Spherical coordinates: Difference between revisions
From Glossary of Meteorology
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|Display title=spherical coordinates | |||
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|Meaning=(''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. | |||
|Explanation=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. | |||
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Latest revision as of 06:46, 30 March 2024
(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.
