Chaotic Synchronization of a Symmetric Gyroscope Excited by a Biharmonic Force

G. F. Pomalegni^{1, 2}, J. M. Aguessivognon¹, C. H. Miwadinou^{1, 3,} and A. V. Monwanou¹

¹Laboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la modélisation des Systèmes Biologiques; Institut de Mathématiques et de Sciences Physiques, Porto-Novo, Bénin

²Ecole de Génie Rural, Université Nationale d’Agriculture, Kétou, Bénin

³Département de Physique, Ecole Normale Supérieure de Natitingou, Université Nationaledes Sciences, Technologies, Ingénierie et Mathématiques (UNSTIM) Abomey, Bénin;Laboratoire de Physique et Applications (LPA), Natitingou, UNSTIM

Cite this paper:
G. F. Pomalegni, J. M. Aguessivognon, C. H. Miwadinou and A. V. Monwanou. Chaotic Synchronization of a Symmetric Gyroscope Excited by a Biharmonic Force. International Journal of Physics. 2024; 12(1):19-33. doi: 10.12691/ijp-12-1-2

Abstract

This work analyzes the chaotic dynamics and the chaotic synchronization and their control in the complex dynamics of a rotating gyroscope modeled following Euler angles using the Lagrange approach. It is obtained for appropriate conditions the chaotic dynamics and its control using the four order Runge-Kutta algorithm. By the backstepping method, the chaotic synchronization conditions of two gyroscopes are obtained by building a Lyapunov function and numerical simulations. The study also pointed out that the first integrals of the moments of inertia of the gyroscope influence the chaotic dynamics and the chaotic synchronization. The analysis of the effects of the amplitudes and frequencies of this excitation makes it possible to find the best areas where the control and synchronization are effective.

Keywords:
gyroscope Lagrange approach biharmonic excitation chaos synchronization

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