Absolutely New, Simple and Effective Theory of Movement Steadiness
International Journal of Theoretical and Applied Mathematics
Volume 4, Issue 4, August 2018, Pages: 35-39
Received: Dec. 3, 2018;
Accepted: Dec. 20, 2018;
Published: Jan. 14, 2019
Views 218 Downloads 46
Smol’yakov Eduard Rimovich, Department of Mathematics, Lomonosov Moscow State University, Moscow, Russia
Follow on us
The absolutely new, simple and effective theory is proposed which differs from the classical Liapunov's theory of the movement steadiness. This theory permits to simplify and to speed up the search for the stable movement many times. The classical theory is very complex for using in the engineer practice and one does not bring success in many cases. It was necessary to create a theory that would be devoid of all shortcomings of the classical theory. In this work, it is proposed exactly such theory. Instead of the very complex Liapunov’s function we propose to use the variations calculation. This gives the invaluable winner in the speed and simplicity while searching for the stable movement.
Dynamical Systems, Movement Steadiness, New Theory
To cite this article
Smol’yakov Eduard Rimovich,
Absolutely New, Simple and Effective Theory of Movement Steadiness, International Journal of Theoretical and Applied Mathematics.
Vol. 4, No. 4,
2018, pp. 35-39.
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Merkin D. A. Introduction into theory of movement stability. Moscow: Nauka, 1987.
Routh E. J. The advanced part of a treatise on the dynamics of a system of rigid bodies. London, 1884.
Ziegler H. Linear Elastic Stability. A. Critical Analysis of Methods // ZAMP. Basel – Zurich, IV, F – 2. 1953.
Hagedorn P. Uber die instabilitat konservativer systeme mit girosropischen Kraften // RationalMech and Anal. 1975, Bd. 58, № 1.
Herrman G. Stability of Equilibrium of Elastic Systems Subjested to Nonconservative Fordes // Applied Mechanics Reviews. 1967. V.20. № 2.
Karapetyan A. V. Stability of Stational movemnts. Moscow : URSS, 1998.
Chetaev N. G. Stability of movement. The works on the analytical mechanics. Moscow: RAN SSSR, 1962.
Krasovskii N. N. Some problems of the movement stability theory. Moscow: Fizmatgis, 1959.
Demidovich B. P. Lecture on mathematical theory of stability. Moscow.: MGU, 1998.
Bliss G. A. Lecture on the variational calculation.. Moscow.: IL, 1950.