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M.A. Novikov, "Methods for Obtaining Sufficient Conditions for the Stability of Autonomous Conservative Systems," Mech. Solids. 51 (6), 643-653 (2016)
Year 2016 Volume 51 Number 6 Pages 643-653
DOI 10.3103/S0025654416060030
Title Methods for Obtaining Sufficient Conditions for the Stability of Autonomous Conservative Systems
Author(s) M.A. Novikov (Matrosov Institute for System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, ul. Lermontova 134, Irkutsk, 664033 Russia, nma@icc.ru)
Abstract A computational method for obtaining sufficient conditions for the stability of the stationary solution of autonomous conservative systems is proposed in the paper. This method is adapted to linear autonomous gyroscopic systems with three degrees of freedom. It is based on the positive definiteness of a parametric quadratic form composed of the gyroscopic force matrices and the potential function. The control parameters for the stability of the zero solution of the gyroscopic system are the entries of the gyroscopic force matrix. The algorithm of the computational method includes estimating one gyroscopic force parameter in the equation constructed from a necessary stability condition.

A special example is used to demonstrate the application of this algorithm. Comparison is performed with some well-known methods for obtaining sufficient conditions on the basis of an incomplete set of first integrals of motion. It is shown that the positive definiteness of the modified potential energy may result in stable as well as unstable motions.
Keywords autonomous conservative system, characteristic equation, stability of motion, positive (or negative) definite quadratic form, gyroscopic system
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Received 16 April 2014
Link to Fulltext http://link.springer.com/article/10.3103/S0025654416060030
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