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A Geometrical Interpretation and Uniform Matrix Formulation of Multibody System Dynamics
Author(s) -
Blajer W.
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200104)81:4<247::aid-zamm247>3.0.co;2-d
Subject(s) - holonomic constraints , multibody system , tangent space , manifold (fluid mechanics) , mathematics , configuration space , equations of motion , tangent vector , constraint (computer aided design) , orthogonality , invariant manifold , nonholonomic system , holonomic , mathematical analysis , slow manifold , matrix (chemical analysis) , linear subspace , tangent , classical mechanics , geometry , computer science , physics , mechanical engineering , singular perturbation , materials science , quantum mechanics , robot , engineering , composite material , mobile robot , artificial intelligence
The purpose of this paper is to associate the multibody dynamics procedures with a geometrical picture involving the concepts of configuration manifolds, tangent vector spaces, and orthogonality of constraint reactions to the constraint surfaces. An unconstrained mechanical system is assigned a free configuration manifold and is treated as a generalized particle on the manifold. The system dynamics is then formulated in the local tangent space to the manifold at the system representation point. Imposed constraints on the system, the tangent space splits into the velocity restricted and velocity admissible subspaces, while the system configuration manifold confines to the holonomic constraint manifold. Based on these geometrical concepts, a uniform vector‐matrix formulation is developed. Both holonomic and nonholonomic systems are treated in a unified way, and the dynamic equations are expressible either in generalized velocities or in quasi‐velocities. Using a geometrically grounded projection method, compact schemes for obtaining different types of equations of motion and for determination of constraint reactions are provided. Some fresh contributions to the theory of constrained systems are reported. A relationship between the present formulation and the other classical methods of analytical dynamics is shown.