A system of skew coordinates is a curvilinear coordinate system where the coordinate surfaces are not orthogonal,[1] in contrast to orthogonal coordinates.
Skew coordinates tend to be more complicated to work with compared to orthogonal coordinates since the metric tensor will have nonzero off-diagonal components, preventing many simplifications in formulas for tensor algebra and tensor calculus. The nonzero off-diagonal components of the metric tensor are a direct result of the non-orthogonality of the basis vectors of the coordinates, since by definition:[2]
where is the metric tensor and the (covariant) basis vectors.
These coordinate systems can be useful if the geometry of a problem fits well into a skewed system. For example, solving Laplace's equation in a parallelogram will be easiest when done in appropriately skewed coordinates.
^Skew Coordinate System at Mathworld
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Lebedev, Leonid P. (2003). Tensor Analysis. World Scientific. p. 13. ISBN 981-238-360-3.
of skewcoordinates is a curvilinear coordinate system where the coordinate surfaces are not orthogonal, in contrast to orthogonal coordinates. Skew coordinates...
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In algebra, a division ring, also called a skew field, is a nontrivial ring in which division by nonzero elements is defined. Specifically, it is a nontrivial...
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then the containment of diagrams means that μi ≤ λi for all i. The skew diagram of a skew shape λ/μ is the set-theoretic difference of the Young diagrams...
According to Zang, numerical simulation can be aided by considering the skew-symmetric form for the advection operator. 1 2 u ⋅ ∇ u + 1 2 ∇ ⋅ ( u u )...
Two skew lines (pipes, perhaps) in general positions in order to determine the location of their shortest connector (common perpendicular) Two skew lines...
\\&=\left(R-R^{\mathsf {T}}\right)\mathbf {u} \end{aligned}}} Since (R − RT) is a skew-symmetric matrix, we can choose u such that [ u ] × = ( R − R T ) . {\displaystyle...
returns distributions, however, tend to exhibit fat-tails (kurtosis) and skew. Modelling the volatility smile is an active area of research in quantitative...
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zero. The A, D, B and E parameters are sometimes named "x-scale", "y-skew", "x-skew" and "y-scale". A better description of the A, D, B and E parameters...
mean a skew quadrilateral. A skew quadrilateral together with its diagonals form a (possibly non-regular) tetrahedron, and conversely every skew quadrilateral...
originally described by Cayley (1846), the Cayley transform is a mapping between skew-symmetric matrices and special orthogonal matrices. The transform is a homography...
Glacier. Named features, from southwest to northeast, include Vishniac Peak, Skew Peak, Parker Mesa, Dykes Peak, Heaphy Spur, Detour Nunatak and Sperm Bluff...
Poisson's ratio and x {\displaystyle x} and y {\displaystyle y} are coordinates. These equations suggest a vertically oriented dumbbell of stresses surrounding...
within Japan has an average age of 33 years, and a male-to-female ratio that skews 40:60. The series' twelfth collected volume was given a first printing of...
focal length in terms of distance. γ {\displaystyle \gamma } represents the skew coefficient between the x and the y axis, and is often 0. u 0 {\displaystyle...
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