The motion of a variable body in an ideal fluid

The dynamics of a deformable body in an unbounded volume of an ideal fluid, which performs irrotational motion and is at rest at infinity, is investigated. It is assumed that a change in the geometry of the masses and shape of the body occurs due to the action of internal forces and that the displacements of the particles of the body are known functions of time in a certain moving frame of reference. The equations of motion of the moving trihedron are represented in the form of Kirchhoff's equations. The conservation laws when there are no external forces are indicated. Using these laws, the equations of motion are reduced to a non-autonomic system of first-order differential equations in the group of displacements of the configurational space. In the case of plane-parallel motion of the body, these equations are explicitly integrated in quadratures. A special case, when the boundary of the body does not change, is considered. It is established that, in the case of non-equal added masses, due to the change in the geometry of the body masses, the body can move from any position into any other position.