A Hamiltonian Formulation on Manifolds for Dynamic Modeling of Constrained Mechanisms and EnergyPreserving Integration

Abstract

The dynamic modeling of multibody system is crucial in motion simulations, design, and control of mechanisms. This paper proposes a Hamiltonian formulation on manifolds for mechanism modeling which involves three key steps: (1) the local parameterization of regular configuration space; (2) the coordinate formulation of the Legendre transformation; and (3) the derivation of Hamiltonian equations. Geometric numerical integrators can be naturally deployed on the proposed formulation and achieve a longtime energypreserving integration. Based on parametric symplectic integrators and the chartsplicing technique, a novel energypreserving scheme is proposed. Simulations on two constrained mechanisms verify our claims.