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Closed-form solutions for the quadratic mixed-parity nonlinear oscillator

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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.

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Acknowledgements

This work was supported by the University of Alicante (Spain) under Project GITE-09006-UA.

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Authors and Affiliations

  1. Instituto Universitario de Física Aplicada a las Ciencias y las Tecnologías, Universidad de Alicante, Apartado 99, 03080, Alicante, Spain

    Augusto Beléndez, Antonio Hernández, Tarsicio Beléndez & Mariela L. Álvarez

  2. Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal, Universidad de Alicante, Apartado 99, 03080, Alicante, Spain

    Augusto Beléndez, Antonio Hernández, Tarsicio Beléndez & Mariela L. Álvarez

  3. Departamento de Física Aplicada, Universidad de Castilla-La Mancha, Avda. España s/n, 02071, Albacete, Spain

    Enrique Arribas

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  1. Augusto Beléndez
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  2. Antonio Hernández
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  3. Tarsicio Beléndez
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Correspondence to Augusto Beléndez.

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Beléndez, A., Hernández, A., Beléndez, T. et al. Closed-form solutions for the quadratic mixed-parity nonlinear oscillator. Indian J Phys 95, 1213–1224 (2021). https://doi.org/10.1007/s12648-020-01796-2

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  • DOI: https://doi.org/10.1007/s12648-020-01796-2

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