 | | 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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| A.Yu. Aleksandrov and A.A. Kosov, "The stability and stabilization of non-linear, non-stationary mechanical systems," J. Appl. Math. Mech. 74 (5), 553-562 (2010) |
| Year |
2010 |
Volume |
74 |
Issue |
5 |
Pages |
553-562 |
| Title |
The stability and stabilization of non-linear, non-stationary mechanical systems |
| Author(s) |
A.Yu. Aleksandrov (St Petersburg, Russia, alex@vrm.apmath.spbu.ru)
A.A. Kosov (Irkutsk, Russia, idstu@icc.ru) |
| Abstract |
Mechanical systems acted upon by extremely non-linear positional forces are considered. The decomposition method is used to determine the sufficient conditions for asymptotic stability of an equilibrium. Problems of stabilizing the equilibrium of non-linear, non-stationary systems with specified potential forces by adding forces of different structure are studied. For systems with a non-stationary, homogeneous, positive-definite potential, the possibility of stabilization by linear dissipative forces, uncharacteristic of linear systems, is established. For systems with an even number of coordinates n≥4, in the presence of dissipative forces with complete dissipation, the possibility of vibrational stabilization by adding circular and gyroscopic forces with coefficients fluctuating about zero is demonstrated. |
| Received |
18 March 2009 |
| Link to Fulltext |
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