Constrained Motion Approach to the Synchronization of the Multiple Coupled Slave Gyroscopes

A set of n gyroscopes are coupled to form a system of slave gyroscopes. A simple approach is developed for synchronizing the motion of these slave gyroscopes whose individual motion may be regular or chaotic, with the motion of an independent master gyroscope irrespective of the chaotic or regular motion exhibited by the master. The problem of synchronization of these multiple gyroscopes is approached from a constrained motion perspective through the application of the fundamental equation of mechanics. The approach yields explicit, closed-form expressions for the control torques that are required to be applied to each of the coupled slave gyroscopes to achieve exact synchronization with the master's motion. The influence of different types of interactions between the slave gyroscopes is investigated with an incidence matrix that describes the coupling between any two of them. The effect of the so-called sleeping condition on the synchronization of the gyroscopes is also explored. To illustrate the efficacy of the methods presented in this paper, we consider numerical examples involving systems of multiple gyroscopes and synchronize them with the motion of a master gyroscope.