I would suggest simultaneous numerical solution of Eqs. (7) and (8) of Note 374(4) with various models for x and x dot. If this does not give meaningful results (a precessing ellipse) then Eq. (9) can be replaced by Eq. (19), the conservation of angular momentum in a fluid, the vorticity equation and Eqs. (7), (8) and (19) solved simultaneously. There are also other equations available such as the continuity equation, the Navier Stokes equation, and the equation of conservation of energy in fluid dynamics. We know that the methods of UFT363 give a precessing ellipse, so that is a useful clue.