STABILIZATION BY ROTATING RIGID BODIES FOR UNSTABLE ROTATION OF A RIGID BODY WITH CAVITIES CONTAINING A FLUID

Abstract

On XIII International congress on theoretical and applied mechanics (ICTAM 1972) A. Y. Ishlinsky [1] has set the problem about definition of conditions for stability of uniform rotations of system in two heavy gyroscopes of Lagrange. The interesting effect of stabilization in unbalanced gyroscope of Lagrange by the second rotating [2, 3] has been found in the works of Donetsk school on mechanics under supervision of P. V. Kharlamov. In S. L. Sobolev's known work [4] it is shown that the Lagrange gyroscope if contains the perfect fluid is rather unstable. Therefore, the problem on the possibility of stabilization in unstable rotation of the gyroscope in question by one or two rotating rigid bodies has been put out. The possibility for stabilization by rotating rigid bodies in unstable rotation of the Lagrange gyroscope containing a perfect fluid is shown in our study. The case of free motion and the case when the Lagrange gyroscope with fluid rotates about a fixed point are considered. The equations of the works [5, 6] are foundations of the conclusion on the motion equations for the considered mechanical system.