🌀 Double Pendulum Chaos

Simulate non-linear Hamiltonian chaos via Lagrangian mechanics solved with 4th-Order Runge-Kutta (RK4). Track sensitive dependence on initial conditions (Butterfly Effect) with an overlaid $0.001$ rad perturbation twin.

Angle 1 ($\theta_1$) Degrees

Angle 2 ($\theta_2$) Degrees

Mass Ratio ($m_2 / m_1$)

Gravity ($g$) m/s²

■ Main System | ■ +0.001 rad Twin (Butterfly Divergence)

Twin Divergence ($\Delta \theta$)

0.001 rad

Exponential divergence

Total Energy ($E = T + V$)

-12.4 J

Hamiltonian conserved

Angular Velocity 1 ($\dot{\theta}_1$)

0.0 rad/s

Upper arm momentum

Angular Velocity 2 ($\dot{\theta}_2$)

0.0 rad/s

Lower tip momentum