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The Necessary Condition for the Existence of Periodic Solutions of Certain Three Dimensional Nonlinear Dynamical Systems

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Abstract:

In this paper, we investigate a class of three dimensional nonlinear dynamical systems whose unperturbed systems have a family of periodic orbits. Firstly, we establish the moving Frenet Frame on these closed orbits. Secondly, the successor functions are defined by the orbits which go through the normal plane. Finally, by judging the existence of solutions of the equations obtained from the Successor functions, we obtain the necessary condition for the existence of periodic solutions of these three dimensional nonlinear dynamical systems. The result has important significance for the basic research of applied mechanics.

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Periodical:

Applied Mechanics and Materials (Volume 252)

Pages:

40-43

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.252.40

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Online since:

December 2012

Authors:

Ting Ting Quan, Jing Li, Min Sun

Keywords:

Frenet Frame, Periodic Solution, Successor Function, Three Dimensional Nonlinear Dynamical Systems

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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