The motion of a heavy symmetrical body with flexible rods about a fixed point (Q1060613)

The motion of a symmetrical solid about its centre of mass is considered in the case, when four mutually orthogonal flexible rods are fixed to it in the equatorial plane of the body ellipsoid of inertia. The deformations of rods are defined by the linear theory of bending of thin viscoelastic rods, and lead to the evolution of the motion of the solid, i.e. the solid approaches steady rotation about the vertical. The approximate equations in Andoyer variables that define the system evolution are obtained by the method of averaging. The stability of the steady rotations obtained is investigated.