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Zbl 1142.70003
Hanssmann, Heinz
A monkey saddle in rigid body dynamics. (English)
[A] Gaeta, Giuseppe (ed.) et al., Symmetry and perturbation theory. Proceedings of the 6th international conference, SPT 2007, Otranto, Italy, June 2--9, 2007. Hackensack, NJ: World Scientific. 92-99 (2008). ISBN 978-981-277-616-7/hbk

Summary: A rigid body with three equal moments of inertia moves in a nonlinear force field with potential $z^3$. Next to $S^1$-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 mass distribution. The continuous symmetries allow to reduce the original problem to a one-degree-of-freedom problem, which exhibits bifurcations related to the elliptic umbilic catastrophe. These bifurcations carry over from the integrable approximation of the original system and further to perturbations that break the $S^1$-symmetry of the potential.

MSC 2000:: *70E15 Motion of rigid bodies
70G65 Symmetries, Lie-group and Lie-algebra methods

Keywords: bifurcations; integrable approximation

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