Interactive Double Pendulum

A real-time physics simulation using Lagrangian mechanics

Controls

Mass 1: 1.00 kg

Mass 2: 1.00 kg

Length 1: 1.50 m

Length 2: 1.50 m

Gravity: 16.00 m/s²

Damping: 0.998

Show Energy Values

About the Lagrangian

The Lagrangian (L) is defined as the difference between kinetic energy (T) and potential energy (V):

L = T - V

This formulation, derived from the Principle of Least Action, elegantly describes the system's dynamics without needing to track individual forces.

Chaos & Sensitivity

The double pendulum is a classic example of chaotic motion. Even tiny changes in initial conditions lead to dramatically different trajectories, making long-term prediction impossible despite deterministic equations.