On a kinematic proof of Andoyer variables canonicity

We present a kinematic proof that the Andoyer variables in rigid body dynamics are canonical. This proof is based on the approach of “virtual rotations” by H. Andoyer. The difference from the original proof by Andoyer is that we do not assume that the fixed in body frame 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 could be quite useful in exposition of the rigid body dynamics in classical mechanics courses.