𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The invariant manifolds of systems with first integrals

✍ Scribed by V.D. Irtegov; T.N. Titorenko

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
253 KB
Volume
73
Category
Article
ISSN
0021-8928

No coin nor oath required. For personal study only.

✦ Synopsis

Several additional possibilities of the Routh-Lyapunov method for isolating and analysing the stationarity sets of dynamical systems admitting of smooth first integrals are discussed. A procedure is proposed for isolating these sets together with the first integrals corresponding to the vector fields for these sets. This procedure is based on solving the stationarity equations of the family of first integrals of the problem in part of the variables and parameters occurring in this family. The effectiveness of this approach is demonstrated for two problems in the dynamics of a rigid body.

πŸ“œ SIMILAR VOLUMES

Reversible systems with first integrals
Reversible systems with first integrals
✍ Mikhail V. Matveyev πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 640 KB

A reversible system of ordinary differential equations (ODE) possessing some first integrals is considered. A simple description of the first integral space is given. It is shown that, under the auxiliary assumption that the integrals are symmetric (i.e., they do not change sign under the action of