Relative equilibria near stable and unstable Hamiltonian relative equilibria

The dynamics around stable and unstable Hamiltonian relative equilibria

For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.

Unstable manifolds of relative equilibria in Hamiltonian systems with dissipation∗

This paper studies the destabilizing effects of dissipation on families of relative equilibria in Hamiltonian systems which are non-extremal constraint critical points in the energy-Casimir or the energy-momentum methods. The dissipation is allowed to destroy the conservation law associated with the symmetry group or Casimirs, as long as the family of relative equilibria stays on an invariant m...

Existence of Relative Periodic Orbits near Relative Equilibria

We show existence of relative periodic orbits (a.k.a. relative nonlinear normal modes) near relative equilibria of a symmetric Hamiltonian system under an appropriate assumption on the Hessian of the Hamiltonian. This gives a relative version of the Moser-Weinstein theorem.

Relative equilibria and conserved quantities in symmetric Hamiltonian systems

Classifying Relative Equilibria

We announce several theorems which suggest a minimal classification of relative equilibria in the planar «-body problem. These theorems also answer several questions on the nature of degenerate relative equilibria classes which were asked recently by S. Smale [3]. A summary of previous results can be found in an earlier paper [1]. It is a pleasure to thank S. Smale for encouragement in this work.