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About a class of nonlinear oscillators with amplitude-independent frequency

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Abstract

This work is concerned with nonlinear oscillators that have a fixed, amplitude-independent frequency. This characteristic, known as isochronicity/isochrony, is achieved by establishing the equivalence between the Lagrangian of the simple harmonic oscillator and the Lagrangian of conservative oscillators with a position-dependent coefficient of the kinetic energy, which can stem from their mass that changes with the displacement or the geometry of motion. Conditions under which such systems have an isochronous center in the origin are discussed. General expressions for the potential energy, equation of motion as well as solutions for a phase trajectory and time response are provided. A few illustrative examples accompanied with numerical verifications are also presented.

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Acknowledgements

Ivana Kovacic acknowledges support received from the Provincial Secretariat for Science and Technological Development, Autonomous Province of Vojvodina (Project No. 114-451-2094).

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Authors and Affiliations

  1. Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, 21125, Novi Sad, Serbia

    Ivana Kovacic

  2. Department of Mathematics and Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, 14853, USA

    Richard Rand

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  1. Ivana Kovacic
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  2. Richard Rand
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Correspondence to Ivana Kovacic.

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Kovacic, I., Rand, R. About a class of nonlinear oscillators with amplitude-independent frequency. Nonlinear Dyn 74, 455–465 (2013). https://doi.org/10.1007/s11071-013-0982-9

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  • DOI: https://doi.org/10.1007/s11071-013-0982-9

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