Jp. Ortega et Ts. Ratiu, Non-linear stability of singular relative periodic orbits in Hamiltonian systems with symmetry, J GEOM PHYS, 32(2), 1999, pp. 160-188
We generalize the sufficient condition for the stability of relative period
ic orbits in symmetric Hamiltonian systems presented in [J. -P. Ortega, T.S
. Ratiu, J. Geom. Phys. 32 (1999) 131-159] to the case in which these orbit
s have non-trivial symmetry. We also describe a block diagonalization, simi
lar in philosophy to the one presented in [J. -P. Ortega, T.S. Ratiu, Nonli
nearity 12 (1999) 693-720] for relative equilibria, that facilitates the us
e of this result in particular examples and shows the relation between the
stability of the relative periodic orbit and the orbital stability of the a
ssociated singular reduced periodic orbit. (C) 1999 Elsevier Science B.V. A
ll rights reserved. Subj. Class.: Dynamical systems 1991 MSG: 34D35; 58F05.