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Regularized, Stabilized, Variational Methods for Multibodies
Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N). Umeå University, Faculty of Science and Technology, Department of Computing Science. (UMIT)
2007 (English)In: The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007) / [ed] Peter Bunus, Dag Fritzson and Claus Führer, Linköping: Linköping University Electronic Press, 2007, 40-48 p.Conference paper (Refereed)
Abstract [en]

A time-discrete formulation of the variational principle of mechanics is used to construct a novel first order, fixed time step integration method for multibody systems subject to mixed constraints. The new stepper, coined Spook, includes physics motivated constraint regularization and stabilization terms. The stepper is proved to be stable for the case of linear constraints, for non-zero regularization and stabilization parameters. For fixed stabilization value, the regularization can be made arbitrarily small, corresponding to arbitrarily stiff penalty forces. The “relaxed” constraint formulation permits a separation of time scales so that stiff forces are treated as relaxed constraints. Constraint stabilization makes the stiff forces modeled this way strictly dissipative, and thus, the stepper essentially filters out the high oscillations, but is rigorously symplectic for the rest of the motion. Spook solves a single linear system per time step and is insensitive to constraint degeneracies for non-zero regularization. In addition, it keeps the constraint violations within bounds of O(h2), where h is the time step. Because it is derived from the discrete variational principle, the stepping scheme globally preserves the symmetries of the physical system. The combination of these features make Spook a very good choice for interactive simulations. Numerical experiments on simple multibody systems are presented to demonstrate the performance and stability properties.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2007. 40-48 p.
, Linköping Electronic Conference Proceedings, ISSN 1650-3686 (print), 1650-3740 (online) ; 27
Keyword [en]
multibody dynamics, real-time simulation, variational methods, regularization methods, numerical integration, differential algebraic equations
National Category
Computational Mathematics Applied Mechanics
Research subject
Computing Science; Numerical Analysis
URN: urn:nbn:se:umu:diva-53907OAI: diva2:514201
The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007), 30-31 October, 2007, Göteborg (Särö)
Available from: 2012-04-10 Created: 2012-04-05 Last updated: 2012-04-10Bibliographically approved

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Lacoursière, Claude
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