# Control of Body Motion in an Ideal Fluid Using the Internal Mass and the Rotor in the Presence of Circulation Around the Body

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## Abstract

In this paper, we study the controlled motion of an arbitrary two-dimensional body in an ideal fluid with a moving internal mass and an internal rotor in the presence of constant circulation around the body. We show that by changing the position of the internal mass and by rotating the rotor, the body can be made to move to a given point and discuss the influence of nonzero circulation on the motion control. We have found that in the presence of circulation around the body the system cannot be completely stabilized at an arbitrary point of space, but fairly simple controls can be constructed to ensure that the body moves near the given point.

## Keywords

Ideal fuid Controllability Kirchhoff equations Circulation around the body## Mathematics Subject Classification (2010)

70Q05 70Hxx 76Bxx## Notes

### Acknowledgments

The authors thank A.V. Borisov and I.S. Mamaev for fruitful discussions. The work of E.V. Vetchanin was supported by the RFBR grant 15-08-09093-a. The work of A.A. Kilin was supported by the RFBR grant 14-01-00395-a.

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