Exact phase space with separatrix, libration, and rotation
Click canvas to add a trajectory at that (θ, ω) point
Parameters
Legend
━━ Separatrix (E=2)
━━ Libration (E<2)
━━ Rotation (E>2)
● Equilibria (stable/unstable)
Last Trajectory
Energy E:—
Type:—
Period (approx):—
About
Equation: θ'' + γθ' + (g/L)sin(θ) = 0. Energy E = ω²/2 − cos(θ). Separatrix at E=2 (g/L=1): the homoclinic orbit asymptotically approaches the unstable fixed point (θ=π). Below: pendulum oscillates (libration). Above: full rotations.