Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems

Stability Transitions for Axisymmetric Relative Equilibria of Euclidean Symmetric Hamiltonian Systems

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 s...

Stability transitions for axisymmetric relative equilibria

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 s...

Relative equilibria and conserved quantities in symmetric Hamiltonian systems

Stability of Hamiltonian Relative Equilibria by Energy Methods

Relative equilibria in Hamiltonian systems: The dynamic interpretation of nonlinear stability on a reduced phase space

Stability of relative equilibria for Hamiltonian systems is generally equated with Liapunov stability of the corresponding fixed point of the flow on the reduced phase space. Under mild assumptions, a sharp interpretation of this stability is given in terms of concepts on the unreduced space. Suppose that (P, ω) is a symplectic manifold on which a Lie group G acts symplectically, and let H : P ...