Motion of two spheres in ideal fluid. I. Equations of motions in the Euclidean space. First integrals and reduction

A. V. Borisov^abc, I. S. Mamaev^abc, S. M. Ramodanov

^a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
^b Udmurt State University
^c Institute of Computer Science

Abstract: The paper deals with the derivation of the equations of motion for two spheres in an unbounded volume of ideal and incompressible fluid in 3D Euclidean space. Reduction of order, based on the use of new variables that form a Lie algebra, is offered. A trivial case of integrability is indicated.

Keywords: motion of two spheres, ideal fluid, reduction, integrability.

UDC: 531.3, 532.5

Received: 12.11.2007