Rotation of a dynamically symmetric body under constant and dissipative torques

Conclusion With the help of the variables k₁ and k₂ we have found quasistationary regimes of axial rotation and have determined their characteristics. For the general case (a>0, b>0, c>0, c<0) the quasistationary axial rotation k₂=k*₂ is asymptotically stable with respect to k₂. Similar regimes but with different values of k*₂ occur when one of the components of the dissipative torque vanishes (a=0, b>0, c>0, c<0 or a>0, b=0 c>0, c<0). Under the quadratic component of the torque (b=c=0, a>0) the axial rotation of the body is determined by the sign of the initial value of k₂. The behavior of the rotation of the body for only the dissipative torque (a>0, b>0, c=0) or only its linear component (a=c=0, b>0) depends on the ratio of the coefficients and b of the linear dissipation and can lead to axial rotation or to rotation in the equatorial plane. It follows from the above diagrams that axial rotation of a body in a medium with weak drag can be stabilized by applying a small constant torque about the axis of dynamical symmetry.Moscow. Translated from Prikladnaya Mekhanika, Vol. 29, No. 3, pp. 82–85, March, 1993.