Why is the double pendulum chaotic?

The coupling between the two pendulums creates nonlinear equations that amplify tiny differences exponentially over time. This is deterministic chaos — the equations are perfectly predictable step by step but long-term prediction is impossible because any measurement error grows exponentially.

Is energy conserved in a chaotic system?

Yes. Switch to the Energy tab — the green Total Energy line stays perfectly flat even during the wildest chaotic motion. Chaos means unpredictable trajectories not energy loss. The system obeys conservation laws exactly.

What are the equations of motion for a double pendulum?

The equations are derived from the Lagrangian and involve coupled nonlinear terms with sin and cos of angle differences. They have no closed-form solution and must be solved numerically. This simulator uses the 4th-order Runge-Kutta method for accurate integration.

Double Pendulum Simulator — Chaos Theory Visualization

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Double Pendulum — Chaos