One technique all timpanists need to learn is DAMPENING (or stopping) the sound of the drum. Dampening stops the sound of one drum so it doesn't ring longer than you want it to or so that is doesn't ring into the next note you play, both of which can muddy the sound of the timpani.
How to dampen the timpani
To dampen the timpani, hold the mallet between your thumb and your palm. Use the pads of your fingers and the side/back of your thumb to dampen the drum.
CLICK HERE for a dampening demonstration
Dampening is not always necessary when there is a rest. Sometimes it sounds good to ring through a rest, and sometimes it doesn't. You must be aware of what the rest of the band is playing, and make appropriate musical choices. Mark your music to indicate which notes should ring and which notes should be cut off.
Remember that you may need to dampen more than one drum - even drums that you haven't been playing! Striking one drum can make another resonate sympathetically.
DAMPENING EXERCISE
Practice playing alternating drums, dampening one drum at the same time as when you strike the other. This is especially good to do with the drums tuned to an interval of a second, so the pitches will clash if you don't dampen them in time.