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New exact analytic solutions are introduced for the rotational motion of arigid body having two equal principal moments of inertia and subjected to anexternal torque which is constant in magnitude. In particular, the solutionsare obtained for the following cases: (1) Torque parallel to the symmetry axisand arbitrary initial angular velocity; (2) Torque perpendicular to thesymmetry axis and such that the torque is rotating at a constant rate about thesymmetry axis, and arbitrary initial angular velocity; (3) Torque and initialangular velocity perpendicular to the symmetry axis, with the torque beingfixed with the body. In addition to the solutions for these three forced cases,an original solution is introduced for the case of torque-free motion, which issimpler than the classical solution as regards its derivation and uses therotation matrix in order to describe the body orientation. This paper buildsupon the recently discovered exact solution for the motion of a rigid body witha spherical ellipsoid of inertia. In particular, by following Hestenes' theory,the rotational motion of an axially symmetric rigid body is seen at any instantin time as the combination of the motion of a "virtual" spherical body withrespect to the inertial frame and the motion of the axially symmetric body withrespect to this "virtual" body. The kinematic solutions are presented in termsof the rotation matrix. The newly found exact analytic solutions are valid forany motion time length and rotation amplitude. The present paper adds furtherelements to the small set of special cases for which an exact solution of therotational motion of a rigid body exists.

Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque