DOUBLE PENDULUM CHAOS DYNAMICS
Extreme sensitivity to initial conditions simulated via 4th-order Runge-Kutta numerical integration.
CHAOS PENDULUM HUD
60 FPS GRAVITY ACCELERATION 9.8 m/sΒ²
TRAIL PERSISTENCE LONG
[Drag second pendulum bob to perturb angle]
π
ACADEMIC & ALGORITHMIC REFERENCERESEARCH & LEARNING VAULT // Lagrangian Double Pendulum & Chaos Theory
Lagrange's equations of motion, Runge-Kutta 4th Order sub-stepping, and the butterfly effect.
// HISTORICAL ORIGINS
A quintessential model in nonlinear dynamics and deterministic chaos, demonstrating extreme sensitivity to initial conditions (Lyapunov exponent).
// GOVERNING EQUATIONS
\frac{d}{dt}\left(\frac{\partial L}{\partial \dot{\theta}_i}\right) - \frac{\partial L}{\partial \theta_i} = 0// BROWSER IMPLEMENTATION
Solves coupled nonlinear second-order differential equations via 4th-Order Runge-Kutta (RK4) integration with 10 sub-steps per frame.
// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOX
120-Swarm Butterfly Divergence
π― Action:Click 'Spawn 20-Divergence Swarm' and watch the tips.
β¨ Observe:Identical pendulums differing by only 0.0001 radians completely diverge into unpredictable orbits.