Rotation of a Dynamically Symmetric Body Under Constant and Dissipative Torques
International Applied Mechanics 01/1993; 29(3):236-239. DOI:10.1007/BF00847004
Posted: 12 Jul 2017
Date Written: January 9, 1993
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, c2=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, c0, b=0 c>0, c0) 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 ß 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.
Keywords: rigid body rotation, dissipative torque, linear dissipation
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