As a percussionist, you already know basic sticking skills. Here are the special rules that apply to playing the timpani:
STICKING RULES
1. Avoid double strokes (RR, LL)
2. Use alternating sticking (RLRL) wherever possible
3. Double strokes make it more difficult to produce clear and consistent articulation.
ROLLS
1. Timpani rolls are traditionally single-stroke rolls (alternating RLRLRLRL) NOT double-stroke or buzz rolls.
2. Let the mallets bounce loosely on the head (use a legato stroke) so you get a nice smooth sound. All the strokes in the roll need to be the same volume and tone - no notes should jump out at the listener.
3. Don't roll too fast.
4. Don't try to roll so fast that you fill in all of the "spaces" in sound. Let the ring of the drum fill in the spaces for you.
5. Roll faster when the head is tight (high end of the drum's range) and slower when it is loose (low end of the drum's range).
6. Count while rolling. Don't lose track of where the beat is and how long your roll should be.