Cylindrical coordinates: Difference between revisions

Latest revision as of 14:01, 20 February 2012

cylindrical coordinates

(Also called cylindrical polar coordinates, circular cylindrical coordinates.) A system of curvilinear coordinates in which the position of a point in space is determined by 1) its perpendicular distance from a given line, 2) its distance from a selected reference plane perpendicular to this line, and 3) its angular distance from a selected reference line when projected onto this plane.

The coordinates thus form the elements of a cylinder, and, in the usual notation, are written r, θ, and z, where r is the radial distance from the cylinder's z axis, and θ is the angular position from a reference line in a cylindrical cross section normal to the z axis. The relations between the cylindrical coordinates and the rectangular Cartesian coordinates (x, y, z) are x = r cos θ, y = r sin θ, z = z.
See also polar coordinates.

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-<div class="definition"><div class="short_definition">(<br/>''Also called'' cylindrical polar coordinates, circular cylindrical coordinates.)  A system of [[curvilinear coordinates]] in which the position of a point in space is determined by  1) its perpendicular distance from a given line, 2) its distance from a selected reference plane  perpendicular to this line, and 3) its angular distance from a selected reference line when projected  onto this plane.</div><br/> <div class="paragraph">The coordinates thus form the elements of a cylinder, and, in the usual notation, are written  ''r'', &#x003b8;, and ''z'', where ''r'' is the radial distance from the cylinder's ''z'' axis, and &#x003b8; is the angular position  from a reference line in a cylindrical [[cross section]] normal to the ''z'' axis. The relations between  the cylindrical coordinates and the [[rectangular Cartesian coordinates]] (''x'', y, ''z'') are ''x'' = ''r'' cos &#x003b8;,  ''y'' = ''r'' sin &#x003b8;, ''z'' = ''z''. <br/>''See also'' [[polar coordinates]].</div><br/> </div>
+<div class="definition"><div class="short_definition">(''Also called'' cylindrical polar coordinates, circular cylindrical coordinates.)  A system of [[curvilinear coordinates]] in which the position of a point in space is determined by  1) its perpendicular distance from a given line, 2) its distance from a selected reference plane  perpendicular to this line, and 3) its angular distance from a selected reference line when projected  onto this plane.</div><br/> <div class="paragraph">The coordinates thus form the elements of a cylinder, and, in the usual notation, are written  ''r'', &#x003b8;, and ''z'', where ''r'' is the radial distance from the cylinder's ''z'' axis, and &#x003b8; is the angular position  from a reference line in a cylindrical [[cross section]] normal to the ''z'' axis. The relations between  the cylindrical coordinates and the [[rectangular Cartesian coordinates]] (''x'', y, ''z'') are ''x'' = ''r'' cos &#x003b8;,  ''y'' = ''r'' sin &#x003b8;, ''z'' = ''z''. <br/>''See also'' [[polar coordinates]].</div><br/> </div>
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