Lyapunov families of periodic motions in a reversible system

The problem of the existence of local one-parameter families of periodic mo tions (Lyapunov families) adjoining the position of equilibrium of reversib le systems is investigated. In the most general situation, an analogue of t he well-known Lyapunov theory is obtained. The bifurcation of the Lyapunov families when a pair of roots of the characteristic equation passes through zero is analysed. In particular, it is shown that, with this scenario, in the non-degenerate case the zero values of the roots are fatal for Lyapunov families. The effect of a "non-holonomic constraint" is investigated. Peri odic motions, close to permanent rotations about a vertical, for heavy homo geneous ellipsoid on an absolutely rough plane, are analysed in an appendix . (C) 2000 Elsevier Science Ltd. All rights reserved.