Simulation of the regular orbit RSA5 with Δt = 1 until t = 100,000. The left panel shows part of the particle trajectory. The right panel shows the evolution of the relative error in the conserved quantities for the RK4 (red line), IMR (blue line), Hamiltonian (green line), and modified Hamiltonian (magenta line) integrators. Both Hamiltonian schemes preserve the energy to machine precision at all times. The original Hamiltonian scheme also conserves momentum to machine precision, with the other three integrators showing worse accuracy (similar, among them).