Pseudo-Rigid Bodies: A Geometric Lagrangian Approach

The pseudo-rigid body model is viewed within the context of continuum mechanics and elasticity theory. A Lagrangian reduction, based on variational principles, is developed for both anisotropic and isotropic pseudo-rigid bodies. For isotropic Lagrangians, the reduced equations of motion for the pseu...

Full description

Saved in:
Bibliographic Details
Published in:Acta applicandae mathematicae 2002-01, Vol.70 (1-3), p.209
Main Author: Sousa Dias, M Esmeralda
Format: Article
Language:English
Subjects:
Decomposition
Geometry
Hypotheses
Lie groups
Mathematics
Mechanics
Ordinary differential equations
Principles
Studies
Theory
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The pseudo-rigid body model is viewed within the context of continuum mechanics and elasticity theory. A Lagrangian reduction, based on variational principles, is developed for both anisotropic and isotropic pseudo-rigid bodies. For isotropic Lagrangians, the reduced equations of motion for the pseudo-rigid body are a system of two (coupled) Lax equations on so(3)xso(3) and a second-order differential equation on the set of diagonal matrices with a positive determinant. Several examples of pseudo-rigid bodies such as stretching bodies, spinning gas cloud and Riemann ellipsoids are presented. [PUBLICATION ABSTRACT]
ISSN:0167-8019
1572-9036
DOI:10.1023/A:1013982416930