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Nonlinear Dynamics

, Volume 56, Issue 3, pp 255–268 | Cite as

A new perturbation procedure for limit cycle analysis in three-dimensional nonlinear autonomous dynamical systems

  • S. H. Chen
  • J. H. Shen
  • K. Y. Sze
Original Paper

Abstract

By introducing a new parametric transformation and a suitable nonlinear frequency expansion, the modified Lindstedt–Poincaré method is extended to derive analytical approximations for limit cycles in three-dimensional nonlinear autonomous dynamical systems. By considering two typical examples, it can be seen that the results of the present method are in good agreement with those obtained numerically even if the control parameter is moderately large. Moreover, the present prediction is considerably more accurate than some published results obtained by the multiple time scales method and the normal form method.

Keywords

New perturbation procedure Limit cycle analysis Modified L–P method Three-dimensional systems 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Applied Mechanics and EngineeringSun Yat-sen UniversityGuangzhouPeople’s Republic of China
  2. 2.Department of Mechanical EngineeringThe University of Hong KongPokfulamPeople’s Republic of China

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