Störmer-Verlet is symplectic: it exactly conserves a modified Hamiltonian near the true one,
so energy errors stay bounded forever. Euler is not symplectic — energy drifts monotonically,
eventually causing orbital collapse or escape. The Poincaré section (orbit traces) reveals the qualitative difference clearly.
Verlet: xn+1 = 2xn − xn-1 + h²∇V.