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Regularization of the Amended Potential and the Bifurcation of Relative Equilibria

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Abstract

In the context of simple mechanical systems with symmetry, we give a method based on blowing up the amended potential for obtaining symmetry-breaking branches of relative equilibria bifurcating from a given set of symmetric relative equilibria. The general method is illustrated with two concrete mechanical examples, the double spherical pendulum and the symmetric coupled rigid bodies.

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Authors and Affiliations

  1. I.I.M.A.S., Universidad Nacional Autonoma de Mexico, Mexico D.F., C.P. 01000, Mexico

    A. Hernández-Garduño

  2. Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125, USA

    J.E. Marsden

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  1. A. Hernández-Garduño
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  2. J.E. Marsden
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Correspondence to A. Hernández-Garduño or J.E. Marsden.

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Hernández-Garduño, A., Marsden, J. Regularization of the Amended Potential and the Bifurcation of Relative Equilibria. J Nonlinear Sci 15, 93–132 (2005). https://doi.org/10.1007/s00332-004-0544-x

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  • DOI: https://doi.org/10.1007/s00332-004-0544-x

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