APLICATIONS OF THE PERPETUAL POINTS IN DYNAMICS

Abstract

It is known that in the dissipative nonlinear dynamics, the equilibrium points have a significant role in the transient behaviour. The perpetual points are defined as points for which at least one of the velocity is different than zero and all accelerations of the system are zero. This paper investigates the perpetual points for a coupled pendulum and the relationship between the perpetual points and the chaotic behavior of the pendulum. In addition, the coupled pendulum exhibits multi-stability, i.e. the occurrence of unpredictable attractors called hidden attractors. These attractors have relatively small basin of attraction and do not intersect the perpetual points. The knowledge of the possible occurrence of the hidden attractors is necessary in order to reduce the risk of the sudden jump to a such undesired behavior.