Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

An extension of the method of averaging


Author: P. R. Sethna
Journal: Quart. Appl. Math. 25 (1967), 205-211
MSC: Primary 34.45
DOI: https://doi.org/10.1090/qam/217384
MathSciNet review: 217384
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  • [1] N. M. Bogoliuboff and Yu. A. Mitropolsky, Asymptotic methods in the theory of nonlinear oscillations, Gordon and Breach, New York, 1962, Chaps. 5 and 6
  • [2] J. K. Hale, Oscillations in nonlinear systems, McGraw-Hill, New York, 1963 MR 0150402
  • [3] Yu. A. Mitropolsky, Problems of the asymptotic theory of nonstationary vibrations, Daniel Davey, New York, 1965
  • [4] V. M. Volosov, The method of averaging, Dokl. Acad. Nauk SSSR 137, 21-24 (1961) = Soviet Math. Dokl. 2, 221-224 MR 0118924
  • [5] N. M. Bogoliuboff and Yu. A. Mitropolsky, Asymptotic methods in the theory of nonlinear oscillations, Gordon and Breach, New York, 1962, p. 497
  • [6] N. M. Bogoliuboff and Yu. A. Mitropolsky, Asymptotic methods in the theory of nonlinear oscillations, Gordon and Breach, New York, 1962, p. 404
  • [7] J. K. Hale, Oscillations in nonlinear systems, McGraw-Hill, New York, 1963, p. 123 MR 0150402
  • [8] J. K. Hale, Oscillations in nonlinear systems, McGraw-Hill, New York, 1963, p. 116 MR 0150402
  • [9] L. D. Landau and E. M. Lifshitz, Mechanics, Pergamon Press, 1960, pp. 93-95 MR 0120782
  • [10] J. L. Bogdanoff, Influence on the behavior of a linear dynamical system of some imposed rapid motions of small amplitude, J. Acoust. Soc. Amer. 34, 1055-1062 (1962)
  • [11] E. R. Lowenstern, The stabilizing effect of imposed oscillations of high frequency on a dynamical system, Philos. Mag. 13, 458 (1932)
  • [12] P. R. Sethna and G. W. Hemp, Nonlinear oscillations of a gyroscopic pendulum with an oscillating point of suspension, Proc. Colloq. Internat. du Centre National de la Recherche Scientifique N- 148, Les vibrations forcées dans les systémes non-lineaires, 1964, pp. 375-392

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DOI: https://doi.org/10.1090/qam/217384
Article copyright: © Copyright 1967 American Mathematical Society

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