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

Abstract

Abstract. The main object ive of the present pape r is to study the transition from period ic regular mo t ion to chaos in a two degrees of fr eedom dynamical system by changing control parameters. The nonlinear differential equations governing motion of the system a rc derived from the Lagrange equations. I3y use of the Poincare map , the dynami cal behavior is identified based on nume rical solutions of the ordinary differential equations. The Lyapunov exponent and the frequency spectrum a re calc ul ated to ide nti fy chaos. From numerical simulations, it is indicated that the periodic, quasi-periodic and chaotic motions occur in the conside red system.