|Title||Invariant relations for nonautonomous systems of differential equations|
|Publication Type||Journal Article|
|Year of Publication||2014|
|Authors||Kovalev, AM, Gorr, GV, Nespirnyy, VN|
|Abbreviated Key Title||Dopov. Nac. akad. nauk Ukr.|
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.
|Keywords||differential equations, nonautonomous systems|
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).