On a Kinematic Proof of the Canonicity of Andoyer Variables

We present a kinematic proof of the fact that the Andoyer variables in rigid body dynamics are canonical. This proof is based on the approach of “virtual rotations” proposed by H. Andoyer. The difference from the original proof by Andoyer is that we do not assume that the frame fixed to the body is the frame of principal moments of inertia, and do not use explicit formulas for the kinetic energy of the body that include moments of inertia. This simple proof can be useful in the exposition of rigid body dynamics in classical mechanics courses.