What is a double pendulum?

A double pendulum is a physical system consisting of one pendulum attached to the end of another. Unlike a simple pendulum, the double pendulum exhibits chaotic motion, making it one of the most famous demonstrations of chaos theory in physics.

Why is a double pendulum chaotic?

A double pendulum is chaotic because the motion of the second pendulum is coupled to the first, creating a nonlinear dynamical system. Even at large angles, the equations of motion become highly nonlinear, causing the system to exhibit extreme sensitivity to initial conditions.

What is sensitive dependence on initial conditions?

Sensitive dependence on initial conditions, often called the butterfly effect, means that tiny differences in the starting position or velocity of a system lead to vastly different outcomes over time. In a double pendulum, changing the initial angle by even a fraction of a degree produces completely different trajectories.

Can you predict double pendulum motion?

Long-term prediction of a double pendulum's motion is practically impossible due to its chaotic nature. While the equations of motion are deterministic, any small measurement uncertainty grows exponentially over time, making accurate long-term forecasting unfeasible even with powerful computers.

Home▸Chaos & Dynamics▸Double Pendulum Chaos Simulator - Butterfly Effect and Lagrangian Mechanics

🧪 Double Pendulum Chaos Simulator - Butterfly Effect and Lagrangian Mechanics

Simulate a double pendulum with adjustable mass and length ratios. Watch tiny differences in initial conditions produce wildly divergent trajectories - a vivid demonstration of chaos theory and sensitive dependence.

Chaos & Dynamics2DModerate60 FPS

⚙ Under the hood

This simulation showcases the chaotic behavior of a double pendulum system. It demonstrates the 'butterfly effect' – where small initial changes can lead to dramatically different outcomes – and introduces the concepts of Lagrangian mechanics.

Double PendulumChaosLagrangian

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install