Difference between revisions of "Spherical coordinates"

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<div class="definition"><div class="short_definition">(<br/>''Also called'' polar coordinates in space, geographical coordinates.) A system  of [[curvilinear coordinates]] in which the position of a point in space is designated by its distance  ''r'' from the origin or pole along the [[radius vector]], the angle &#x003c6; between the radius vector and a  vertically directed [[polar axis]] called the [[cone angle]] or colatitude, and the angle &#x003b8; between the  plane of &#x003c6; and a fixed [[meridian]] plane through the polar axis, called the [[polar angle]] or longitude.</div><br/> <div class="paragraph">A constant-amplitude radius vector '''r''' confines a point to a sphere of radius ''r'' about the pole.  The angles &#x003c6; and &#x003b8; serve to determine the position of the point on the sphere. The relations  between the spherical coordinates and the [[rectangular Cartesian coordinates]] (''x'', ''y'', ''z'') are ''x'' =  ''r'' cos &#x003b8; sin &#x003c6;; ''y'' = ''r'' sin &#x003b8; sin &#x003c6;; ''z'' = ''r'' cos &#x003c6;.</div><br/> </div>
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<div class="definition"><div class="short_definition">(''Also called'' polar coordinates in space, geographical coordinates.) A system  of [[curvilinear coordinates]] in which the position of a point in space is designated by its distance  ''r'' from the origin or pole along the [[radius vector]], the angle &#x003c6; between the radius vector and a  vertically directed [[polar axis]] called the [[cone angle]] or colatitude, and the angle &#x003b8; between the  plane of &#x003c6; and a fixed [[meridian]] plane through the polar axis, called the [[polar angle]] or longitude.</div><br/> <div class="paragraph">A constant-amplitude radius vector '''r''' confines a point to a sphere of radius ''r'' about the pole.  The angles &#x003c6; and &#x003b8; serve to determine the position of the point on the sphere. The relations  between the spherical coordinates and the [[rectangular Cartesian coordinates]] (''x'', ''y'', ''z'') are ''x'' =  ''r'' cos &#x003b8; sin &#x003c6;; ''y'' = ''r'' sin &#x003b8; sin &#x003c6;; ''z'' = ''r'' cos &#x003c6;.</div><br/> </div>
 
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Latest revision as of 15:11, 20 February 2012



spherical coordinates

(Also called polar coordinates in space, geographical coordinates.) A system of curvilinear coordinates in which the position of a point in space is designated by its distance r from the origin or pole along the radius vector, the angle φ between the radius vector and a vertically directed polar axis called the cone angle or colatitude, and the angle θ between the plane of φ and a fixed meridian plane through the polar axis, called the polar angle or longitude.

A constant-amplitude radius vector r confines a point to a sphere of radius r about the pole. The angles φ and θ serve to determine the position of the point on the sphere. The relations between the spherical coordinates and the rectangular Cartesian coordinates (x, y, z) are x = r cos θ sin φ; y = r sin θ sin φ; z = r cos φ.