Naslov
Two Variants of a Lie-group Integration Scheme for Dynamics Simulation of Constrained Multibody Systems

Autori
Mueller, Andreas ; Terze, Zdravko

Vrsta, podvrsta
Ostale vrste radova, rukopis

Godina
2016

Ključne riječi
Lie group integration ; constrained mechanical systems ; screw systems ; rigid body dynamics ; coordinate-free representation

Sažetak
The dynamics simulation of constrained multibody systems (MBS) using a Munthe-Kaas Lie group integration scheme is treated in this paper. The paper addresses two problems: 1) the choice of an appropriate configuration space, and 2) the incorporation of geometric constraints together with the reduction of numerical constraint violation within the Lie group integration scheme. A coordinate-free Lie group index 1 DAE formulation for constrained MBS is introduced. Two variants of this formulation are investigated where the configuration space of a rigid body is embedded either in the Lie group SE(3) of proper rigid body motions or in the direct product SO(3) X R^3. Each variant gives rise to a Lie group integration scheme. The consequences of using either variant are analyzed and discussed from a geometric point of view. It is concluded that the SE(3) formulation is best suited for capturing generic MBS motions. This is confirmed by the presented numerical examples. For constraint stabilization the known projection method is adapted to the Lie group setting. To this end local exponential coordinates are introduced on the configuration space.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Strojarstvo, Zrakoplovstvo, raketna i svemirska tehnika

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