Journal of Applied Mathematics
Volume 2003 (2003), Issue 4, Pages 187-226
doi:10.1155/S1110757X03110224
The dynamics of Cosserat nets
Department of Physics, Lancaster University, Bailrigg, Lancaster LA 4YB, UK
Received 22 October 2001; Revised 10 July 2002
Copyright © 2003 J. Gratus and R. W. Tucker. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.