Symplectic Integrator

System: Nonlinear pendulum Kepler orbit Double pendulum (single arm) Hénon-Heiles Method: Störmer-Verlet (symplectic) Forward Euler (non-symplectic) RK4 (non-symplectic) Step size h: 0.05 Energy: — E drift: — Trail length: 300 Reset Show all 3 methods

Symplectic integrators (Verlet, leapfrog) preserve the symplectic form dq∧dp exactly. Energy oscillates but doesn't drift. Euler/RK4 can spiral outward (energy gain) or collapse (energy loss).