Kirchhoff equations
Encyclopedia
In fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

, the Kirchhoff equations, named after Gustav Kirchhoff
Gustav Kirchhoff
Gustav Robert Kirchhoff was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects...

, describe the motion of a rigid body
Rigid body
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it...

 in an ideal fluid.


where and are the angular and linear velocity vectors at the point , respectively; is the moment of inertia tensor, is the body's mass; is
a unit normal to the surface of the body at the point ;
is a pressure at this point; and are the hydrodynamic
torque and force acting on the body, respectively;
and likewise denote all other torques and forces acting on the
body. The integration is performed over the fluid-exposed portion of the
body's surface.

If the body is completely submerged body in an infinitely large volume of irrotational, incompressible, inviscid fluid, that is at rest at infinity, then the vectors and can be found via explicit integration, and the dynamics of the body is described by the Kirchhoff
Gustav Kirchhoff
Gustav Robert Kirchhoff was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects...

 – Clebsch equations:



Their first integrals read
.

Further integration produces explicit expressions for position and velocities.
The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK