Volume 1, Issue 3
Exact and Approximate Values of the Period for a "Truly Nonlinear" Oscillator: $\ddot{x} + x + x^{1/3} = 0$

Ronald E. Mickens & Dorian Wilkerson

Adv. Appl. Math. Mech., 1 (2009), pp. 383-390.

Published online: 2009-01

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  • 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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@Article{AAMM-1-383, author = {}, title = {Exact and Approximate Values of the Period for a "Truly Nonlinear" Oscillator: $\ddot{x} + x + x^{1/3} = 0$}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {3}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/8376.html} }
TY - JOUR T1 - Exact and Approximate Values of the Period for a "Truly Nonlinear" Oscillator: $\ddot{x} + x + x^{1/3} = 0$ JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 383 EP - 390 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aamm/8376.html KW - AB -

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.

Ronald E. Mickens & Dorian Wilkerson. (1970). Exact and Approximate Values of the Period for a "Truly Nonlinear" Oscillator: $\ddot{x} + x + x^{1/3} = 0$. Advances in Applied Mathematics and Mechanics. 1 (3). 383-390. doi:
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