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...ystem.html Skew Coordinate System] at [[Mathworld]]</ref> 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 comp ...

...] ([[Orthogonal matrix|special orthogonal matrix]]) between two coordinate systems from a set of (weighted) vector observations. Solutions to Wahba's problem ...frame and <math>\mathbf{R}</math> is a 3 by 3 rotation matrix between the coordinate frames.<ref>The rotation <math>\mathbf{R}</math> in the problem's definitio ...

{{Short description|Geographic coordinate system}} {{broader|Geographic coordinate system}} ...

...ilinear form, the vector space may contain [[null vector]]s, non-zero self-orthogonal vectors, in which case perpendicularity is replaced with [[hyperbolic ortho ...algebra)|basis]], such as in the contexts of [[orthogonal polynomials]], [[orthogonal functions]], and [[combinatorics]]. ...

[[File:Quadriken-orth-flaech-syst.svg|thumb|upright=1.2|Orthogonal surfaces through a point]] ....svg|thumb|upright=1.2|Two planes (purple, blue) as members of a threefold orthogonal system intersect a cylinder at curvature lines (blue circle, purble line)]] ...

...''log-polar coordinates''' (or '''logarithmic polar coordinates''') is a [[coordinate system]] in two dimensions, where a point is identified by two numbers, one == Definition and coordinate transformations == ...

...], a '''fractional coordinate system''' (crystal coordinate system) is a [[coordinate system]] in which basis vectors used to describe the space are the lattice ...mathbf{a}_2</math>, and <math>\mathbf{a}_3</math> shown within a Cartesian coordinate system.]] ...

...to the image plane), which in this context is called an '''[[Orthogonality|orthogonal]] axonometry'''. ...xonometric projection]]'', which in English literature usually refers to ''orthogonal axonometry''. ...

...f confocal ellipses and hyperbolas, any ellipse intersects any hyperbola [[orthogonal]]ly (at right angles). ...ance between <math>F_1</math> and {{nobr|<math>F_2</math>),}} then in this coordinate system <math>F_1=(c,0),\; F_2=(-c,0).</math> ...

Holonomic systems can always be written in Pfaffian constraint form. ...ty of the mass can be defined in terms of an <math>x</math>-<math>y</math> coordinate system: ...

=== Coordinate transformations === ...to explain each other, because as we move along the coordinate line in one coordinate system we can use the other to describe our position. In this way Coordinat ...

...on [[proper orthogonal decomposition]], as well as other complex dynamical systems, such as biological networks.<ref>{{cite arXiv |last1=Mangan |first1=Niall ...

...e]]. Three sets of parameters can be calculated for a beam, one for each [[orthogonal]] direction, x, y, and z.<ref name="Wiedemann">{{cite book |last1=Wiedemann ...nd is also referred to as the ''longitudinal coordinate''. Two transverse coordinate axes, x and y, are defined perpendicular to the z axis and to each other.<r ...

==Symmetry and coordinate system== ...nate system]] instead of a [[spherical coordinate system]]. In a Cartesian coordinate system the [[atomic orbital]]s are often expressed as ...

...eger row and column coordinates and are distinguished with a single binary coordinate. [[Hexagonal sampling]] is the optimal approach for [[Isotropy|isotropicall ...the introduction of HECS was limited because of the lack of an efficient [[coordinate system]].<ref name="Rummelt11" /> ...

to the zenith. So given an astronomical picture with a coordinate system with a known direction In the [[Celestial coordinate system|equatorial system]] of right ascension, {{math|α}}, and declination, ...

...es. The defining characteristic of Schwarzschild chart is that the radial coordinate possesses a natural geometric interpretation in terms of the surface area a ...define this tensor is to define it in compatible local [[Atlas (topology)|coordinate charts]] and verify that the same tensor is defined on the overlaps of the ...

...com/books?id=YUz5XpLUH9gC&pg=PA182|title=Coordinate Measuring Machines and Systems|date=1995-04-10|publisher=CRC Press|isbn=978-0-8247-9581-8|language=en}}</r ...}} Rather than measuring the desired vector (in this case, [[orthogonality|orthogonal]] width), the instrument is measuring the [[hypotenuse]] of a triangle in w ...

...[stator]] currents of a [[three-phase]] [[AC motor]] are identified as two orthogonal components that can be visualized with a vector. One component defines the ...isher=EPR|author2=Pillay, P. |author3=Harley R. G. |journal=Electric Power Systems Research|volume=8|year=1984|pages=15–26|doi=10.1016/0378-7796(84)90030-0}}< ...

...cation of his [[Hamiltonian optics]] method.<ref>W. R. Hamilton, Theory of systems of rays, Part First and Part Second. Part first: Trans. Royal Irish Academy ...follow the path along the surface. The path would not return to the same z-coordinate after one circuit. Contradiction. ...