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

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

Published online: 2009-01

Cited by

Export citation
• 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.

• Keywords

• AMS Subject Headings

• BibTex
• RIS
• TXT
@Article{AAMM-1-383, author = {Ronald E. and Mickens and and 20593 and and Ronald E. Mickens and Dorian and Wilkerson and and 20594 and and Dorian Wilkerson}, 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: $\ddot{x} + x + x^{1/3} = 0$ AU - Mickens , Ronald E. AU - Wilkerson , Dorian 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:
Copy to clipboard
The citation has been copied to your clipboard