Talk:Spherical coordinate system

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Previous discussions pertaining to the old article have been archived to Talk:Spherical coordinate system/Archive. --Carl (talk|contribs) 01:25, 18 September 2006 (UTC)

Contents

[edit] Printing

I printed out this page and the images came out as black squares. get new images, these ones are garbage! —Preceding unsigned comment added by 62.136.133.147 (talk) 08:26, 5 May 2008 (UTC)

[edit] Elements

This needs to be fixed, its why is there no info for spherical coordinates like they have for cylindrical, such as dV and dS:

(From cylindrical article) Line and volume elements

In many problems involving cylindrical polar coordinates, it is useful to know the line and volume elements; these are used in integration to solve problems involving paths and volumes.

The line element is dl = dr\,\mathbf{\hat r} + r\,d\theta\,\boldsymbol{\hat\theta} + dz\,\mathbf{\hat z}.

The volume element is dV = r\,dr\,d\theta\,dz.

The gradient is \nabla = \mathbf{\hat r}\frac{\partial}{\partial r} + \boldsymbol{\hat \theta}\frac{1}{r}\frac{\partial}{\partial \theta} + \mathbf{\hat z}\frac{\partial}{\partial z}.

Even mathworld has dS......

I have added surface and volume. –Pomte 11:13, 10 April 2007 (UTC)

[edit] American convention

This article itself states that the international recommended standard for spherical polars is r, ϑ, φ for distance, zenith, and azimuth. If this is so, why use the american convention for the rest of the article? Shouldn't we use the international convention on the basis of the international applicability of the article?

In the diagram, the "r" length isn't the "r" mentioned in the text right? It's confusing that it was labelled r.

Perhaps there should be different diagrams for the different coordinate systems. Unfortunately, someone has to draw them. Shinobu 10:15, 16 November 2006 (UTC)

The symbols in the text and in the figure don't match. for instance: the azimuth angle in the text is referred to as θ, but the same symbol is taken for the polar angle in the diagramm. The polar angle in the text is a small phi (φ) and a capital phi (Φ) is taken for the azimuth angle in the figure. That is very confusing. (RolandRo 12:37, 11 January 2007 (UTC))

I have about the same problem, but all phi:s in the text are small (lowercase). I think it's the weird TeX small phi, that looks very much like a capital phi. It's a matter of different fonts. Rursus 18:04, 4 February 2007 (UTC)
I changed all φ to Φ to avoid confusion. TeX is showing the uppercase phi. If someone feels φ should be used instead, please revert all instances of them, even in TeX. –Pomte 11:13, 10 April 2007 (UTC)
But TeX isn't showing a capital phi \Phi\,, it's showing a lowercase phi \phi\,. If you want to use the other TeX lowercase phi \varphi\,, that's OK, but please don't use uppercase - the convention is to use lowercase (as in the diagram). --Zundark 11:26, 10 April 2007 (UTC)
Ugh, sorry, I got confused. Should I revert despite visual discrepancy? If the \varphi symbol is indeed convention, I'll convert all \phi to \varphi. I've seen \phi more often than \varphi, but that's no good indicator. –Pomte 11:37, 10 April 2007 (UTC)
I've already reverted. (My revert also reverted your later edit - you can restore that, of course.) I think \phi is more usual than \varphi for this purpose. The visual discrepancy depends on what font you are using - there's no way to fix it for everyone (except by doing everything in TeX), so I think we have to live with it. --Zundark 11:43, 10 April 2007 (UTC)


I do not understand the statement that the so-called American notation makes things more compatible with polar or cylindrical coordinates. On the contrary: using the notation in the article (with ranges indicated for φ,θ), cylindrical coordinates would be of the form (ρ,z,θ). Whereas starting with the notation (r,θ) (or (ρ,θ)) for polar coordinates, cylindrical and spherical coordinates are obtained by simply making the coordinate pair a coordinate triple (with the caveat that ρ would be \rho=\sqrt{x^2+y^2} rather than \rho=\sqrt{x^2+y^2+z^2} with both cylindrical or polar, i.e., the projection onto the xy-plane).

It seems to me that the debate is more between how physicists and mathematicians use different notations, rather than between an American notation and a notation elsewhere. Looking at three calculus textbooks written by reputable American authors, all use the (length,azimuth,zenith) notation. Since I also read French, I took a look at the literature, and there the issue is the same: mathematicians tend to write (length,azimuth,zenith), physicists tend to write (length,zenith,azimuth). The idea is that, making a broad generalizing statement, in mathematics we do not really work with spherical coordinates, they are merely a tool, just another change of basis. Whereas in physics, they are commonly used as a coordinate system proper, in which case it is important that such things as the right hand rule applies, because it makes computations easier to manage. Jarino1 18:44, 9 July 2007 (UTC)

The difference isn't in the placement of the coordinates; it's which letters are used for which coordinates. In mathematics θ is used for the azimuthal angle and φ is used for the zenith angle. Whereas in physics θ is used for the zenith angle and φ is used for the azimuthal angle. This should be made clear on the article.
I myself have studied under the mathematical convention in the United States and it is always denoted (ρ, θ, φ); so I disagree with the placement of the coordinates on the article; but this is a separate issue.
The mathematical convention is more compatible with polar and cylindrical coordinates because on the xy-plane, the azimuthal angle (which is denoted by θ) is the same as the polar angle used in polar and cylindrical coordinates (which is also denoted by θ). --Spoon! 21:32, 12 September 2007 (UTC)

[edit] Longitude

I don't think this statement is correct:

The longitude is the azimuth angle shifted 180° from θ to give a domain of -180° ≤ θ ≤ 180°.

Assuming the x axis goes from the center of the Earth through the equator at 0 deg longitude, then I believe the correct wording is:

The longitude is the azimuth angle but for 180° < θ < 360°, subtract 360° so that -180° < longitude ≤ 180°.

Actually, it would probably be more correct to bring up East and West when talking about longitude, but in any case, saying a shift by 180 deg is wrong (unless the x axis is supposed to point through the 180 deg longitude point which I doubt) DaraParsavand 19:01, 18 January 2007 (UTC)

You're right, it's only a shift on half the values. I think it's pointless to discern whether any shift starts at θ = 0° or θ = 90° or anywhere else, so I've left it as an east-west distinction. –Pomte 11:37, 10 April 2007 (UTC)


[edit] Angles

Radians should be used, not degrees. Jarino1 18:55, 9 July 2007 (UTC)

[edit] Comparsion with Euler angles

Conventional spherical coordinates as described in this article are a combination of rotations along the z and y axes. However, Euler angles are most commonly combinations of z and y rotations. Maybe someone could mention a few words about this issue? I was a bit confused by this difference. I propose to discuss this at Talk:Euler angles. Han-Kwang (t) 10:50, 4 December 2007 (UTC)

[edit] Angle symbols swapped?

Compared to the first diagram, has the theta and phi swapped when it gets to this point

Conversely, Cartesian coordinates may be retrieved from spherical coordinates by:

{x}=r \, \sin\varphi \, \cos\theta \quad
{y}=r \, \sin\varphi \, \sin\theta \quad
{z}=r \, \cos\varphi. \quad

137.205.76.233 (talk) 18:34, 9 March 2008 (UTC)

I also think that this is the case. I have been working in OpenGL with cartesian and spherical coordinates and the current symbols are definately swapped. Z must be invariant with θ. At least my math classes nomiated them so. -67.171.122.139 (talk) 18:23, 13 May 2008 (UTC)

[edit] θ is referred to elevation

φ is referred to as the azimuth and θ is referred to elevation, right? —Preceding unsigned comment added by 131.180.34.78 (talk) 13:01, 22 May 2008 (UTC)