07-173 Heinz Hanßmann

A monkey saddle in rigid body dynamics (1492K, PostScript) Jul 5, 07

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Abstract. A rigid body with three equal moments of inertia is moving in a nonlinear force field with potential z^3. Next to the S^1-symmetry about the vertical axis and a further S^1-symmetry introduced by normalization, there is a discrete symmetry due to a special choice of the mass distribution. The continuous symmetries allow to reduce to a one-degree-of-freedom problem, which exhibits bifurcations related to the elliptic umbilic catastrophe. This bifurcation carries over from the integrable approximation to the original system and further to perturbations that break the S^1-symmetry of the potential.

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