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Pseudo-Rigid Bodies: A Geometric Lagrangian Approach

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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.

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  1. Dep. Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049–001, Lisboa, Portugal

    M. Esmeralda Sousa Dias

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  1. M. Esmeralda Sousa Dias
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Esmeralda Sousa Dias, M. Pseudo-Rigid Bodies: A Geometric Lagrangian Approach. Acta Applicandae Mathematicae 70, 209–230 (2002). https://doi.org/10.1023/A:1013982416930

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