Method to Construct Periodic Solutions of Controlled Second-Order Dynamical Systems
- Authors: Klimina L.A.1, Selyutskiy Y.D.1
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Affiliations:
- Institute of Mechanics, Lomonosov Moscow State University
- Issue: Vol 58, No 4 (2019)
- Pages: 503-514
- Section: Stability
- URL: https://journals.rcsi.science/1064-2307/article/view/220404
- DOI: https://doi.org/10.1134/S1064230719030109
- ID: 220404
Cite item
Abstract
Nonconservative mechanical systems with one degree of freedom are considered. The goal is to provide the existence of steady-state oscillations with the prescribed properties. The system’s behavior is modeled by a second-order autonomous dynamical system with one variable parameter describing the amplifying coefficient of the control action. A numerical-analytic method to find the amplifying coefficient is proposed. Conditions of the orbital stability are obtained for the steady-state oscillations. An example of the application of the method is provided. The proposed approach can be applied to solve control problems and to find periodic solutions of second-order autonomous dynamical systems.
About the authors
L. A. Klimina
Institute of Mechanics, Lomonosov Moscow State University
Author for correspondence.
Email: klimina@imec.msu.ru
Russian Federation, Moscow, 119192
Yu. D. Selyutskiy
Institute of Mechanics, Lomonosov Moscow State University
Email: klimina@imec.msu.ru
Russian Federation, Moscow, 119192