Nonlinear Pendulum

Full ODE θ̈ = −(g/L)sin(θ) — period diverges to infinity at separatrix

θ = 0.000 rad | ω = 0.000 rad/s | Period: 2.000π s | Energy: 0.000

angle θ₀: 1.00 rad damping: length L: 1.0m

speed:

The nonlinear pendulum ODE θ̈ = −(g/L)sin θ has no closed-form period except via elliptic integrals: T = 4√(L/g) K(sin(θ₀/2)), where K is the complete elliptic integral of the first kind. Near θ₀ = π, the separatrix is reached and the period diverges to infinity.