On the motion of a puck on a horizontal plane in the model of viscous friction with variable coefficient

The problem of the motion of a homogeneous right circular cylinder with an annular base (a puck) on a horizontal plane with viscous friction is considered. Each point of the base of the puck in contact with the plane is acted upon by the viscous friction force which is proportional to the velocity of this point, and the proportionality coefficient linearly depends on the density of the normal reaction at this point. The density of the normal reaction is determined within the framework of a dynamically consistent model. Some properties of the motion are investigated. In particular, it is shown that for a given direction of the initial angular velocity of the puck, the trajectory of the center of mass of the puck can deviate both to the left and to the right of the straight line directed along the vector of the initial velocity of the center of mass depending on the parameters of the viscous friction model.