Trajectory of a Spinning Tennis Ball

Abstract

Consider a tennis ball with mass m and diameter d, moving in air near the earth surface. The ball is spinning with angular velocity $\vec{\omega}$ (the vector $\vec{\omega}$ has the direction of the axis of rotation and magnitude ω = dφ(t)/dt = $\dot{\varphi}$(t), where φ(t) is an angle of rotation). We will impose a Cartesian coordinates system (xyz) on the surface of the earth with the z axis directed vertically.