On the attitude motion of a self-excited rigid body

Leimanis (1965) has published a monograph, which contains Boedewadt's solution of Euler's equations of motion for a symmetric rigid body subject to a time-independent, self-excitement in a body-fixed direction. In addition, the monograph provided also Boedewadt's solution for the corresponding angles of rotation. It is pointed out that the solution of Euler's equations of motion provides a poor approximation to the problem of nearly symmetric rigid bodies in cases in which a high degree of accuracy (less than 1 percent error) is required. A much more accurate approximate solution has been provided by Longuski (1980). The result given by Leimanis in the case of the Eulerian angles is incorrect for arbitrary constant torques. The approximate solution given by Longuski, however, is extremely accurate and suitable for computer design work and error analysis of spacecraft performance. The present investigation is concerned with a review of the solutions and the specific regions of validity of the solution for the Eulerian angles.