There is a moment during the impact of a ball and a racket that the velocities of the ball and the racket are the same. This is the moment of zero relative velocity. At this moment, the ball is being pushed out of the racket by a spring force. If a force opposite to the spring force is applied to the ball, the racket will prolong its contact with the ball. This force can be created by a jumpulse, a sudden change of force. Any amount of sudden increase of force applied around the moment of zero relative velocity will prolong the contact between the ball and the racket. If this force is equal and opposite to this spring force, the ball the racket can have "permanent" contact. Thus, prolonged contact can be achieved by a precisely timed jumpulse.
Double hitting is more difficult to achieve than prolonged contact. In order for the accelerating racket to catch up with the non-acceleration ball, the exit velocity of the ball from the racket must be close enough to the velocity of the racket. To achieve similar velocities during exit, the jumpulse must be sufficiently large so that it can sufficiently balance spring force. In fact, the requirement of double-hitting is almost as stringent as permanent contact, which requires the jumpulse to produce a force equal and opposite to the spring force. Human touch is an example of permanent contact, where the jumpulse applied must have precise timing and magnitude.
To summarize, double-hit lies between prolonged contact and permanent contact from the point of view of physics. Prolonged contact always exists when double-hit occurs. In practice, double-hit would be more difficult to achieve than prolonged contact. Double-hit has the advantage in practice of being detectable, while prolonged contact may be hard to detect. For this reason, double-hit is a good method to practice prolonged contact.
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