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On geometric dynamics of rigid multi‐body systems
Author(s) -
Stramigioli Stefano,
Duindam Vincent
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700076
Subject(s) - gravitational singularity , ball (mathematics) , mechanical system , rigid body , extension (predicate logic) , configuration space , differential equation , mathematics , topology (electrical circuits) , class (philosophy) , computer science , mathematical analysis , classical mechanics , physics , quantum mechanics , combinatorics , artificial intelligence , programming language
Abstract Standard methods to model multibody systems are aimed at systems with configuration spaces isomorphic to ℝ n . This limitation leads to singularities and other artifacts in case the configuration space has a different topology, for example in the case of ball joints or a free‐floating mechanism. This paper discusses an extension of classical methods to allow for a very general class of joints, including all joints with a Lie group structure. The model equations are derived using the Boltzmann‐Hamel equations and have very similar structure and complexity as obtained using classical methods, but they do not suffer from singularities. Furthermore, the equations are explicit differential equations that can be directly implemented in simulation software. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)