 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10522 |
| In Russian (ΟΜΜ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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| V.V. Kozlov, "Rational integrals of quasi-homogeneous dynamical systems," J. Appl. Math. Mech. 79 (3), 209-216 (2015) |
| Year |
2015 |
Volume |
79 |
Issue |
3 |
Pages |
209-216 |
| DOI |
10.1016/j.jappmathmech.2015.09.001 |
| Title |
Rational integrals of quasi-homogeneous dynamical systems |
| Author(s) |
V.V. Kozlov (Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia, vvkozlov@mi.ras.ru, kozlov@pran.ru) |
| Abstract |
Dynamical systems, described by quasi-homogeneous systems of differential equations with polynomial right-hand sides, are considered. The Euler-Poisson equations from solid-state dynamics, as well as the Euler-Poincaré equations in Lie algebras, which describe the dynamics of systems in Lie groups with a left-invariant kinetic energy, can be pointed out as examples. The conditions for the existence of rational first integrals of quasi-homogeneous systems are found. They include the conditions for the existence of invariant algebraic manifolds. Examples of systems with rational integrals which do not admit of first integrals that are polynomial with respect to the momenta are presented. Results of a general nature are also demonstrated in the example of a Hess-Appel'rot invariant manifold from the dynamics of an asymmetric heavy top. |
| Received |
27 December 2014 |
| Link to Fulltext |
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