Heinz Hanßmann
A monkey saddle in rigid body dynamics
(1492K, PostScript)

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.