Check out the dynamic markings in this bass trombone part...
Bennett, William Sterndale / DIE NAJADEN, OP.15
William Sterndale Bennett was a young prodigy composer mentored by Mendelssohn, among others.
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Yup. I think at the time it was a somewhat dated, mostly Austrian idiom for requesting a sort of "push" accent to the articulation. You might see "f", "sf", "sfz", or "rfz" in similar applications.
In other words, it was written for the typical trombone player!
[Mendelssohn] took me to his house and gave me the printed score of [his overture] 'Melusina', and afterwards we supped at the 'Hôtel de Bavière', where all the musical clique feed ... The party consist[ed] of Mendelssohn, [Ferdinand] David, Stamity [sic] ... and a Mr. Schumann, a musical editor, who expected to see me a fat man with large black whiskers.
Sometimes tympanists will use their opposite hand to dampen the sound after they strike the head. Using the hand, hell, or fingers lends a slightly different effect on the end of the note (the right side of the note). Using different sticks and mallets with different wraps (size, softness/density, etc.) will also affect the right side of the note. In the end, it’s up to what the conductor wants.
On a rolled note it's almost a cliché... whack the first mallet and quiet roll after that.