On the transition from regular to chaotic behaviors in the two degrees of freedom dynamical system

Nguyen Van Khang, Nguyen Hoang Duong
Author affiliations

Authors

  • Nguyen Van Khang Hanoi University of Technology
  • Nguyen Hoang Duong

DOI:

https://doi.org/10.15625/0866-7136/29/3/5545

Abstract

The main objective of the present paper is to study the transition from periodic regular mot ion to chaos in a two degrees of freedom dynamical system by changing control parameters. The nonlinear differential equations governing motion of the system are derived from the Lagrange equations. By use of the Poincare map, the dynamical behavior is identified based on numerical solutions of the ordinary differential equations. The Lyapunov exponent and the frequency spectrum are calculated to identify chaos. From numerical simulations, it is indicated that the periodic, quasi-periodic and chaotic motions occur in the considered system.

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Published

22-09-2007

Issue

Section

Research Article