Premium
On the choice of coordinates for computational multibody dynamics
Author(s) -
Yang Yinping,
Betsch Peter
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110029
Subject(s) - generalized coordinates , direction cosine , euler angles , orthogonal coordinates , bipolar coordinates , log polar coordinates , multibody system , action angle coordinates , spherical coordinate system , orientation (vector space) , equations of motion , polar coordinate system , motion (physics) , local coordinates , euler's formula , dynamics (music) , mathematics , mathematical analysis , classical mechanics , geometry , physics , acoustics
The choice of coordinates for the description of multibody dynamics has a strong impact on the form of the equations of motion. In the talk two alternative formulations are compared: (i) joint coordinates along with Euler angles for the orientation of rigid bodies, and (ii) redundant coordinates where the orientation of rigid bodies is described in terms of direction cosines. In the case of multibody systems with tree structure the use of generalized coordinates yields equations of motion in the form of ordinary differential equations. In contrast to that, the choice of redundant coordinates yields differential‐algebraic equations. The two alternative formulations are compared and their influence on the numerical time integration is highlighted. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)