Does your 4D matrix have bottom row (0,0,0,1). (It probably should do). If so I'd suggest that the upper left 3*3 minor is the rotation matrix and the (1*3) column vector to the right is the translation.
At any rate, applying that matrix as a linear transformation and then translating by that amount would be equilvalent to your 4D transformation.
You might want the rotation about the centre of the stick. In that case conjugate your matrix by the translation that sends the centre of the stick to the origin.
Apologies if I've totally misunderstood your question.