A projection continuation approach for minimal coordinate set constrained dynamics

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 to track the evolution of the subspace of independent coordinates. It does not visibly affect the quality of the solution but avoids the artificial algorithmic irregularities or discontinuities in the generalized velocities that could otherwise result from arbitrary reparameterizations of the coordinate set. The characteristics of the proposed subspace evolution approach are exemplified by solving simple single- and multi-degree-of-freedom problems.