The modified Poincare-Dulac method in analysis of autooscillations of nonlinear mechanical systems

European Workshop on Advanced Control and Diagnosis

Melnikov, Gennady I.^1 ; Ivanov, Sergei E.^2 ; Melnikov, Vitaly G.^1

Department of Theoretical and Applied Mechanics, University ITMO, St.Petersburg, Russia^1

Department of Information Systems, University ITMO, St.Petersburg, Russia^2

关键词: Auto-oscillations;    Degree of freedom;    Dissipative forces;    Dynamic equations;    Economization;    Mechanical systems;    Nonlinear mechanical systems;    Nonlinear terms;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/570/2/022002/pdf
DOI  :  10.1088/1742-6596/570/2/022002

来源: IOP

【 摘 要 】

A dynamic equation of a mechanical system with one degree of freedom with functionally odd nonlinear recover forces and small dissipative forces is considered. An improved method of transformation and integration of the equation, based on a method of normalization of Poincare-Dulac is developed. The improvement of the method is in application of the Chebyshev's economization to high-order nonlinear terms.