On permanent rotations of a string-driven rigid body
Considered two problems of motion of a rigid body suspended on the rod. In the first part of report the body with an ellipsoidal cavity full-filled by viscous liquid is considered. By using Routh’s method there were obtained steady motions of this mechanical system. It was proved that all steady motions were permanent rotations of the system as a whole about fixed upright. The stability and branching conditions of steady motions were also obtained.
In the second part it is considered the body suspended on the rod and immersed into viscous liquid. Basing on experimental and theoretical data there was constructed the mathematical model of interaction between rigid body and resistant media. Some properties of this dynamical system were pointed out.