The classical applications of coupled motion of rigid body with incompressible liquid are the journal bearings or squeeze film dampers. The world's dynamic and hydrodynamic scientists are interested in these problems, which have interdisciplinary characters. The general solution of this is very complicated, that's why simplified assumptions are necessary for example constant velocity among the radial direction. The most frequent assumption is an approximate circle orbit of shaft centre with constant precession angular velocity. For the analysis of liquid motion Navier Stokes and continuity equations and boundary conditions were used.
Liquid is considered as real incompressible and flow is laminar.
The control volume method is used for another analysis. Using special transformations it is possible to separate the motion of rigid body and liquid from themselves. For the analysis of liquid motion it is possible to use another suitable program system. The case of long journal bearings is presently being analysed. It is possible to use some approaches to analyze stability, for example an eigenvalue problem using eqs.