Chains of rigid bodies and their numerical simulation by local frame methods

Abstract

We consider the dynamics and numerical simulation of systems of linked rigid bodies (chains). We describe the system using the moving frame method approach of [18]. In this framework, the dynamics of the $ j $th body is described in a frame relative to the $ (j-1) $th one. Starting from the Lagrangian formulation of the system on $ {{\rm{SO}}}(3)^{N} $, the final dynamic formulation is obtained by variational calculus on Lie groups. The obtained system is solved by using unit quaternions to represent rotations and numerical methods preserving quadratic integrals.