lamellar field
A vector field , defined in an open set of , is lamellar if the condition
is satisfied in every point of .
Here, is the curl or rotor of . The condition is equivalent with both of the following:
- •
-
•
The vector field has a which has continuous partial derivatives and which is up to a unique in a simply connected domain; the scalar potential means that
The scalar potential has the expression
where the point may be chosen freely, .
Note. In physics, is in general replaced with . If the is interpreted as a , then the potential is equal to the work made by the when its point of application is displaced from to infinity.
Title | lamellar field |
Canonical name | LamellarField |
Date of creation | 2013-03-22 14:43:44 |
Last modified on | 2013-03-22 14:43:44 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 18 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 26B12 |
Synonym | lamellar |
Synonym | irrotational |
Synonym | conservative |
Synonym | laminar |
Related topic | CurlFreeField |
Related topic | PoincareLemma |
Related topic | VectorPotential |
Related topic | GradientTheorem |
Defines | scalar potential |
Defines | potential |
Defines | rotor |