Finite-dimensional approximation of the motions of incompressible fluids within an ellipsoid

The motion of an inviscid incompressible liquid in an ellipsoid is studied. The accuracy of a description of such motion is primarily determined by how well the active modes have been taken into account by the model. A system of ordinary differential equations is used to formulate an approximation of hydrodynamics. This approximation reduces the problem to the choice of a system of reference fields along which the expansion is constructed. Field velocity is determined by a polynomial representation of coordinates. The rotational stability of a liquid around one of the major axes of an ellipsoid is studied using the system of equations which has been developed. It is shown that in the first approximation the development of instability may be described within the framework of a three- or five-mode model dependent on ellipsoidal parameters.