Journal of Applied Mathematics
Volume 2003 (2003), Issue 4, Pages 187-226
doi:10.1155/S1110757X03110224
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 SO(3) 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.