Motion of a body with undeformable shell and variable mass geometry in an unbounded perfect fluid.

*(English)*Zbl 1143.76414Introduction: This paper proceeds with the analysis of one generalization [V. V. Kozlov and S. M. Ramodanov, J. Appl. Math. Mech. 65, No. 4, 579–587 (2001); translation from Prikl. Mat. Mekh. 65, No. 4, 592–601 (2001; Zbl 1046.76008), Dokl. Akad. Nauk 382, No. 4, 478–481 (2002)] of a classical problem on rigid body motion in an unbounded perfect fluid that moves irrotationally being quiescent at infinity, concerning the case of variable body’s geometry. An unrestrained motion (no external forces) of a variable body has been studied in the case when the body’s geometry of mass and shape are changing under an action of internal forces.

These changes are supposed to be described by given functions of time with respect to a certain moving coordinate system. In such formulation the problem of variable body motion is reduced to the study of the indicated coordinate system. The following new effect has been observed in the papers cited above: the law describing the changes in the body’s geometry always can be chosen in such a way that the considered body could be transferred to any (arbitrarily far) position in the surrounding fluid. It has been also shown that the complete control over the motion of such a system is possible even if the shape of the body’s surface does not change. It means that the body moves only due to the changes of its interior mass geometry. The only restriction is that not all of the body’s added masses (which depend only on the shape of its surface) be equal to each other. It should be noted that the previous results concerning the possibility of an unbounded motion for a variable body were based on such a mechanism governing the body’s geometry that involves the changes both in the surface shape and volume of the body. In the paper we study the mechanism of rigid shell body motion only due to the variation of the mass geometry. In addition, we consider the motion of a variable body in a uniform force field.

These changes are supposed to be described by given functions of time with respect to a certain moving coordinate system. In such formulation the problem of variable body motion is reduced to the study of the indicated coordinate system. The following new effect has been observed in the papers cited above: the law describing the changes in the body’s geometry always can be chosen in such a way that the considered body could be transferred to any (arbitrarily far) position in the surrounding fluid. It has been also shown that the complete control over the motion of such a system is possible even if the shape of the body’s surface does not change. It means that the body moves only due to the changes of its interior mass geometry. The only restriction is that not all of the body’s added masses (which depend only on the shape of its surface) be equal to each other. It should be noted that the previous results concerning the possibility of an unbounded motion for a variable body were based on such a mechanism governing the body’s geometry that involves the changes both in the surface shape and volume of the body. In the paper we study the mechanism of rigid shell body motion only due to the variation of the mass geometry. In addition, we consider the motion of a variable body in a uniform force field.

##### MSC:

76B99 | Incompressible inviscid fluids |