On the choice of configuration space for numerical Lie group integration of constrained rigid body systems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:262

Article; Proceedings Paper

Muller, A.¹  Terze, Z.² 

[1] Shanghai Jiao Tong Univ, Univ Michigan, Joint Inst, Shanghai 200030, Peoples R China

[2] Univ Zagreb, Fac Mech Engn & Naval Architecture, Zagreb 41000, Croatia

关键词: Lie group integration;    Rigid body dynamics;    Multibody systems;    Constraint satisfaction;    Screw systems;    Munthe-Kaas scheme;   

DOI  :  10.1016/j.cam.2013.10.039

来源: Elsevier

【 摘 要 】

Standard numerical integration schemes for multibody system (MBS) models in absolute coordinates neglect the coupling of linear and angular motions since finite positions and rotations are updated independently. As a consequence geometric constraints are violated, and the accuracy of the constraint satisfaction depends on the integrator step size. It is discussed in this paper that in certain cases perfect constraint satisfaction is possible when using an appropriate configuration space (without numerical constraint stabilization). Two formulations are considered, one where R-3 is used as rigid body configuration space and another one where rigid body motions are properly modeled by the semidirect product SE (3) = SO (3) x R-3. MBS motions evolve on a Lie group and their dynamics is naturally described by differential equations on that Lie group. In this paper the implications of using the two representations on the constraint satisfaction within Munthe-Kaas integration schemes are investigated. It is concluded that the SE (3) update yields perfect constraint satisfaction for bodies constrained to a motion subgroup of SE (3), and in the general case both formulations lead to equivalent constraint satisfaction. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free