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IssuesArchive of Issues2021-2pp.171-178

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Zhuravlev V.Ph. and Petrov A.G., "Analysis of the Action of Perturbations of Linear Resonant Systems with Two Degrees of Freedom," Mech. Solids. 56 (2), 171-178 (2021)
Year 2021 Volume 56 Number 2 Pages 171-178
DOI 10.3103/S0025654421020163
Title Analysis of the Action of Perturbations of Linear Resonant Systems with Two Degrees of Freedom
Author(s) Zhuravlev V.Ph. (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, zhurav@ipmnet.ru)
Petrov A.G. (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, petrovipmech@gmail.com)
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.
Keywords resonant systems, two degrees of freedom, linear perturbations, evolution of an elliptical trajectory
Received 12 March 2020Revised 14 March 2020Accepted 16 March 2020
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