Störmer-Verlet Integration Scheme for Multibody System Dynamics in Lie-Group Setting

Stormer-Verlet integration scheme has many attractive properties when dealing with ODE systems in linear spaces: it is explicit, 2nd order, linear/angular momentum preserving and it is symplectic for Hamiltonian systems. In this paper we investigate its application for numerical simulation of the multibody system dynamics (MBS) by formulating StormerVerlet algorithm for the constrained mechanical systems with the direct rotation group SO(3) upgrade in Lie-group setting. Starting from the investigations on the single rigid body rotational dynamics, the paper introduces modified RATTLE integration scheme with the SO(3) rotational upgrade that is designed via exponential map and utilization of the rotation group Lie-algebra so(3), which is determined from the canonical coordinate of Hamiltonian system during integration of the system dynamics. CONFIGURATION SPACE AND BASIC FORMULATION In the adopted approach, the configuration space of MBS comprising k bodies is modeled as a Lie-group