How to construct body-fitted coordinate system in Paraview

Hi, I have a series of vtk files storing the flow field information, representing a vibrating body (only along y-axis) in a large domain. So the locations of body and mesh grid would change with time.

For example, at t = 0.01, the body is located above y=0.

At t=0.05, the body is below y=0.

If I want to take the center of body as the origin point, is there any way in Paraview to construct such body-fitted coordinate system, so that I can project all the flow field snapshots onto it and extract information to do proper orthogonal decomposition?

Any suggestion is welcome! Thanks!