๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Invariant sets and symmetric periodic motions of reversible mechanical systems

โœ Scribed by V.N. Tkhai

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
700 KB
Volume
60
Category
Article
ISSN
0021-8928

No coin nor oath required. For personal study only.

โœฆ Synopsis

A method of constructing and classifying all symmetric periodic motions of a revers~le mechanical system is proposed. The principal solution of the above problem is given for the Hill problem, the restricted three-body problem (including the photogravitational problem), the problem of a heavy rigid body with a fixed point, and that of a heavy rigid body on a rough plane. In particular, problems requiring a systematic numerical study are thereby formulated.

๐Ÿ“œ SIMILAR VOLUMES

First integrals and families of symmetri
First integrals and families of symmetric periodic motions of a reversible mechanical system
โœ V.N. Tkhai ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 297 KB

A reversible mechanical system which allows of first integrals is studied. It is established that, for symmetric motions, the constants of the asymmetric integrals are equal to zero. The form of the integrals of a reversible linear periodic system corresponding to zero characteristic exponents and t

Periodic motions of a reversible second-
Periodic motions of a reversible second-order mechanical system: Application to the Sitnikov problem
โœ V.N. Tkhai ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 528 KB

A theory of the symmetric periodic motions (SPMs) of a reversible second-order system is presented which covers both oscillations and rotations. The structural stability property of the generating autonomous reversible system, which lies in the fact that the presence or absence of SPMs in a perturbe