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irrotational field (Definition)

Suppose $ \Omega$ is an open set in $ \mathbb{R}^3$, and $ \mathbf{V}$ is a vector field with differentiable real (or possibly complex) valued component functions. If $ \nabla\times \mathbf{V}=0$, then $ \mathbf{V}$ is called an irrotional vector field, or curl free field.

If $ \mathbf{U}$ and $ \mathbf{V}$ are irrotational, then $ \mathbf{U}\times\mathbf{V}$ is solenoidal.



"irrotational field" is owned by mathcam. [ full author list (2) | owner history (2) ]
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See Also: curl, lamellar field

Other names:  irrotational vector field, curl free field, curl-free vector field
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Cross-references: solenoidal, irrotational, functions, component, complex, real, differentiable, vector field, open set
There is 1 reference to this entry.

This is version 6 of irrotational field, born on 2002-11-13, modified 2003-10-18.
Object id is 3591, canonical name is IrrotationalField.
Accessed 5671 times total.

Classification:
AMS MSC: 26B12 (Real functions :: Functions of several variables :: Calculus of vector functions)
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