Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Slightly damped librations


Author: J. A. Morrison
Journal: Quart. Appl. Math. 24 (1967), 365-370
MSC: Primary 34.45
DOI: https://doi.org/10.1090/qam/216111
MathSciNet review: 216111
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Abstract: The application of a generalized method of averaging to the problem of slightly damped librations in a perturbed one degree of freedom system is considered. The librations are those arising in the critical case in which the rate of change of the phase in the unperturbed system has a zero. The perturbed system is reduced to a form suitable for the application of the generalized method of averaging, and the first order averaged equation is derived for the slow rate of change of the amplitude of the librations, due to the damping.


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

  • [1] N. N. Bogoliubov and Y. A. Mitropolsky, Asymptotic methods in the theory of non-linear oscillations, Translated from the second revised Russian edition. International Monographs on Advanced Mathematics and Physics, Hindustan Publishing Corp., Delhi, Gordon and Breach Science Publishers, New York, 1961. MR 0141845
  • [2] J. M. Gormally, Solution methods in canonical perturbation theory, Lecture Notes for the Summer Institute in Dynamical Astronomy, Stanford University, 1965
  • [3] J. A. Morrison, A generalized method of averaging, with applications to slightly damped nonlinear oscillations, to appear in the Journal of Mathematical Analysis and Applications
  • [4] V. M. Volosov, Some types of calculations in the theory of non-linear vibrations, related to averaging, Ž. Vyčisl. Mat. i Mat. Fiz. 3 (1963), 3–53 (Russian). MR 0155050
  • [5] V. M. Volosov, Averaging in systems of ordinary differential equations, Uspehi Mat. Nauk 17 (1962), no. 6 (108), 3–126 (Russian). MR 0146454

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DOI: https://doi.org/10.1090/qam/216111
Article copyright: © Copyright 1967 American Mathematical Society


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