Exact and Approximate Values of the Period for a "Truly Nonlinear" Oscillator: $\ddot{x} + x + x^{1/3} = 0$
Year: 2009
Author: Ronald E. Mickens, Dorian Wilkerson
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 3 : pp. 383–390
Abstract
We investigate the mathematical properties of a "truly nonlinear" oscillator differential equation. In particular, using phase-space methods, it is shown that all solutions are periodic and the fixed-point is a nonlinear center. We calculate both exact and approximate analytical expressions for the period, where the exact solution is given in terms of elliptic functions and the method of harmonic balance is used to calculate the approximate formula.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-AAMM-8376
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 3 : pp. 383–390
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 8