Acta Applicandae Mathematica

, Volume 70, Issue 1–3, pp 209–230

Pseudo-Rigid Bodies: A Geometric Lagrangian Approach

  • M. Esmeralda Sousa Dias


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 reduction pseudo-rigid bodies Euler–Lagrange equations isotropic anisotropic 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • M. Esmeralda Sousa Dias
    • 1
  1. 1.Dep. MatemáticaInstituto Superior TécnicoLisboaPortugal

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