Abstract
Questions of the stability of the equilibrium position for nonlinear oscillating systems relative to perturbations acting constantly on the system are considered. Theorems are proved governing the stability and instability conditions of the equilibrium point of a nonlinear system of general form. The stability is investigated by using Lyapunov function apparatus.
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N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Moscow (1963).
V. M. Volosov, “On averaging in an unbounded interval,” Dokl. Akad. Nauk SSSR,145, No. 5, 965–966 (1962).
A. M. Molchanov, “Stability in the case of neutrality of the linear approximation,” Dokl. Akad. Nauk SSSR,141, No. 1, 24–27 (1961).
V. I. Arnol'd, “Small denominators and problems of stability of motion in classical and celestial mechanics,” Usp. Matem. Nauk,18, No. 6, 91–191 (1963).
A. M. Lyapunov, General Problem of Stability of Motion [in Russian], Moscow (1950).
V. M. Volosov, “On the averaging method,” Dokl. Akad. Nauk SSSR,137, No. 1, 21–24 (1961).
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Translated from Matematicheskie Zametki, Vol. 3, No. 3, pp. 307–318, March, 1968.
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Khapaev, M.M. Investigation of stability in the theory of nonlinear oscillations. Mathematical Notes of the Academy of Sciences of the USSR 3, 194–200 (1968). https://doi.org/10.1007/BF01387334
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DOI: https://doi.org/10.1007/BF01387334