Moser-Veselov Integrators for a Geometrically Exact Rod Model

Geometric integrators transfer powerful unified geometric concepts of Hamiltonian continuum dynamics to computational continuum dynamics. In this talk, we apply the discrete Clebsch approach of Cotter and Holm (2006) to the convective representation of a geometrically exact rod to give momentum maps encoding discrete conservation laws. These conservation laws take the form of Moser-Veselov (MV) integration schemes which are solved through finding symmetric solutions to a corresponding matrix algebraic Ricatti equation. We apply Cardoso and Leite's (2001) necessary and sufficient condition for the existence of unique symmetric solutions to this algebraic equation to yield an upper bound on the time step. Using this time step, we present an adaptive Moser-Veselov algorithm which remains tractable and robust under large shear deformation of the rod. Numerical results demonstrate conservative properties of these integrators.