Just for your kind information:
With 'Pauke' we mean the same drum as 'Grosse Trommel' and it can be translated as 'bass drum'. (We don't say 'Pauke Trommel' but 'Pauke' only and it is an old wording for a 'kick drum/ bass drum' in a drumset, too.)
'Trommel' is just a general word for a drum in Germany: this can be any kind of drum from the African djembe to snare drums etc..
The German word 'Timpani' is used only for an orchestral 'Pauke', which mainly are manufactured in copper (those with the half-round shell and the mentioned t-rods).
The word 'Tom' (or 'Tomtom') we know only in the context of a drumset as 'rack tom' or similar.
Perhaps this helps a little bit clarifying (if not: let me know, please).
Ralf