Curl: Difference between revisions
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imported>Paul Wormer (New page: Given a 3-dimensional vector field '''F'''('''r'''), the '''curl''' (also known as '''rotation''') of '''F'''('''r''') is the differential vector operator nabla (symbol '''&na...) |
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Revision as of 12:12, 15 April 2009
Given a 3-dimensional vector field F(r), the curl (also known as rotation) of F(r) is the differential vector operator nabla (symbol ∇) applied to F. The application of ∇ is in the form of a cross product:
where ex, ey, and ez are unit vectors along the axes of a Cartesian coordinate system of axes.
As any cross product the curl may be written in a few alternative ways.
As a determinant (evaluate along the first row):
As a vector-matrix-vector product
In terms of the antisymmetric Levi-Civita symbol
(the component of the curl along the Cartesian α-axis).