Variational integrators on manifolds for constrained mechanical systems

Variational integrators play a pivotal role in the simulation and control of constrained mechanical systems. Recognizing the need for a Lagrange-multiplier-free approach in such systems, this study introduces a novel method for constructing variational integrators on manifolds. Our approach unfolds in three key steps: (1) local parameterization of configuration space; (2) formulation of forced discrete Euler-Lagrange equations on manifolds; (3) derivation and implementation of highorder variational integrators. Numerical tests are conducted for both conservative and forced mechanical systems, demonstrating the excellent global energy behavior of the proposed variational integrators.