SINOPSIS

The subject of consideration comprises nonlinear systems of ordinary integral-differential equations which appear in dynamics of relative motion of ideal homogeneous incompressible fluid in connection with a variational method by Bateman−Luke−Whitham; the equations are similar to Hamiltonian equations. The paper presents an analysis of properties of the said simultaneous equations and a known method for their approximate solution − by excluding quasi-velocities of the fluid and reducing the system to certain simultaneous equations of second order with respect to the coordinates of a free surface. An alternative approach is presented for a rectangular vessel partially filled with fluid. It is based on a direct integration of the original exact equations by the Runge-Kutta technique. An algorithm for numerical solution of the equations has been developed and is demonstrated by the example of nonlinear free oscillations (sloshing) of fluid in a tilted rectangular vessel after its being accelerated.