Rigid body rotation evolution due to a disturbing torque which is known in a body frame

摘要

This paper deals with the problem of rigid body rotation evolution under the action of a torque which depends on the projections of rigid body angular velocity onto the body frame only. This is the so called rigid body with self-excitation. If the magnitude of the torque is arbitrary, the solution to the problem is known in the simplest cases only. The problem with small self-excitation is considered in the paper. This problem is of great importance from the standpoint of a number of applications in spacecraft and rigid body dynamics. Perhaps the most important example is spinstabilized spacecraft rotation evolution due to an internal disturbing torque. In the case of a small torque, it is possible to use perturbation methods to obtain complete analytical and geometrical descriptions of the rotation. In this paper, the common approach to investigating the problem of rigid body rotation under the action of a small torque known in the body frame is described. Using this approach, two problems are solved: the problem of maintaining the angular velocity of a gyroscope using a control torque quadratic in the angular velocity (the problem of Grammel for the case of a small torque), and the problem of asymmetric spacecraft rotation evolution with an electric propulsion thruster. [References: 13]