x y z
u´ --- + v´ --- + w´ --- = 0, (8)
a2 b2 c2
so that a liquid particle remains always on a similar ellipsoid.
The hydrodynamical equations with moving axes, taking into account the
mutual gravitation of the liquid, become
1 dp du du du du
----- -- + 4[pi][rho]Ax + -- - vR + wQ + u´-- + v´-- + w´-- = 0, ... , ... , (9)
[rho] dx dt dx dy dz
where
_
/ [oo] abcd[lambda]
A, B, C = | ----------------------------------------------
_/ 0 (a² + [lambda], b² + [lambda], c² + [lambda])P