Nonlinear stability of singular relative periodic orbits in Hamiltonian systems with symmetry
The authors generalize the sufficient condition for the stability of relative periodic orbits in symmetric Hamiltonian systems, presented in their previous work [\textit{J.-P. Ortega} and \textit{T. S. Ratiu}, A Dirichlet criterion for the stability of periodic and relatively periodic orbits in Hamiltonian systems, J. Geom. Phys. 32, 131-159 (1999; Zbl 0977.34051)] to the case where these orbits have a nontrivial symmetry. Moreover, a block diagonalization of the so-called stability form corresponding to the relative periodic orbit is described and the relations between the stability of the relative periodic orbit and the orbital stability of the associated singular reduced periodic orbit are clarified. The obtained results are illustrated by examples of spherical pendulum equations, Manev problem and the Lagrange top equations.
scientific article; zbMATH DE number 1396338
scientific article