An impetus-striction simulation of the dynamics of an elastica

摘要

This article concerns the three-dimensional, large deformation dynamics of an inextensible, unshearable rod. To enforce the conditions of inextensibility and unshearability, a technique we call the impetus-striction method is exploited to reformulate the constrained Lagrangian dynamics as an unconstrained Hamiltonian system in which the constraints appear as integrals of the evolution. We show here that this impetus-striction formulation naturally leads to a numerical scheme which respects the constraints and conservation laws of the continuous system. We present simulations of the dynamics of a rod that is fixed at one end and free at the other.