Symplectic integrators for index one constraints
For researchers in geometric numerical integration and control theory, this provides a practical symplectic integration scheme for constrained Hamiltonian systems, though the extension from unconstrained to index one constraints is incremental.
This paper demonstrates that symplectic Runge-Kutta methods effectively integrate Hamiltonian systems with index one constraints, which arise in sub-Riemannian geometry and control theory. The methods preserve symplecticity and handle constraints without numerical drift.
We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity constraints nondegenerate in the velocities, such as those arising in sub-Riemannian geometry and control theory.