Journal of Nonlinear Science

, Volume 15, Issue 2, pp 93-132

First online:

Regularization of the Amended Potential and the Bifurcation of Relative Equilibria

  • A. Hernández-GarduñoAffiliated withI.I.M.A.S., Universidad Nacional Autonoma de Mexico, Mexico D.F., C.P. 01000 Email author 
  • , J.E. MarsdenAffiliated withControl and Dynamical Systems, California Institute of Technology, Pasadena, CA 91125 Email author 

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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.