eng Science and Education Publishing International Journal of Physics 2333-4576 2024-01-25 12 1 19 33 10.12691/ijp-12-1-2 IJP20241212 article G. F. Pomalegni 1 2 J. M. Aguessivognon 2 C. H. Miwadinou clement.miwadinou@imsp-uac.org 2 3 4 A. V. Monwanou 4 Laboratoire de M¨¦canique des Fluides, de la Dynamique Nonlin¨¦aire et de la mod¨¦lisation des Syst¨¨mes Biologiques; Institut de Math¨¦matiques et de Sciences Physiques, Porto-Novo, B¨¦nin 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. https://pubs.sciepub.com/ijp/12/1/2/ijp-12-1-2.pdf gyroscope Lagrange approach biharmonic excitation chaos synchronization