Closed-form solutions for the quadratic mixed-parity nonlinear oscillator
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Title: | Closed-form solutions for the quadratic mixed-parity nonlinear oscillator |
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Authors: | Beléndez, Augusto | Hernández Prados, Antonio | Beléndez, Tarsicio | Arribas Garde, Enrique | Alvarez, Mariela L. |
Research Group/s: | Holografía y Procesado Óptico |
Center, Department or Service: | Universidad de Alicante. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal | Universidad de Alicante. Instituto Universitario de Física Aplicada a las Ciencias y las Tecnologías | Universidad de Castilla-La Mancha. Departamento de Física Aplicada |
Keywords: | Dynamical systems | Nonlinear oscillators | Conservative systems | Elliptic integrals | Jacobian elliptic functions |
Knowledge Area: | Física Aplicada |
Date Created: | 18-May-2019 |
Issue Date: | Jun-2021 |
Publisher: | Springer Nature | Indian Association for the Cultivation of Science |
Citation: | Indian Journal of Physics. 2021, 95: 1213-1224. https://doi.org/10.1007/s12648-020-01796-2 |
Abstract: | Closed-form exact solutions for periodic motions of a nonlinear oscillator, which contains a quadratic mixed-parity restoring force, are derived analytically. This oscillator is characterised by two real parameters, which are the coefficients of the linear and the quadratic terms, and has single-well potential. All possible combinations of positive and negative values of these coefficients providing periodic motions are considered, and two families of exact solutions are obtained in terms of Jacobi elliptic functions. The periods are given in terms of the complete elliptic integral of the first kind, the behaviour of these periods as a function of the initial amplitude is analysed, and the exact solutions for certain values of these parameters are plotted. |
Sponsor: | This work was supported by the University of Alicante (Spain) under Project GITE-09006-UA. |
URI: | http://hdl.handle.net/10045/115267 |
ISSN: | 0973-1458 (Print) | 0974-9845 (Online) |
DOI: | 10.1007/s12648-020-01796-2 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © 2020 IACS |
Peer Review: | si |
Publisher version: | https://doi.org/10.1007/s12648-020-01796-2 |
Appears in Collections: | INV - GHPO - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
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Belendez_etal_2021_IndianJPhys_final.pdf | Versión final (acceso restringido) | 730,98 kB | Adobe PDF | Open Request a copy |
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