The dynamics of a rigid body in potential flow with circulation
Abstract
We consider the motion of a twodimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing symplectic reduction with respect to the group of volumepreserving diffeomorphisms and obtain the relevant Poisson structures after a further Poisson reduction with respect to the group of translations and rotations. In this way, we recover the equations of motion given for this system by Chaplygin and Lamb, and we give a geometric interpretation for the KuttaZhukowski force as a curvaturerelated effect. In addition, we show that the motion of a rigid body with circulation can be understood as a geodesic flow on a central extension of the special Euclidian group SE(2), and we relate the cocycle in the description of this central extension to a certain curvature tensor.
 Publication:

Regular and Chaotic Dynamics
 Pub Date:
 October 2010
 DOI:
 10.1134/S1560354710040143
 arXiv:
 arXiv:1003.0080
 Bibcode:
 2010RCD....15..606V
 Keywords:

 Mathematical Physics;
 76M60;
 53D20;
 37K65
 EPrint:
 28 pages, 2 figures