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The exact analytic solution is introduced for the rotational motion of arigid body having three equal principal moments of inertia and subjected to anexternal torque vector which is constant for an observer fixed with the body,and to arbitrary initial angular velocity. In the paper a parametrization ofthe rotation by three complex numbers is used. In particular, the rows of therotation matrix are seen as elements of the unit sphere and projected, bystereographic projection, onto points on the complex plane. In thisrepresentation, the kinematic differential equation reduces to an equation ofRiccati type, which is solved through appropriate choices of substitutions,thereby yielding an analytic solution in terms of confluent hypergeometricfunctions. The rotation matrix is recovered from the three complex rotationvariables by inverse stereographic map. The results of a numerical experimentconfirming the exactness of the analytic solution are reported. The newly foundanalytic solution is valid for any motion time length and rotation amplitude.The present paper adds a further element to the small set of special cases forwhich an exact solution of the rotational motion of a rigid body exists.

Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque