Double Pendulum Mechanics

Rigorous classical mechanics simulation of coupled dual pendulums governed by Euler-Lagrange equations. Features real-time chaotic trajectory ribbon tracing, total mechanical energy tracking, and a live Phase Space (θ₁, dθ₁/dt) orbit inset.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Mass Ratio (m₂/m₁) 1

Ratio of bob 2 mass to bob 1 mass

Mathematical Formulation

69 chars high

Analytical Equation

\mathcal{L} = T - V, \quad \frac{d}{dt}\left(\frac{\partial \mathcal{L}}{\partial \dot{\theta}_i}\right) - \frac{\partial \mathcal{L}}{\partial \theta_i} = 0

Compact Formula

alpha1 = num1(th1,th2,w1,w2)/den1; alpha2 = num2(th1,th2,w1,w2)/den2;

Renderer Logic

// Euler-Lagrange Double Pendulum
const alpha1 = num1 / den1;
const alpha2 = num2 / den2;
w1 += alpha1 * dt; w2 += alpha2 * dt;
th1 += w1 * dt; th2 += w2 * dt;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#classical-mechanics #lagrangian #double-pendulum #phase-space #physics-study #chaos

Author: Classical Mechanics Core Target: 60 FPS

Double Pendulum Mechanics

Live Parameters

Mathematical Formulation

Mathematical Tags

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