Stabilization of the Rotation Axis of a Solid by Coupled Perfectly Rigid Bodies

The problem of stabilizing the axis of a solid by coupled perfectly rigid bodies (PRBs) is solved. The solid executes a plane-parallel motion. The PRBs can rotate as a single rigid body about the centroidal axis of the solid and counterrotate about its transverse axes through equal angles. There is a particle inside the solid which causes its imbalance. It is established that the principal state (if any) of the system—rotation about the centroidal axis—is stable, whereas the rest (unwanted) states are unstable __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 122–129, August 2005.