The dynamics of Cosserat nets

Abstract

A formulation of the dynamics of a collection of connected simple 1-dimensional Cosserat continua and rigid bodies is presented in terms of sections of an $\text{SO}\left(3\right)$ fibration over a 1-dimensional net. A large class of junction conditions is considered in a unified framework. All the equations of motion and junction conditions are derived as extrema of a constrained variational principle on the net and are analysed perturbatively for structures with Kirchhoff constitutive properties. The whole discussion is based on the notion of a Cosserat net and its contractions obtained by taking certain limits that transform Cosserat elements to rigid structures. Generalisations are briefly discussed within this framework.