Surprisingly Beethoven only wrote one violin concerto and it proved so popular that he transcribed it for the piano too
Again, only one, and given its exceptional quality and the number of first-rate violinists Beethoven knew, it is surprising he did not write more. He composed it for Franz Clement, who gave it its first performance, but actually dedicated it to his old friend Stephan von Breuning. It is possible Beethoven simply went off Clement, whose playing was rather showy and whose talent declined rather than improved. For instance, Beethoven would not allow Clement to lead the orchestra at the first performance of his Ninth Symphony.
The Concerto – uniquely – makes a star of the timpanist. He has four solo beats right at the start. So popular was the Concerto, that Beethoven (at his publisher’s request) made a piano transcription of it, which he dedicated to Stephan’s wife Julie. (Mastermind question: What is Beethoven 6th Piano Concerto? Answer: the piano transcription of his Violin Concerto.)
In the cadenza of the piano transcription, the pianist is accompanied by the timpani alone. Most likely Beethoven knew and liked the timpanist involved!
Yehudi Menuhin wrote that he was once performing the Violin Concerto somewhere in the American Midwest. He knew from the opening four beats on the timpani that the performance would be a disaster.