Symplectic integrators for index one constraints

TL;DR

This paper demonstrates that symplectic Runge-Kutta methods are effective for numerically integrating Hamiltonian systems with index one constraints, relevant in areas like sub-Riemannian geometry and control theory.

Contribution

It establishes the effectiveness of symplectic Runge-Kutta methods for constrained Hamiltonian systems with index one constraints, expanding their applicability.

Findings

Symplectic Runge-Kutta methods preserve the structure of constrained Hamiltonian systems.

Effective for systems with position and velocity constraints in variational problems.

Applicable to sub-Riemannian geometry and control theory models.

Abstract

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.