Circulation
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
of a vector field $ \mathbf a ( \mathbf r) $
along a closed curve $ L $
The integral
$$ \oint _ { L } \mathbf a d \mathbf r . $$
In coordinate form the circulation is equal to
$$ \int\limits _ { L } ( a _ {x} dx + a _ {y} dy + a _ {z} dz). $$
The work performed by the forces of the field $ \mathbf a ( \mathbf r ) $ in displacing a test body (of unit mass, charge, etc.) along $ L $ is equal to the circulation of the field along $ L $. See Stokes theorem.
Comments
This notion is also called a line integral (of a vector field) along a closed curve.
How to Cite This Entry:
Circulation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Circulation&oldid=46347
Circulation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Circulation&oldid=46347
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article