I feel as if I understand the conceptual difference between Lagrangian and Eulerian descriptions. But I can't seem to follow the math. I have one example that I would greatly appreciate an explanation or full calculation for
Here $x_i$ denotes the position of a particle in the current configuration, and $X_i$ denotes its position in the reference configuration.
I am entirely on board on the velocity in the Lagrangian description. I cannot for the life of me figure out how the Eulerian description is computed nor why.
Can someone show me how the Eulerian description of the velocity is calculated?
I realize this belongs more in engineering than math, but the engineering stack is pretty dead.