Please see attached for the problem I am doing.
I think I am making things too complicated.
In the material description of a fluid particle, the vorticity tensor in involved.
First I do not understand how the dimension is going to work out when the question has a sin( product of tensor and time) ...
Second, when I want to define the material description implicitly, I have the vorticity tensor in the way and it make things look very complicated.
You could try switching to polar coordinates. Your expression for XL would look a lot simpler.