Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems

Details Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems

2007-05-10

arxiv.org/abs/0705.1552v2

Nonlinearity 21 325--352 2008

Physics

Mathematical Physics

Minor revisions. Typographical errors corrected

Scientific paper

10.1088/0951-7715/21/2/008

In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of Hamiltonian systems with Euclidean symmetry, we investigate different mechanisms of stability: stability by energy-momentum confinement, KAM, and Nekhoroshev stability, and we explain the transitions between these. We apply our results to the Kirchhoff model for the motion of an axisymmetric underwater vehicle, and we numerically study dissipation induced instability of KAM stable relative equilibria for this system.

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