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About this paper
A. Müller
This research systematically analyzes how the choice of configuration space impacts constraint preservation in numerical simulations of constrained rigid bodies. It demonstrates that modeling rigid body motion using the special Euclidean group (SE(3)) leads to machine-precision satisfaction of kinematic constraints for lower kinematic pairs, in contrast to the traditional direct product Lie group (SO(3) " R^3) which exhibits integration-scheme-dependent constraint violations.
Key insights
- Kinematic constraints are exactly preserved in numerical integration steps if they restrict the body's motion to a subgroup of the chosen configuration space Lie group.
- The Special Euclidean Group SE(3) naturally encompasses the kinematics of most lower kinematic pairs (e.g., spherical, revolute, prismatic joints) as its subgroups, ensuring geometric consistency.
- The traditional SO(3) ", R^3 formulation generally fails to represent the kinematics of common lower pairs as its subgroups, leading to inherent and accumulating constraint violations during numerical integration.
Summary by alphaXiv.
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