Sometimes general curvilinear coordinates are convenient, as in high-deformation continuum mechanics, or even necessary, as in general relativity.
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The EP's cover art is a estrasolar system coordinates, formatted curvilinear coordinates in grey with the color blue as a background.
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Often the metric is diagonal, as is the case for orthogonal coordinates ( see line element ), but not in general curvilinear coordinates.
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With this simple definition of a curvilinear coordinate system, all the results that follow below are simply applications of standard theorems in differential topology.
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Another example, Centrifugal force ( planar motion ) discusses a variety of coordinate systems, including the arc-length and curvilinear coordinate systems.
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In geometry, "'curvilinear coordinates "'are a coordinate system for Euclidean space in which the coordinate lines may be curved.
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Let dq 1, dq 2 and dq 3 denote the corresponding infinitesimal changes in curvilinear coordinates q 1, q 2 and q 3 respectively.
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The covariant and contravariant basis vectors types have identical direction for orthogonal curvilinear coordinate systems, but as usual have inverted units with respect to each other.
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Well-known examples of curvilinear coordinate systems in three-dimensional Euclidean space ( "'R "'3 ) are spherical polar coordinates.
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Often a more accurate representation of the potential " V " is obtained by the use of internal curvilinear coordinates, so-called valence coordinates.