Nonlinear Dynamics of a Nonlinear Damping Gyroscope and Its Passive Control

This article deals with the analysis of the effects of passive control on the complex dynamics of a nonlinear damping gyroscope. After modeling the gyroscope dynamics under the influence of the control force, using the harmonic balance method, the amplitudes of the harmonic oscillations are determined. Subsequently, the Routh–Hurwitz criterion is used to analyze and determine the stability domains of the oscillations. The influence of the control force parameters on the amplitude of the oscillations is studied. The control of chaotic dynamics and the coexistence of gyroscope attractors are performed through bifurcation diagrams, Lyapunov exponents, phase portraits, and time series. Numerical simulations are used to confirm the effectiveness of the control force. This article revealed that the amplitude of the harmonic oscillations, the chaotic dynamics, and the coexistence of the attractors of the rotating gyroscope are better controlled when the latter vibrates in the opposite direction to the passive control force.