Effect of biharmonic excitation on complex dynamics of a two-degree-of-freedom heavy symmetric gyroscope

Abstract

This work analyzes the chaotic dynamics and the coexistence of attractors and their control in the complex dynamics of a rotating gyroscope modeled following Euler angles using the Lagrange approach. The fixed points of the system is checked and their stability analyzed. The complete dynamics of the gyroscope is studied and the coexistence of attractors analyzed using Runge-Kutta algorithm of order 4. It is obtained for appropriate conditions the coexistence of chaotic and/or regular attractors. The study also pointed out that the dissipation and the first integrals of the moments of inertia of the gyroscope influence the chaotic dynamics as well as the coexistence of the attractors. Finally, the control of the coexistence of attractocs obtained is done using a biharmonic excitation. The analysis of the effects of the amplitudes and frequencies of this excitation makes it possible to find the best areas where the control is effective.