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Exact solutions are found for Euler's equations of rigid body motion forgeneral asymmetrical bodies under the influence of torque by using Jacobielliptic functions. Differential equations are determined for the amplitudesand the parameters of the elliptic functions. The solution is then applied tothe detumbling of a satellite with arbitrary initial rotation rates wherenumerical solutions are seen to be in agreement with the analytical solution.The body fixed frame solution is then transformed to the inertial frame by useof a quaternion rotation matrix to depict the motion in figures and inanimations within a Mathematica notebook which is openly published on theWolfram community.

Exact solutions to Euler's equations for rigid body motion with application to detumbling satellites