To give notes their proper value and avoid altering the harmonies of the other instruments with extraneous sounds, it is necessary to damp the vibrations of the skins.
However, there are cases where the resonance enriches the sound and is not disturbing. There are no fixed rules for these situations and only the player can decide whether it's better to damp the vibrations or not.
The most popular system for stopping vibration on the tympani is to hold the stick with the thumb and index finger while stopping the skin with the other three fingers (fig. 1). However, even this method may be inadequate when the resonance is great because with only three fingers you can't apply sufficient force to a large enough area. If you then use a vertical grip, which causes you to constantly turn your wrist to press better, you need to be even more expert so as not to allow the instruments to resonate more than necessary.
For this reason, if you want to make it easier to stop vibrations, it will be helpful to use a grip where the palm is horizontal or at least an intermediate grip.
By keeping the palm facing the floor, you can also stop the skins of two tympani simultaneously (fig. 2 and 3), because you only need to open your fingers to be already in position.
On the other hand, with a vertical grip, after striking you need to rotate the wrist for better pressure, thus requiring an extra motion that makes execution more difficult.
At any rate, to stop vibrations in a professional manner, you need to acquire sensitivity of touch through gradual, linear exercises. It has to do with learning to either press decisively or caress the skin, depending on the need.
There is an entire section in the Timpani method (pp. 33 - 38 and 51- 53) dedicated to damping exercises, complete with pieces where you can apply the studied techniques.