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

A set of ‘n' gyroscopes are coupled together 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 Udwadia-Kalaba equation. The approach yields explicit, closed form expressions for the control torques that are required to be applied to each of the coupled slave gyroscopes and achieves 'exact' synchronization with the master's motion. The effect of the ‘no-sleeping' condition on the synchronization of the gyros is discussed. An incidence matrix is also introduced to describe the coupling interaction between individual slave gyros.