Talk:Del in cylindrical and spherical coordinates

message: Hi, I think this page is a very useful resource. I would like to know what happened to pdf version of it.  —Preceding unsigned comment added by 201.233.89.229 (talk) 16:03, 13 January 2008 (UTC)
thread_title:  The pdf version 

message: uhh, I'm fairly sure you have theta and phi reversed from their standard usages (i.e., standard usage is that theta is the angle in the xy plane).  certainly the main wikipedia article on coordinate systems indicates theta is in the xy plane (though the article also mentions inconsistency between American usage and (rest of the world?) regarding phi being latitude versus colatitude.
I am indeed an American, and I've tended to think that phi == colatitude is a mistake all in all, but has the theta/phi role reversal happened everywhere else?
--Ethelred 18:59, 30 August 2006 (UTC)
replies: text: These nabla formulas are consistent with taking:
* r ≥ 0  is the distance from the origin to a given point P.
* 0 ≤ θ ≤ 180° is the angle between the positive z-axis and the line formed between the origin and P.
* 0 ≤ φ ≤ 360° is the angle between the positive x-axis and the line from the origin to the P projected onto the xy-plane.
(I have checked them with the ones in the famous book by J.D.Jackson, Classical Electrodynamics)
This is the "non-american" convention. I think this should be stressed somewhere, since the wikipedia article on spherical coordinates uses the amercan one instead. I think it would be very useful to put some small image in the "Definition of coordinates" row.
Luca Naso 09:07, 19 March 2007 (UTC)

text: The present notation is consistent with the (new) definition at the top of the page, and with the spherical coordinates article. PAR (talk) 05:26, 14 April 2008 (UTC)
thread_title:  spherical coordinates formula wrong? 

message: I think that \varphi is more of a norm in mathematical notation when writing in spherical coordinates than \phi is.  Is there some decided policy about this?  Has it been discussed?
:It's the same thing, the only difference is the size of the letters. Admiral Norton 13:29, 14 October 2007 (UTC)
replies: text: That may depend on your font. In TeX's Computer Modern, \phi and \varphi are decidedly different.  —Preceding unsigned comment added by 18.80.7.48 (talk) 19:03, 23 December 2008 (UTC)
thread_title: \phi or \varphi?

message: Please correct the definition of a vector \mathbf{A} in cylindrical and spherical coordinates. In both cases the angular local basis vectors are orthogonal to \mathbf{A} itself. For sperical coordinates this means that \mathbf{A} = A_\rho \boldsymbol{\hat \rho}. The radial basis vector is parallel to \mathbf{A} and is itself a function of the angular components : 
 
\boldsymbol{\hat \rho} = \boldsymbol{\hat \rho}(A_\phi,A_\theta)
:\mathbf{A} is a vector field and we're interested in its properties at some arbitrary point \boldsymbol r = (r, \theta, \phi) in spherical coordinates. The immediate implication is that \boldsymbol r = r \boldsymbol {\hat r}. There is no relation between \mathbf{A} and \boldsymbol {\hat r} however. Your function is actually: \boldsymbol {\hat r} = \boldsymbol {\hat r}(\theta, \phi), whereas \mathbf{A}=(A_r, A_\theta, A_\phi) in spherical coordinates.
:Klaas van Aarsen 17:14, 12 May 2006 (UTC)
thread_title:  vectors in curvlinear coordinates 

message: I changed a sin^2 term to a sin term in the vector laplacian, spherical coordinates. The only other statement of the vector laplacian I can find is Weissteins math world, and it agrees with the change. I have a mathematica program that gives faulty answers using the old version, correct answers using the new (and Weisstein) version. If anyone has a reference please check, just to make sure. This is one page that should have no errors. PAR (talk) 22:31, 9 December 2007 (UTC)
thread_title:  Vector Laplacian - spherical coordinates 

message: I´ve got a Question about the notation what means the wedge over the coordinates at A_\rho\boldsymbol{\hat \rho} + A_\phi\boldsymbol{\hat \phi} + A_z\boldsymbol{\hat z} ? I searched at the linked pages , but i didn´t find a explanation. The German version of the article use also this notation and doesn´t linked it too...  Perhaps you can link the definition in the article or explain it. 
(sorry for my english...) A2r4e1 (talk) 23:06, 9 December 2007 (UTC)
replies: text: Hi - it means a unit vector in that direction (e.g. \boldsymbol{\hat r} is a vector pointing in the direction of increasing r and its length is unity. PAR (talk) 06:27, 10 December 2007 (UTC)
replies: text: Ah ok. Thanks. A2r4e1 (talk) 20:15, 10 December 2007 (UTC)
thread_title:  Question about notation 

message: I've stumbled upon this page - it's the reason for which Wikipedia was created!  I'd nominate it for featured article if I thought they would let it pass.76.173.17.102 (talk) 06:11, 16 December 2007 (UTC)
thread_title:  Gorgeous 

message: Please someone add the basic rules on how to transform the various formulae from one another. Bh3u4m (talk) 12:17, 18 December 2007 (UTC)
thread_title:  Transformation 

message: In this page 's' is used to represent the radial vector, which is a convention I have never seen.  Wikipedia's article on Cylindrical_coordinates specifies using \rho, which is apparently in agreement with ISO_31-11.  All of the math and electromagnetics books I've used (in the US), use simply 'r'.  It seems to me that it should be changed either to '\rho' or 'r'.  
Mattskee (talk) 01:03, 1 October 2008 (UTC)
thread_title:  Cylindrical coordinates: S as the radial vector? 

message: It would be great if the biharmonic operator is there as well. Otherwise, it is a great page.
JiriVejrazka (talk) 15:38, 26 August 2009 (UTC)
thread_title:  Biharmonic operator 

message: The notation isn't consistent when looking from the top of the table downwards..
: What exactly is the inconsistency? PAR (talk) 20:58, 4 February 2011 (UTC)
thread_title:  Inconsistent variables 

message: Hi
Wondering whether this page could be generated automatically by a computer algebra software such as ginac or maxima. This would allow to generate it for different coordinate system conventions. Of course, this is a project somewhat different from wikipedia per se. Anyone interested?
Josce (talk) 14:42, 25 July 2011 (UTC)
replies: text: This page lists a few maxima scripts that generate some of the differential operators. I add it as an external link.Josce (talk) 10:29, 26 July 2011 (UTC)
thread_title:  Automatic generation of this table 

message: Looks like it's wrong. Used it for homework and got the wrong answer. Wolfram suggests this.  — Preceding unsigned comment added by 129.97.150.205 (talk) 18:56, 28 September 2011 (UTC)
replies: text: I just took a quick look and as far as I can tell the result given by Wolfram is the same as the one given by Wikipedia.  Yes they have expressed it a bit differently, but that doesn't make it wrong.  The two are completely equivalent.  If you disagree, perhaps you can point out which term you think is wrong?  TDL (talk) 18:31, 14 September 2013 (UTC)
replies: text: You are absolutely right!  I was careless and didn't notice that they are neatly written in terms of the scalar laplacian.  — Preceding unsigned comment added by 129.31.244.87 (talk) 22:48, 25 September 2013 (UTC)
thread_title:  Vector Laplacian for Cylindrical 

message: I was deriving all of these formulae myself and just got to doing the "r" component of the vector laplacian.  I arrived at the same formula shown in the Wolfram article.  (Incidentally, their article also lacks proper rigour: the index for a vector component should be up; not down.  Further, if the covariant derivative is defined using the Christoffel Connection, as you need to to derive these formulae, then the covariant derivative of the metric is zero.)  — Preceding unsigned comment added by 129.31.244.79 (talk) 18:00, 14 September 2013 (UTC)
replies: text: I just took a quick look and as far as I can tell the result given by Wolfram is the same as the one given by Wikipedia.  Yes they have expressed it a bit differently, but that doesn't make it wrong.  The two are completely equivalent.  If you disagree, perhaps you can point out which term you think is wrong?  TDL (talk) 18:31, 14 September 2013 (UTC)
replies: text: You are absolutely right!  I was careless and didn't notice that they are neatly written in terms of the scalar laplacian.  — Preceding unsigned comment added by 129.31.244.87 (talk) 22:48, 25 September 2013 (UTC)
thread_title:  It most certainly <i>is</i> wrong 

message: Hi,
I think that this link will prove very useful:
http://www-solar.mcs.st-and.ac.uk/~alan/MT3601/Fundamentals/node15.html
Such a wonderful simplicity must not be ignored!
Should a new section have to be included?
Thanks for the good work, -Aa.  — Preceding unsigned comment added by 193.205.210.33 (talk) 18:49, 21 October 2011 (UTC)
replies: text: Hi. Just wanted to say thanks for sharing this. Helped me a lot. Dalba (talk) 16:30, 12 July 2015 (UTC)
thread_title:  General Orthogonal Coordinates 

message: Since this also includes parabolic coordinates, perhaps the name should be changed to "Del in curvilinear coordinates" or something similar.  — Preceding unsigned comment added by Xooll (talk • contribs) 23:30, 6 May 2012 (UTC)
thread_title:  Change of name? 

message: Just an idea, it's something I came here to look for (this time). (This is an amazing page otherwise, we all know that!)  — Preceding unsigned comment added by 88.96.19.110 (talk) 00:27, 6 November 2013 (UTC)
replies: text: The determinant of the Jacobian is effectively already listed as the differential volume dV. Klaas van Aarsen (talk) 19:26, 31 March 2014 (UTC)
thread_title:  How about a row for the Jacobian of each coordinate system (wrt Cartesians) 

message: In the Notes section, I made the references to "domain" and "image" into links to their respective pages.  (See .)  These terms have multiple meanings, however, and although I'm pretty sure I linked to the correct ones, I request one of the main authors to verify that I have.Christopher.ursich (talk) 05:59, 3 March 2014 (UTC)
replies: text: Looks fine to me.--Salix alba (talk): 07:16, 3 March 2014 (UTC)
thread_title:  Links for "domain" and "image" 

message: I edited and then reverted the area element as a sum of three differentials, for example,
(1)   d\vec A = dxdy\hat z + dydz\hat x + dzdx\hat y
My first edit removed the plus signs because this is not how the surface integral is usually set up.  I had second thoughts when I realized that nevertheless, d\vec A, as shown above, is a vector area element. The usual way is to use a cross product and a surface defined in parametric form:
(2)   d\vec A = d\vec\ell_\alpha\times d\vec\ell_\beta =
(dy_\alpha dz_\beta -    dz_\alpha dy_\beta)\hat x +
(dz_\alpha dx_\beta -    dx_\alpha dz_\beta)\hat y +
(dx_\alpha dy_\beta -    dy_\alpha dx_\beta)\hat z 
We can now "force" (1) to occur with 
(3)     dz_\alpha =0\qquad dz_\beta<0\qquad dx_\beta=0
In this context, writing (1) is putting the proverbial round peg into a square hole.  I don't correct WP pages unless I am 100% sure I am right, but seeing (1) makes me uneasy. Students need know only the most basic surface integrals to learn Gauss' and Maxwell/Ampere's laws of electromagnetism.  For that population, at least, it is better to state that:
d\vec A_3 = dxdy\hat z 
d\vec A_1 = dydz\hat x 
d\vec A_2 = dzdx\hat y
are all vector area elements.  With this one possible blemish, this seems to be an excellent page. --guyvan52 (talk) 20:53, 7 June 2014 (UTC)
thread_title:  Qualms about the area elements 

message: Verification of all the equations on this table is a massive problem.  Not only must we find sources, but those sources are meaningless unless someone carefully verifies that each equation is correct.  Then there is the problem of the surface element described above. Another problem is that each piece of information is inside a table, and putting footnotes inside tables is tedious -- we need to check every single formula, and hence every single box in the grid. So I thought it would be fun to make this a Wikiversity learning project.  If you go to v:Coordinate systems/Derivation of formulas, you will see that I pulled everything out of the table and made it sequential (took me hours).  Red links indicate unverified sections, and all but this one section is currently redlinked.  I put my concern about the surface element there.  Please come to Wikiversity and help sort this out.  This page gets over 10,000 hits a month. So we must be certain that it is right. I will pull out my NRC and verify some of the more well known identities in a few days.  The Wikiversity project asks students to either find references or derive the equations (both is best).--guyvan52 (talk) 05:37, 11 June 2014 (UTC)
thread_title:  The wikiversity link, 

message: I noticed that the azimuthal angle symbol here is different than the one in the page Spherical coordinate system, It would probably take a bit of work to edit (I am probably not qualified as I struggle with Latex or wiki's version of it) It should be consistent, especially for those just learning the subject and may become confused
Pjbeierle (talk) 05:56, 8 September 2014 (UTC)
replies: text: Done.  Changed \phi to \varphi. --Fylwind (talk) 18:35, 14 September 2015 (UTC)
thread_title:  lack of notation consistency with other articles 

message: Perhaps this is an unfamiliar convention for the unit vectors, but it seems like the two terms in the numerator of the definition of z-hat in spherical coordinates should be subtracted not added? If θ goes from the positive z axis down to the negative axis, then wouldn't z-hat have a negative component in the theta-hat direction? Sorry for not putting in the proper symbols, new here. Edit: this is in the "source coordinates" table. And4e (talk) 02:22, 27 November 2015 (UTC)
thread_title:  Conversion of z unit vector into spherical coordinates 

message: Truly an excellent page. Are there any suggestions now that it still contains errors? if it is agreed that it doesn't I suggest that the page be fully protected against vandalism like that that occurred on the Spherical Harmonics page where some 4s were changed to 6s, a change not readily identified. Xxanthippe (talk) 04:00, 11 August 2017 (UTC)
thread_title: Errors?

message: Xxanthippe is correct on two accounts:
#This an excellent page that could almost become the "industry standard"  for those seeking a quick and convenient, but also reliable access to these equations.
#ALL errors need to be removed. To understand my (and Xxanthippe's) concern, look at this recent IP edit: https://en.wikipedia.org/w/index.php?title=Del_in_cylindrical_and_spherical_coordinates&type=revision&diff=821614653&oldid=815379593 
This might be an appropriate project for the WikiJournal of Science.  I am affiliated with that Journal but not very active at the moment.  But I am active in a project that would greatly benefit from a wiki-version of a trusted source.  This equation sheet for an OpenStax  textbook might evolve into a formula students would use during exams.  The current draft includes a permalink to a trusted wiki so that students could also use it as a study guide.  I discovered the aforementioned problem with IP edit while working on Volume 2 of this project.  I consider that IP edit to be both plausible and questionable, and had no idea which permalink to include in the current draft of the formula sheet.  
Is there any way we could get a team of Wikipedia "Del" experts to fine-tooth comb these equations?  It would be a large and time-consuming project that would require many people and many person-hours, something that would probably require a grant to fund.  OpenStax is a large and successful effort. The WikiJournal of Science is a struggling "startup". I have only a little experience in grant seeking, but I am intrigued by what a joint Wikipedia/WikiJournal/OpenStax effort could accomplish. --Guy vandegrift (talk) 15:43, 17 February 2018 (UTC)
thread_title: I agree with the above and would like to respond

message: In every conversion table except for the first one (titled "Coordinate conversions"), the identity conversions (e.g. Cartesian to Cartesian) are omitted. Shouldn't the first table also omit them?  — Preceding unsigned comment added by Sir Patoot (talk • contribs) 13:11, 6 March 2021 (UTC)
thread_title:  Futile Coordinate Conversion 

message: I’m pretty sure theta and phi are flipped in comparison to the rest of the expressions in the table — Preceding unsigned comment added by Sandro729 (talk • contribs) 12:43, 3 December 2021 (UTC)
thread_title:  Laplacian in spherical coordinates 

message: I propose to change the page name to "Del in Cartesian, cylindrical and spherical coordinates" as more descriptive than the present title. Anyone have any thoughts?
Davidofithaca (talk) 03:48, 5 November 2022 (UTC)
thread_title:  Change of Page Name 

message: The table of conversions with "from" and "to" conversions is transposed out of order. For example, if you were converting from the cartesian "x + y + z" to spherical coordinates you would use the top right panel, however currently the table lists this top right panel as from spherical to cartesian. The table needs to be transposed to fix this, or just switch the from and to words. Braden Yonano (talk) 02:05, 21 November 2022 (UTC)
thread_title:  Table of Conversions Needs to be "Transposed" 

message: The formulas for the "vector gradient" are, in fact, the formulas for the vector differential, dA, which is the transpose of ∇A, i.e., dA(v) = (v·∇)A = v·(∇A). Indeed, the matrix of the gradient of a vector field in Cartesian coordinates as given in the table is the Jacobian matrix, which is the the matrix of dA. See Vector calculus identities. Since this article is about the del operator, not the differential operator, the formulas should be replaced by the correct ones. The terms of each formula are judiciously arranged in the form of a matrix corresponding to the matrix of the tensor. To preserve this form pairs of corresponding off-diagonal coefficients should be transposed. Since I am not competent to do this myself, I leave the task to somebody else. Zophar (talk) 19:15, 13 June 2023 (UTC)
thread_title:  Formulas for vector gradient 

message: One of my most visited webpages, thanks! I think adding a footnote about how the tensor divergence results in the first index being contracted would be useful information for future users. That is, the expressions are e^\alpha \partial_\alpha T^{\alpha \beta} e_{\alpha} e_{\beta}, where e_\alpha is the unit vector of the coordinate system. Uhroon (talk) 11:46, 17 April 2024 (UTC)
replies: text: Evidently you are trying to emphasize that in this article the tensor divergence is defined (in rectangular Cartesian coordinates) as \mathbf{e}_i \cdot \partial_i \mathbf{T}, not \partial_i \mathbf{T} \cdot \mathbf{e}_i, and the vector gradient is defined as \partial_i \mathbf{A} \otimes \mathbf{e}_i, not \mathbf{e}_i \otimes \partial_i \mathbf{A}, but you have not made your points clear, either here or in your notes. For more on this, see my post here, directly above yours, and also Vector gradient and Tensor divergence. The tensor curl (not included in the article) may be defined as either \mathbf{e}_i \times \partial_i \mathbf{T} or -\partial_i \mathbf{T} \times \mathbf{e}_i. Zophar (talk) 18:09, 20 April 2024 (UTC)
thread_title:  Indices that are contracted 

message: Maybe another footnote could be added to mention what the convention for the outer product is. I got slightly misled as I think of e_i \otimes e_j as the ij th element of the matrix, whereas I learnt it is common in certain fields to consider it as the ji th element. Uhroon (talk) 18:16, 17 April 2024 (UTC)
thread_title:  Convention for tensor product