STEADY-STATE MOTIONS OF TWO LINKED BODIES

The investigation of steady-state motions was regarded as one of the most difficult problems yet in the dynamics of a single rigid body [1, p. 217]. This problem has been dealt with in numerous publications. A generalization of the problem-the investigation of steady-state motions of a body on a suspension-drew attention of numerous authors who created "an extremely interesting section of mechanics" [2, p. 385]. ʹThe well though-out choice of basic, design, and intermediate systems of coordinates and desired variables is not of the least importance for the investigation to be successful" [2, p. 435]. It is well known that uniform rotations of a free rigid body, on which no external forces or torques act, are possible only about a principal axis passing through the center of mass of the body. For a heavy rigid body with a fixed point, the axes of possible uniform rotations form a cone. Apart from the axis on which the center of mass lies, any generatrix of this cone corresponds to a fixed value of the angular velocity. The result obtained in the present paper essentially differs from the results mentioned above. It turns out that the attachment of a body S to a body S by means of a spherical joint at a fixed point 0 and elastic links makes it possible for any axis of the body S to be an axis of uniform rotation. To each axis, there corresponds a definite value of the angular velocity. This effect is similar to that of self-balancing [5, pp. 172-180].