Abstract
We develop the method of structural transformations of dynamical systems (proposed earlier by Koshlyakov) for systems containing nonconservative positional structures. The method under consideration is based on structural transformations that enable one to eliminate nonconservative positional terms from the original system without changing its stability properties.
Similar content being viewed by others
REFERENCES
D. R. Merkin, Gyroscopic Systems [in Russian], Nauka, Moscow (1974).
V. V. Strygin and V. A. Sobolev, Separation of Motions by the Method of Integral Manifolds [in Russian], Nauka, Moscow (1988).
N. G. Chetaev, Stability of Motion [in Russian], Gostekhizdat, Moscow (1955).
V. N. Koshlyakov, “On structural transformations of equations of perturbed motion for a certain class of dynamical systems,” Ukr. Mat. Zh., 49, No.4, 535–539 (1997).
V. N. Koshlyakov, “On structural transformations of dynamical systems with gyroscopic forces,” Prikl. Mat. Mekh., 61, Issue 5, 774–780 (1997).
F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1967).
R. Bellman, Introduction to Matrix Analysis, McGraw-Hill, New York (1960).
B. V. Bulgakov, Applied Theory of Gyroscopes [in Russian], Moscow University, Moscow (1976).
Ya. N. Roitenberg, Gyroscopes [in Russian], Nauka, Moscow (1975).
S. A. Agafonov, “On stability of nonconservative systems,” Vestn. Mosk. Univ., Ser. Mat. Mekh., No. 4, 87–90 (1972).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Koshlyakov, V.N., Makarov, V.L. Structural Analysis of One Class of Dynamical Systems. Ukrainian Mathematical Journal 52, 1247–1255 (2000). https://doi.org/10.1023/A:1010353004574
Issue Date:
DOI: https://doi.org/10.1023/A:1010353004574