together at first.
- After a few seconds their trails diverge completely.
Try this
- Reduce the initial angle: at small amplitudes the motion is regular again.
- Change the mass of one lower bob.
Also available in: Pêndulo duplo: caos determinístico (Português) · Péndulo doble: caos determinista (Español)
