The problem of a spinning, axisymmetric, or nearly axisymmetric rigid body subject to constant body-fixed forces and moments about three axes is considered. Approximate closed-form analytical solutions are derived for velocity and for the transverse displacement. The analytical solutions are valid when the excursion of the spin axis with respect to an inertially fixed direction is small (which is usually the case for spin-stabilized spacecraft and rockets). Numerical simulations confirm that the solutions are highly accurate when applied to typical motion of a spacecraft, such as the Galileo.
Analytical Solutions for Translational Motion of Spinning-Up Rigid Bodies Subject to Constant Body-Fixed Forces and Moments
Ayoubi, M. A., and Longuski, J. M. (January 11, 2008). "Analytical Solutions for Translational Motion of Spinning-Up Rigid Bodies Subject to Constant Body-Fixed Forces and Moments." ASME. J. Appl. Mech. January 2008; 75(1): 011004. https://doi.org/10.1115/1.2755110
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