Physics Simulation

Double Pendulum

Interactive chaos simulation using Lagrangian mechanics and RK4 integration. Visualize how small differences in initial conditions lead to dramatically different trajectories.

Status Running ●

Time (s) 0.00

θ₁ (°) 0.00

θ₂ (°) 0.00

Energy (J) 0.00

Pendulum Params

L₁ (length) 120px

L₂ (length) 120px

m₁ (mass) 1.0

m₂ (mass) 1.0

g (gravity) 9.81

Initial Angles

θ₁ (°) 120°

θ₂ (°) 150°

Trail Settings

Trail length 600

Pendulums 3

Multiple pendulums show chaos—identical except for tiny initial angle differences.

Simulation

Equations of Motion

θ₁'' = [-g(2m₁+m₂)sin(θ₁) - m₂g·sin(θ₁-2θ₂) - 2sin(θ₁-θ₂)m₂(θ₂'²L₂+θ₁'²L₁cos(θ₁-θ₂))] / [L₁(2m₁+m₂-m₂cos(2θ₁-2θ₂))]

θ₂'' = [2sin(θ₁-θ₂)(θ₁'²L₁(m₁+m₂)+g(m₁+m₂)cos(θ₁)+θ₂'²L₂m₂cos(θ₁-θ₂))] / [L₂(2m₁+m₂-m₂cos(2θ₁-2θ₂))]

Integrated using RK4 (4th-order Runge-Kutta) with dt=0.02. Trails cycle through a rainbow gradient showing temporal evolution.