Nonlinear Pendulum — Phase Portrait & Separatrix

Damping γ: 0.00 Speed: 3 Clear Trajectories Click phase space to place trajectory

The nonlinear pendulum θ̈ = −sin(θ) − γθ̇ reveals three regimes in phase space: libration (closed orbits around θ=0), rotation (orbits wrapping around indefinitely), and the separatrix (homoclinic orbit at energy E=2, threshold between regimes). Damping collapses all trajectories toward the stable equilibrium.