Projection Continuation for Minimal Coordinate Set Dynamics of Constrained Systems

Abstract

The formulation of constrained system dynamics using coordinate projection onto a subspace locally tangent to the constraint manifold is revisited using the QR factorization of the constraint Jacobian matrix to extract a suitable subspace, and integrating the evolution of the QR factorization along with that of the constraint Jacobian matrix, as the solution evolves. A true continuation algorithm is thus proposed for the subspace of independent coordinates, which does not visibly affect the quality of the solution, but avoids the artificial algorithmic discontinuities in the generalized velocities that would result from arbitrary reparameterization of the coordinate set. This property is exemplified by solving simple multi-degree-of-freedom problems with and without the proposed continuation.