Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Motion in the neighborhood of a stationary point

Author: J. A. Morrison
Journal: Quart. Appl. Math. 26 (1968), 111-118
MSC: Primary 34.53
DOI: https://doi.org/10.1090/qam/232053
MathSciNet review: 232053
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Abstract: A perturbed system of differential equations is considered, wherein the zero order rate of change of one variable, which depends on the other, slowly changing, variables, vanishes at a particular point. A detailed analysis of the motions in certain close neighborhoods of the stationaiy point of the perturbed system is given, the method of averaging being applied, after some preliminary transformations have been made. It is found that the motions corresponding to the averaged equations are damped under the stability conditions given in [1] by Volosov and Morgunov, who considered a more general problem. However, our analysis reveals the nature of the motion in the neighborhood of the stationary point, and, moreover, our results are valid for a time interval of the order of the reciprocal of the perturbation parameter, rather than the reciprocal of just its square root.

References [Enhancements On Off] (What's this?)

  • [1] V. M. Volosov and B. I. Morgunov, Some stability conditions connected with resonance investigations, (in Russian), Dokl. Akad. NaukSSSR 170, 239-241 (1966). Soviet Math. Dokl. 7, 1159-1161 (1966) MR 0203186
  • [2] J. A. Morrison, Slightly damped librations, Quart. Appl. Math. 24, 365-370 (1967) MR 0216111
  • [3] N. N. Bogoliubov and Y. A. Mitropolsky, Asymptotic methods in the theory of nonlinear oscillations, Gordon and Breach, New York, 1961 MR 0141845

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DOI: https://doi.org/10.1090/qam/232053
Article copyright: © Copyright 1968 American Mathematical Society

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