Article | The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007); 30-31 October; 2007; Göteborg (Särö) | Regularized; Stabilized; Variational Methods for Multibodies

Regularized; Stabilized; Variational Methods for Multibodies
Claude Lacoursière: HPC2N/Vrlab, Sweden \ Department of Computing Science, Umeå University, Sweden
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The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007); 30-31 October; 2007; Göteborg (Särö)
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Linköping University Electronic Press; Linköpings universitet

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.

The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007); 30-31 October; 2007; Göteborg (Särö)

Claude Lacoursière
Regularized; Stabilized; Variational Methods for Multibodies

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The 48th Scandinavian Conference on Simulation and Modeling (SIMS 2007); 30-31 October; 2007; Göteborg (Särö)

Claude Lacoursière
Regularized; Stabilized; Variational Methods for Multibodies
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