biharmonic excitation; chaos and bifurcation; coexistence of attractors; Lagrange approach; rotating gyroscope; Bi-harmonic; Biharmonic excitation; Chaos and bifurcation; Chaotic dynamics; Coexistence of attractor; Complex dynamics; Heavy symmetric gyroscopes; Rotating gyroscope; Two-degree-of-freedom; Atomic and Molecular Physics, and Optics; Mathematical Physics; Condensed Matter Physics
Abstract :
[en] 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.
Miwadinou, C.H. ; Laboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques, Porto-Novo, Benin ; Département de Physique, École Normale Supérieure de Natitingou, Université Nationale des Sciences, Technologiques, Ingénierie et Mathématiques (UNSTIM), Abomey, Benin
Monwanou, A.V. ; Laboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques, Porto-Novo, Benin
Language :
English
Title :
Effect of biharmonic excitation on complex dynamics of a two-degree-of-freedom heavy symmetric gyroscope
The authors thank very much the anonymous referees whose useful criticisms, and suggestions have helped strengthen the content and the quality of the paper. J. M. Aguessivognon sincerely thank Professor Christophe COLLETTE, Director of the Precision Mechatronics Laboratory; Department of Aerospace and Mechanics; Faculty of Applied Sciences on the one hand and Uliège then the Belgian State on the other hand for their various supports.
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