Description
Interactive double-pendulum simulation that allows users to explore the system's chaotic behavior by adjusting the angle, length, angular velocity, and mass of each arm.
Physical model
The system is modeled using Lagrangian mechanics, resulting in two coupled, nonlinear, second-order differential equations for the angles θ₁ and θ₂. The simulation integrates these equations numerically using the fourth-order Runge–Kutta method (RK4).
For small amplitudes, the motion is approximately periodic, but for most initial conditions the double pendulum exhibits deterministic chaos: trajectories that start from nearly identical initial conditions diverge exponentially over time. It is one of the clearest educational examples of a nonlinear dynamical system that is sensitive to initial conditions and is widely used to teach classical mechanics and chaotic systems.
Developers
Marco P. M. de Souza
References
S. Thornton, J. Marion, Classical Dynamics of Particles and Systems (Cengage Learning, 2011).