Continuous flow · dim 4
Double pendulum
The simplest mechanical system that exhibits chaotic motion. Conservative (no friction) chaos for moderate-to-large initial energies.
Equations
Coupled Euler-Lagrange equations for two pendula joined end to end (4-D phase space: θ_1, θ_2, dθ_1/dt, dθ_2/dt).At a glance
| Parameters | m_1, m_2, l_1, l_2, g, initial conditions |
|---|---|
| Chaotic for | moderate-to-large initial angles |
| History | Studied since Daniel Bernoulli (1733); chaos understood in the 1960s-70s. |
Try it
Open the interactive playground at /tools/double-pendulum.