This book started with the simple idea that rotation can be synthesized when we started thinking about tactics as vectors, but as we considered more advanced tactics, the theory also needed a little more rigor. Here, I explain a little strict reasoning.
7.1 Tactic Diagram by Vector
Until now, tactical diagrams have been represented by directional spin vectors. However, it is difficult to think of a complicated three-dimensional problem from a two-dimensional diagram alone. Therefore, I decided to use the English acronym for each spin vector to indicate the spin.
7.2 Consideration of Spin Composition and Vector Notation
Since the rotation vector is a force, tracing the original rotation does not mean that a force has been applied, and is an invalid vector that does not accelerate the rotation. You need to subtract that amount from the rotation you tried to add. The resulting vector must take that into account.
When the ball's initial spin is fast and the next racket swing to rotate the ball is slow, since the ball cannot move the racket, the difference of the speed is converted into flight by the reaction force. In view this point, it is desirable to represent with vectors