Gauss' least constraints principle and rigid body simulations

Abstract : Most of well-known approaches for rigid body simulations are formulated in the contact-space. Thanks to Gauss’ principle of least constraints, the frictionless dynamics problems are formulated in a motion-space. While the two formulations are mathematically equivalent, they are not computationally equivalent. The motion-space formulation is better conditionned, always sparse, needs less memory, and avoids some unnecessary computations. A preliminary experimental comparison suggests that an algorithm operating in the motionspace takes advantage of sparsity to perform increasingly better than a contact-space algorithm as the average number of contact points per object increases.
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Stéphane Redon, Abderrahmane Kheddar, Sabine Coquillart. Gauss' least constraints principle and rigid body simulations. Robotics and Automation, 2002. Proceedings. ICRA'02. IEEE International Conference on, 2002, Washington, DC, United States. pp.517--522, ⟨10.1109/ROBOT.2002.1013411⟩. ⟨hal-01147672⟩

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