Originally Posted by pvaudio
While your descriptions from a math standpoint are indeed correct, they only really apply to the classical definition of strokes. They don't apply to modern stroke mechanics. As a simple example, for both flat and "spin" shots, the racquet velocity should be perpendicular to the stringbed by your definition. If you hit a shot with underspin, as in a slice, this doesn't hold. Here, the racquet face is slightly open, so the strings are pointing slightly upward. The racquet velocity will be from high to low, so at impact, the racquet's velocity vector most certainly can be perpendicular to the string bed's normal vector. How? Easy, the ball is not going straight across the net, it needs elevation as well. I think what you meant to say is that for a flat ball, the racquet face must be normal to the direction of the racquet's travel through prior to and after impact. Because as I just pointed out, at impact, you can get any sort of spin you want and have the stringbed's normal vector be normal to the velocity vector.
The racquet velocity and orientation doesn’t know anything about modern or classical definition of strokes. This math stuff is working in any sports and motions.
When you hit any stroke you better clearly understand what motion of your body creates flat component V
RF – translational motion of the ball (ball’s speed) and how you are going to build V
RS – particular spin at the moment of contact.
For example, in case of the serve V
RF can be constructed by using:
1. Arm counterclockwise rotation – arm pronation
2. Wrist flexion
3. Trunk particular rotations and etc.
The serve V
RS can be made by using:
1. Wrist ulnar deviation
2. Elbow flexion and so on.
Then you also should pay attention to the racquet orientation at the moment of contact.
Unfortunately, people usually learn it by trial and error method or copy somebody’s stroke.