Feedback Integrators for Mechanical Systems with Holonomic Constraints

The feedback integrators method is improved, via the celebrated Dirac formula, to integrate the equations of motion for mechanical systems with holonomic constraints so as to produce numerical trajectories that remain in the constraint set and preserve the values of quantities, such as energy, that are theoretically known to be conserved. A feedback integrator is concretely implemented in conjunction with the first-order Euler scheme on the spherical pendulum system and its excellent performance is demonstrated in comparison with the RATTLE method, the Lie–Trotter splitting method, and the Strang splitting method.