Symplectic vs Euler energy drift · Phase space area preservation
Integrator Settings
Energy Conservation
Verlet ΔE/E₀0
Euler ΔE/E₀—
Steps taken0
Orbit periods0
Physics
The Störmer–Verlet method: qn+1 = 2qn − qn−1 + Δt² a(qn).
It is symplectic: it exactly preserves the symplectic 2-form dq∧dp, so phase space volumes are conserved. For the Kepler problem this means long-term bounded energy error (oscillating, not drifting), unlike Euler which shows secular growth.
Purple = Verlet trajectory. Red = (forward) Euler for comparison. The energy chart shows the dramatic difference over many orbits.