Acta Applicandae Mathematica

, Volume 70, Issue 1, pp 209–230

Pseudo-Rigid Bodies: A Geometric Lagrangian Approach

Authors

  • M. Esmeralda Sousa Dias
    • Dep. MatemáticaInstituto Superior Técnico
Article

DOI: 10.1023/A:1013982416930

Cite this article as:
Esmeralda Sousa Dias, M. Acta Applicandae Mathematicae (2002) 70: 209. doi:10.1023/A:1013982416930

Abstract

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)×so(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.

symmetry reductionpseudo-rigid bodiesEuler–Lagrange equationsisotropicanisotropic
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© Kluwer Academic Publishers 2002