Invariant relations for nonautonomous systems of differential equations

TitleInvariant relations for nonautonomous systems of differential equations
Publication TypeJournal Article
Year of Publication2014
AuthorsKovalev, AM, Gorr, GV, Nespirnyy, VN
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2014.02.013
Issue2
SectionMathematics
Pagination13-19
Date Published2/2014
LanguageRussian
Abstract

The method of invariant relations developed by Poincaré, Levi-Civita, and Kharlamov is generalized for differential equations with right-hand sides depending on the time. As an example, the motion equations of a nonautonomous heavy gyrostat are considered, conditions for the existence of uniform rotational motions are obtained, and invariant manifolds are constructed.
Keywordsdifferential equations, nonautonomous systems
References: 

1. Puankare A. Selected works. Vol. 1. New methods of celestial mechanics. Moscow: Nauka, 1971 (in Russian).
2. Levi-Chivita T., Amaldi U. Course of Theoretical Mechanics. In 2 vols. Vol. 2, pt. 2. Moscow: Izd-vo inostr. lit., 1951 (in Russian).
3. Kharlamov P. V. Mekhanika tverdogo tela, 1974, Iss. 6: 15–24 (in Russian).
4. Gashenko I. N., Gorr G. V., Kovalev A. M. Classical problems of the dynamics of a rigid body. Kyiv: Nauk. dumka, 2012 (in Russian).
5. Gorr G. V., Kudryashova L. V., Stepanova L. A. Classical problems of the dynamics of a rigid body. Kyiv: Nauk. dumka, 1978 (in Russian).
6. Gorr G. V., Maznev A. V. Dynamics of a gyrostat having a fixed point. Donetsk: DonNU, 2010 (in Russian).
7. Kovalev A. M. Mekhanika tverdogo tela, 2002, Iss. 32: 16–31 (in Russian).
8. Kovalev A. M. Nonlinear control problems and observations in the theory of dynamical systems. Kyiv: Nauk. dumka, 1980 (in Russian).
9. Kovalev A. M. Prikl. matematika i mekhanika, 2008, 72, Iss. 2: 266–272 (in Russian).
10. Kovalev A. M., Suikov A. S. Dopov. Nac. akad. nauk Ukr., 2008, No. 12: 22–27 (in Russian).
11. Pontryagin L. S. Ordinary differential equations. Moscow: Nauka, 1970 (in Russian).