 | | 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.Yu. Ol'shanskii, "Partial linear integrals of the Poincaré-Zhukovskii equations (the general case)," J. Appl. Math. Mech. 81 (4), 270-285 (2017) |
| Year |
2017 |
Volume |
81 |
Issue |
4 |
Pages |
270-285 |
| DOI |
10.1016/j.jappmathmech.2017.12.004 |
| Title |
Partial linear integrals of the Poincaré-Zhukovskii equations (the general case) |
| Author(s) |
V.Yu. Ol'shanskii (Institute for Precision Mechanics and Control Problems, Russian Academy of Sciences, Saratov, Russia, olshanskiy_vlad@mail.ru) |
| Abstract |
The existence conditions for a linear invariant relation of the Poincaré-Zhukovskii equations in the general case when the matrix of the cross terms of the Hamiltonian can be asymmetric are obtained. A new scalar form of the equations is indicated, and they are reduced to the Riccati equation in the case of motion with a linear invariant relation. A particular solution of the Riccati equation, which defines a three-parameter family of periodic solutions of the Poincaré-Zhukovskii equations, is presented. A four-parameter family of solutions of the Poincaré-Zhukovskii equations, each of which exponentially rapidly approaches a corresponding periodic solution with time, is constructed. The conditions for precessional motion with a linear invariant relation are found. |
| Received |
24 August 2016 |
| Link to Fulltext |
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