Helmholtz decomposition
The Helmholtz theorem states that any vector may be decomposed into an irrotational (curl-free) and a solenoidal (divergence-free) part under certain conditions (given below). More precisely, it may be written in the form:
(1) |
where is a scalar potential and is a vector potential. By the definitions of scalar and vector potentials it follows that the first term on the right-hand side is irrotational and the second is solenoidal. The general conditions for this to be true are:
-
1.
The divergence of must vanish at infinity.
-
2.
The curl of must also vanish at infinity.
Title | Helmholtz decomposition |
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Canonical name | HelmholtzDecomposition |
Date of creation | 2013-03-22 17:59:40 |
Last modified on | 2013-03-22 17:59:40 |
Owner | invisiblerhino (19637) |
Last modified by | invisiblerhino (19637) |
Numerical id | 5 |
Author | invisiblerhino (19637) |
Entry type | Definition |
Classification | msc 26B12 |
Synonym | fundamental theorem of vector calcululs |