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

Zdravko Terze | Zendy; Andreas Mueller | Zendy; Dario Zlatar | Zendy

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

Author(s) -

Zdravko Terze,

Andreas Mueller,

Dario Zlatar

Publication year - 2013

Publication title -

fsb (university of zagreb)

Language(s) - English

Resource type - Conference proceedings

DOI - 10.1115/detc2013-12308

Subject(s) - verlet integration , lie group , group (periodic table) , rigid body , hamiltonian (control theory) , rotation around a fixed axis , ode , mathematics , scheme (mathematics) , computer science , classical mechanics , mathematical analysis , physics , geometry , mathematical optimization , molecular dynamics , quantum mechanics

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

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