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Van der Pol oscillator with time variable parameters

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Abstract

In this paper, the analytical solving procedure of the oscillator with slow time variable mass is developed. The solution is based on the Jacobi elliptic function whose properties: frequency, amplitude and modulus are obtained according to the requirements given for the amplitude of the displacement and the amplitude of the velocity of vibration and also period of vibration. The suggested procedure is applied for the solution of the time variable Van der Pol oscillator. The limit value of the initial mass of the oscillator is determined which separates the case when the limit cycle motion occurs, and the case when the amplitude of vibration tends to zero independently of the initial displacement. A numerical example is considered. The analytical solution is compared with the numerically obtained one and it is concluded that they are in good agreement.

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  1. Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, 21000, Novi Sad, Serbia

    L. Cveticanin

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  1. L. Cveticanin
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Correspondence to L. Cveticanin.

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Cveticanin, L. Van der Pol oscillator with time variable parameters. Acta Mech 224, 945–955 (2013). https://doi.org/10.1007/s00707-012-0785-y

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  • DOI: https://doi.org/10.1007/s00707-012-0785-y

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