Abstract
Approximate real analytic solutions are derived for the motion of a near-symmetric rigid body subject to constant body-fixed moments about three axes. The solution for Euler's equations of motion is expressed in terms of Fresnel integrals and is exact for symmetric bodies. An approximate solution for the Eulerian angles is found in terms of Fresnel integrals and sine and cosine integrals. Although the expressions for the Eulerian angles are complicated, the behavior of the angular momentum vector in inertial space exhibits a simple spiral path. Numerical examples reveal that the solutions are very accurate when applied to typical spinning spacecraft.
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