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Parallel Algorithm for Modeling Multi-Rigid Body System Dynamics With Nonholonomic Constraints

[+] Author Affiliations
Rudranarayan Mukherjee

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA

Pawel Malczyk

Warsaw University of Technology, Warsaw, Poland

Paper No. DETC2013-13305, pp. V07AT10A038; 9 pages
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7A: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5596-6
  • Copyright © 2013 by ASME


This paper presents a new algorithm for serial or parallel implementation of computer simulations of the dynamics of multi-rigid body systems subject to nonholonomic and holonomic constraints. The algorithm presents an elegant approach for eliminating the nonholonomic constraints explicitly from the equations of motion and implicitly expressing them in terms of nonlinear coupling in the operational inertias of the bodies subject to these constraints. The resulting equations are in the same form as those of a body subject to kinematic joint constraints. This enables the nonholohomic constraints to be seamlessly treated in either a (i) recursive or (ii) hierarchic assembly-disassembly process for solving the equations of motion of generalized multi-rigid body systems in serial or parallel implementations. The algorithm is non-iterative and although the nonholonomic constraints are imposed at the acceleration level, constraint satisfaction is excellent as demonstrated by the numerical test case implemented to verify the algorithm. The paper presents procedures for handling both cases where the nonholonomic constraints are imposed between terminal bodies of a system and the environment as well as when the constraints are imposed between bodies in the interior of the system topology. The algorithm uses a mixed set of coordinates and is built on the central idea of eliminating either constraint loads or relative accelerations from the equations of motion by projecting the equations of motion into the motion subspaces or their orthogonal complements.

Copyright © 2013 by ASME



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