Method to Construct Periodic Solutions of Controlled Second-Order Dynamical Systems

  • L. A. KliminaEmail author
  • Yu. D. Selyutskiy


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.



This work was supported by Russian Foundation for Basic Research, project nos. 18-31-20029 and 17-08-01366.


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of Mechanics, Lomonosov Moscow State UniversityMoscowRussia

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