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- ::''For an extension to three dimensions, see [[spherical polar coordinates]].'' {{Image| Polar coordinates .png|right|250px|Two dimensional polar coordinates ''r'' and θ of vector <math>\scriptstyle \vec{\mathbf{r}}</math>}}3 KB (451 words) - 23:53, 20 February 2010
- {{Image|Spherical polar.png|right|250px|Spherical polar coordinates}} In [[mathematics]] and [[physics]], '''spherical polar coordinates''' (also known as '''spherical coordinates''') form a coordinate system for27 KB (4,267 words) - 10:14, 8 April 2023
- 12 bytes (1 word) - 14:55, 8 February 2008
- #REDIRECT [[Spherical polar coordinates]]41 bytes (4 words) - 11:53, 20 February 2008
- #Redirect [[Spherical polar coordinates]]41 bytes (4 words) - 12:29, 14 May 2008
- 124 bytes (20 words) - 10:03, 6 February 2009
- 12 bytes (1 word) - 09:52, 16 January 2008
- 116 bytes (14 words) - 03:44, 13 July 2009
- Auto-populated based on [[Special:WhatLinksHere/Polar coordinates]]. Needs checking by a human. {{r|Spherical polar coordinates}}532 bytes (68 words) - 19:37, 11 January 2010
- Auto-populated based on [[Special:WhatLinksHere/Spherical polar coordinates]]. Needs checking by a human. {{r|Polar coordinates}}1,006 bytes (129 words) - 20:33, 11 January 2010
Page text matches
- #REDIRECT [[Polar coordinates]]31 bytes (3 words) - 11:29, 22 January 2008
- #REDIRECT [[Polar coordinates]]31 bytes (3 words) - 21:55, 12 February 2009
- #REDIRECT [[Spherical polar coordinates]]41 bytes (4 words) - 11:53, 20 February 2008
- #REDIRECT [[Spherical polar coordinates]]41 bytes (4 words) - 09:44, 29 November 2009
- #Redirect [[Spherical polar coordinates]]41 bytes (4 words) - 12:29, 14 May 2008
- #REDIRECT [[Spherical polar coordinates]]41 bytes (4 words) - 09:05, 15 January 2008
- Solutions of the Laplace equation in spherical polar coordinates.102 bytes (12 words) - 05:20, 4 September 2009
- {{r|Polar coordinates}} {{r|Spherical polar coordinates}}879 bytes (114 words) - 03:09, 8 March 2024
- Auto-populated based on [[Special:WhatLinksHere/Polar coordinates]]. Needs checking by a human. {{r|Spherical polar coordinates}}532 bytes (68 words) - 19:37, 11 January 2010
- {{r|Polar coordinates}} {{r|Spherical polar coordinates}}629 bytes (80 words) - 17:36, 11 January 2010
- ::''For an extension to three dimensions, see [[spherical polar coordinates]].'' {{Image| Polar coordinates .png|right|250px|Two dimensional polar coordinates ''r'' and θ of vector <math>\scriptstyle \vec{\mathbf{r}}</math>}}3 KB (451 words) - 23:53, 20 February 2010
- {{r|Polar coordinates}}172 bytes (18 words) - 20:07, 7 March 2024
- Auto-populated based on [[Special:WhatLinksHere/Spherical polar coordinates]]. Needs checking by a human. {{r|Polar coordinates}}1,006 bytes (129 words) - 20:33, 11 January 2010
- {{r|Polar coordinates}}735 bytes (92 words) - 03:09, 8 March 2024
- {{r|Spherical polar coordinates}}801 bytes (103 words) - 15:47, 11 January 2010
- ==Polar coordinates== In connection with [[Polar coordinates|polar coordinates]], two dimensional velocity can be decomposed into radial velocity, away fr4 KB (723 words) - 00:50, 1 November 2009
- *[[Spherical polar coordinates]]631 bytes (84 words) - 06:48, 31 January 2009
- {{r|Spherical polar coordinates}}550 bytes (71 words) - 15:57, 11 January 2010
- {{r|Spherical polar coordinates}}626 bytes (80 words) - 18:22, 11 January 2010
- {{r|Spherical polar coordinates}}660 bytes (83 words) - 18:09, 11 January 2010
- {{r|Spherical polar coordinates}}774 bytes (101 words) - 18:00, 11 January 2010
- {{r|Spherical polar coordinates}}823 bytes (102 words) - 10:51, 11 January 2010
- {{r|Spherical polar coordinates}}707 bytes (90 words) - 16:01, 11 January 2010
- {{r|Spherical polar coordinates}}965 bytes (124 words) - 17:23, 11 January 2010
- {{r|Spherical polar coordinates}}955 bytes (150 words) - 03:40, 13 July 2009
- {{r|Spherical polar coordinates}}1 KB (173 words) - 05:43, 6 March 2024
- ...rdinates by <math>x=r\cos\theta</math> and <math>y=r\sin\theta</math>. In polar coordinates, Laplace's equation is: ...coordinates are obtained from the components of <math>\nabla\phi</math> in polar coordinates:7 KB (1,247 words) - 05:26, 22 November 2013
- ...c is the radius of the great circle times this angle. Write in [[spherical polar coordinates]] the [[dot product]]2 KB (419 words) - 07:31, 20 April 2024
- ...f 1/''R'' are multiplied by angular functions depending on the [[spherical polar coordinates|spherical polar]] angles of '''R''' and also by coefficients with physical ...s in terms of [[spherical harmonics]], functions which depend on spherical polar coordinates. The Cartesian approach has the advantage that no prerequisite knowledge of12 KB (1,953 words) - 04:38, 5 October 2009
- Take the origin of a [[spherical polar coordinates|spherical polar coordinate]] system in the center of symmetry of the charge ...r than the largest radius ''r''<sub>1</sub> of the shell); the [[Spherical polar coordinates#Infinitesimal surface and volume element|surface element]] is6 KB (988 words) - 17:21, 2 November 2021
- {{Image|Spherical polar.png|right|250px|Spherical polar coordinates}} In [[mathematics]] and [[physics]], '''spherical polar coordinates''' (also known as '''spherical coordinates''') form a coordinate system for27 KB (4,267 words) - 10:14, 8 April 2023
- The quantities {''r'', θ, φ} are known as [[spherical polar coordinates]] and its Jacobian is ''r''<sup>2</sup>sinθ. As an example we consider the spherical polar coordinates mentioned above. Here '''x''' = '''f'''('''t''') ≡ '''f'''(''r'', &th8 KB (1,229 words) - 08:32, 14 January 2009
- ...dinates are written as ''x''<sup>''j''</sup>. For example, for [[spherical polar coordinates]], ''x''<sup>1</sup> ≡ ''r'', ''x''<sup>2</sup> ≡ θ, ''x' ====Example: Sperical polar coordinates====13 KB (1,900 words) - 10:49, 30 November 2009
- For instance, in the case of [[spherical polar coordinates]] ''r'', θ, and φ7 KB (1,067 words) - 07:27, 23 October 2021
- ...theta; are part of the solution of the [[Laplace equation]] in [[spherical polar coordinates]]. ...ta;-dependent part of the [[Laplace operator]] ∇² in spherical polar coordinates.7 KB (1,091 words) - 06:21, 10 September 2009
- ...practical advantage that the ''z′''-axis has the usual [[spherical polar coordinates]] α ≡ φ (longitude angle) and β ≡ θ (colat ...l modification of the previous proof. We start by retrieving the spherical polar coordinates <math>\omega_2\;</math> and16 KB (2,502 words) - 12:28, 24 March 2010
- Here '''r''' has the spherical polar coordinates (''r'', θ, φ) and '''r''''3 KB (409 words) - 00:52, 4 June 2009
- ...rotor is usually described by means of [[spherical coordinates|spherical polar coordinates]], which form a coordinate system of 3-dimensional space. In the physics co ...is the [[Laplacian]]. The Laplacian is given above in terms of spherical polar coordinates. The energy operator written in terms of these coordinates is:25 KB (3,876 words) - 03:13, 1 October 2013
- ...cs''' are defined as solutions of the [[Laplace equation]] in [[spherical polar coordinates]]. There are two kinds of solid harmonic functions: the ''regular solid har Expression in spherical polar coordinates gives:16 KB (2,612 words) - 09:02, 9 February 2010
- ...all that in [[Spherical polar coordinates#Differential operators|spherical polar coordinates]]10 KB (1,681 words) - 12:22, 11 June 2009
- In [[spherical polar coordinates]] ...nant) of this transformation from [[Cartesian coordinates]] to [[spherical polar coordinates]] is14 KB (2,220 words) - 12:28, 26 October 2021
- ...symmetry, indeed, in the same kind of physical problems where spherical polar coordinates are preferred over other coordinate systems such as [[Cartesian coordinates ...onic functions appear as the solution of the Laplace equation in spherical polar coordinates, their name followed immediately. In German the functions are called "Kugel34 KB (5,282 words) - 14:21, 1 January 2011
- ====Polar coordinates==== ...at the same time extended to general motion within a plane, as shown next. Polar coordinates in the plane employ a radial unit vector '''u'''<sub>ρ</sub> and an angula37 KB (6,109 words) - 17:53, 8 October 2021
- ...lots]]. In fact, the angular parts (functions depending on the [[spherical polar coordinates|spherical polar angles]] θ and φ) are commonly plotted. The angul10 KB (1,514 words) - 19:38, 20 November 2009
- ...e functions are given in Cartesian form but, when expressed in [[spherical polar coordinates]], are functions of the colatitude angle θ and longitudinal (azimuth5 KB (822 words) - 17:36, 14 November 2007
- {{Image|Polar coordinates.png|right|150px|Polar coordinates (''R'', θ).}}27 KB (4,192 words) - 17:33, 19 August 2020
- ...''(''x'',''y'',''z'') depends on ''r'' only, when expressed in [[spherical polar coordinates]] (''r'', θ, φ). ...rque more explicitly by expressing the gradient '''∇''' in spherical polar coordinates and writing the cross product as a determinant, using that the derivatives23 KB (3,890 words) - 10:45, 11 June 2009
- ...take advantage of the complex exponential, and write complex numbers in [[polar coordinates|polar]] form20 KB (3,304 words) - 17:11, 25 August 2013
- ...take advantage of the complex exponential, and write complex numbers in [[polar coordinates|polar]] form18 KB (3,028 words) - 17:12, 25 August 2013
- ...plex number <math>a + bi</math>, it is convenient to express the number in polar coordinates <math>(r,\theta)</math> where <font style="vertical-align:20%;"><math>r = \ It can be seen from similarity with the above formula for polar coordinates that <font style="vertical-align:+10%;"><math>r = e^c</math></font> and <fo19 KB (3,039 words) - 12:51, 7 March 2023
- ...rtesian coordinates. If one expresses regular solid harmonics in spherical polar coordinates, the cosine-type functions contain the factor cos |''m''| φ and the sin15 KB (2,490 words) - 12:23, 19 April 2009
- where ''r'', θ, and φ are [[spherical polar coordinates]] of a point with respect to a system of axes centered on the central ion.15 KB (2,390 words) - 10:11, 5 February 2010
- where θ and φ are the [[spherical polar coordinates|spherical polar angles]] of '''r''' with respect to a coordinate system in ...interaction this is most easily proved by integrating over the [[spherical polar coordinates|spherical polar angles]] of the dipole vector, while using the volume eleme56 KB (8,720 words) - 07:31, 20 April 2024
- Indeed, in terms of [[spherical polar coordinates]] the operator is,16 KB (2,632 words) - 04:33, 23 September 2021
- Using polar coordinates with the magnitude of the radius to the roots given by |''s''| (See figure)20 KB (3,032 words) - 09:34, 9 October 2013
- * [[Polar coordinates]] * [[Spherical polar coordinates]]25 KB (3,396 words) - 13:29, 2 April 2024
- the operator ∇² expressed in [[spherical polar coordinates]], can be written as19 KB (2,981 words) - 18:31, 3 November 2021