The dynamics of a rigid body in potential flow with circulation

被引：0
作者：
J. Vankerschaver
E. Kanso
J. E. Marsden
机构：
[1] California Institute of Technology,Control and Dynamical Systems
[2] Ghent University,Dept. of Mathematical Physics and Astronomy
[3] University of Southern California,Aerospace and Mechanical Engineering
来源：
Regular and Chaotic Dynamics | 2010年 / 15卷
关键词：
fluid-structure interactions; potential flow; circulation; symplectic reduction; diffeomorphism groups; oscillator group; 76B47; 53D20; 74F10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider the motion of a two-dimensional 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 volume-preserving 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 Kutta-Zhukowski force as a curvature-related 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.
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页码：606 / 629
页数：23
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