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Lyapunov families of periodic motions in a reversible system

✍ Scribed by V.N. Tkhai

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
751 KB
Volume
64
Category
Article
ISSN
0021-8928

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✦ Synopsis

The problem of the existence of local one-parameter families of periodic motions (Lyapunov families) adjoining the position of equilibrium of reversible systems is investigated. In the most general situation, an analogue of the 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-hoionomic constraint" is investigated. Periodic motions, close to permanent rotations about a vertical, for heavy homogeneous ellipsoid on an absolutely rough plane, are analysed in an appendix.

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