Symplectic Pendulum
phase portrait · Hamiltonian mechanics · area preservation
Length
1.0
Gravity
9.8
Damping
0.00
Driving F
0.00
Drive ω
0.67
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Phase Grid
Symplectic maps
preserve phase-space area (Liouville's theorem). The pendulum Hamiltonian is:
H = p²/2mL² − mgL cos θ
Conservative orbits are closed curves. Add damping to see spirals collapse; add forcing for chaos (Duffing).