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ANALYSIS OF THE ACTION OF PERTURBATIONS OF LINEAR RESONANT SYSTEMS WITH TWO DEGREES OF FREEDOM

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Abstract—

A system with two degrees of freedom in the case of a double natural frequency is considered. The unperturbed system consists of two independent oscillators. The system coordinates describe an elliptical trajectory with four orbital elements. An analysis of the action of linear perturbations (forces) on the orbital elements is carried out. Perturbations are subdivided into six types of forces, and for each type of forces a system of differential equations for the orbital elements is obtained. For all six types of forces, a general solution of the system of differential equations in elementary functions is found.

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Funding

The present work was supported by the Ministry of Science and Higher Education within the framework of the Russian State Assignment under contract (state registration number АААА-А20-120011690138-6).

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics RAS, 119526, Moscow, Russia

    V. Ph. Zhuravlev & A. G. Petrov

Authors
  1. V. Ph. Zhuravlev
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  2. A. G. Petrov
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Corresponding authors

Correspondence to V. Ph. Zhuravlev or A. G. Petrov.

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Translated by I. K. Katuev

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Zhuravlev, V.P., Petrov, A.G. ANALYSIS OF THE ACTION OF PERTURBATIONS OF LINEAR RESONANT SYSTEMS WITH TWO DEGREES OF FREEDOM. Mech. Solids 56, 171–178 (2021). https://doi.org/10.3103/S0025654421020163

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  • DOI: https://doi.org/10.3103/S0025654421020163

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