Chapter 12.2, Problem 12.74P

A particle of mass m is projected from point A with an initial velocity v₀ perpendicular to line OA and moves under a central force F directed away from the center of force O. Knowing that the particle follows a path defined by the equation $r=r_0/\sqrt{\cos 2\theta }$ and using Eq. (12.25), express the radial and transverse components of the velocity v of the particle as functions of $\theta$ .