On the stability of certain motions of a rigid body with elastic rods and liquid: PMM vol. 36, n≗ 1, 1972, pp. 43–59

Abstract

We consider the motion of a free rigid body with three pairs of elastic rods and with a cavity containing a liquid, in two cases: in a central Newtonian force field and in the absence of external forces. By an application of Rumiantsev's theorem [1] we obtain sufficient stability conditions for relative equilibrium in a circular orbit and to uniform rotations of this system. We show that the presence of a liquid with a free surface in the cavity and the connection of elastic rods to the body have a destabilizing effect on the stability of the corresponding unperturbed motions of the unaltered system. We also point out sufficient stability conditions in the case when less than three pairs of rods are attached to the body. For a large Young's modulus the stability conditions obtained lead (in the absence of the liquid) to the well-known sufficient conditions for the stability of a rigid body. Stability conditions for the case when one pair of rods is attached to the body and when there is no liquid are compared with the stability conditions obtained in [2, 3]. In connection with the assertion made in [2, 3] regarding the novelty of the method used, we remark that this method was previously developed by Rumiantsev and was applied to the solution of a number of problems on the stability of the steady-state motions of a rigid body with a liquid filling [4].