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Energy consistent time integration of planar multibody systems
Author(s) -
Uhlar Stefan,
Betsch Peter
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610040
Subject(s) - multibody system , planar , generalized coordinates , equations of motion , coordinate system , rigid body , matrix (chemical analysis) , algebraic number , mathematics , computer science , control theory (sociology) , mathematical analysis , classical mechanics , physics , geometry , computer graphics (images) , materials science , control (management) , artificial intelligence , composite material
The planar motion of rigid bodies and multibody systems can be easily described by coordinates belonging to a linear vector space. This is due to the fact that in the planar case finite rotations commute. Accordingly, using this type of generalized coordinates can be considered as canonical description of planar multibody systems. However, the extension to the three‐dimensional case is not straightforward. In contrast to that, employing the elements of the direction cosine matrix as redundant coordinates makes possible a straightforward treatment of both planar and three‐dimensional multibody systems. This alternative approach leads in general to differential‐algebraic equations (DAEs) governing the dynamics of rigid body systems. The main purpose of the present paper is to present a comparison of the two alternative descriptions. In both cases energy‐consistent time integration schemes are applied. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)