Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 nonlinear oscillations, Gordon and Breach, New York, 1961, p. 412 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 calculation connected with averaging in the theory of nonlinear vibrations, USSR Computational Mathematics and Mathematical Physics 3, 1-64 (1963), translation from Russian original, Zhurn. vychislit matem. i matem. fiz 3, 3-53 (1963) MR 0155050
  • [5] V. M. Volosov, Averaging in systems of ordinary differential equations, Russian Mathematical Surveys 17, No. 6, 1-126 (1962), translation from Russian original, Uspekhi Matematicheskikh Nauk 17, 6 (108), 3-126 (1962) MR 0146454

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 34.45

Retrieve articles in all journals with MSC: 34.45

Additional Information

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

American Mathematical Society