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For example, the three-dimensional Cartesian coordinates (x, y, z) is an orthogonal coordinate system, since its coordinate surfaces x = constant, y = constant, and z = constant are planes that meet at right angles to one another, i.e., are perpendicular. Orthogonal coordinates are a special but extremely common case of curvilinear coordinates.
In non-orthogonal coordinates the length of = + + is the positive square root of = (with Einstein summation convention). The six independent scalar products g ij = h i . h j of the natural basis vectors generalize the three scale factors defined above for orthogonal coordinates.
The line segments AB and CD are orthogonal to each other. In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.Whereas perpendicular is typically followed by to when relating two lines to one another (e.g., "line A is perpendicular to line B"), [1] orthogonal is commonly used without to (e.g., "orthogonal lines A and B").
Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system (,,) that generalizes the two-dimensional elliptic coordinate system. Unlike most three-dimensional orthogonal coordinate systems that feature quadratic coordinate surfaces , the ellipsoidal coordinate system is based on confocal quadrics .
A coordinate system for which some coordinate curves are not lines is called a curvilinear coordinate system. [13] Orthogonal coordinates are a special but extremely common case of curvilinear coordinates. A coordinate line with all other constant coordinates equal to zero is called a coordinate axis, an oriented line used
Geodetic coordinates P(ɸ,λ,h). Geodetic coordinates are a type of curvilinear orthogonal coordinate system used in geodesy based on a reference ellipsoid.They include geodetic latitude (north/south) ϕ, longitude (east/west) λ, and ellipsoidal height h (also known as geodetic height [1]).
Any orthogonal basis can be used to define a system of orthogonal coordinates. Orthogonal (not necessarily orthonormal) bases are important due to their appearance from curvilinear orthogonal coordinates in Euclidean spaces, as well as in Riemannian and pseudo-Riemannian manifolds.
Pages in category "Orthogonal coordinate systems" The following 20 pages are in this category, out of 20 total. This list may not reflect recent changes. ...