User talk:Maschen/Archive 5

Sock
How the heck did that guy get a paper published in the Journal of Applied Physics? My knowledge of physics is limited, but based on your comments, it sounds like he "discovered" something that is already well known. OhNo itsJamie Talk 19:56, 3 January 2014 (UTC)
 * I think I figured it out. IOSR doesn't appear to be a notable org, and this is not the well known Journal of Applied Physics.  The IOSR one claims to be peer reviewed, but I have to wonder these "peers" are. OhNo itsJamie  Talk 20:00, 3 January 2014 (UTC)


 * Indeed! No clue why his work became published, he seems to be claiming that "charge variation" is something new, that the electric charge of a particle varies with velocity when it does not (the total electric charge of a particle is constant, charge density (charge per unit volume) of extended objects can vary because of length contraction).
 * As you say, the IOSR journal claims to publish things very quickly, and claims to employ [ http://iosrjournals.org/iosr-jap.html double blind peer review]. It seems to be like arxiv.org, which also publishes papers very quickly, and in general is unreliable since even cranks and crackpots can slip through. Probably the same for IOSR... M&and;Ŝc2ħεИτlk 20:17, 3 January 2014 (UTC)

Speedy deletion nomination of Template:User:Maschen/Ldelim


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Speedy deletion nomination of Template:Leftdelimiter


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Your submission at Articles for creation: The Machine (Dutch band) (January 12)
 Thank you for your recent submission to Articles for Creation. Your article submission has been reviewed. Unfortunately, it has not been accepted at this time. Please view your submission to see the comments left by the reviewer. You are welcome to edit the submission to address the issues raised, and resubmit if you feel they have been resolved.
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 * Hi FoCuSandLeArN, thanks for taking the time to review. It's not disappointing, so don't worry, I was partially expecting the article to be declined, but decided to follow the advice here at WP rock music.
 * Best regards! M&and;Ŝc2ħεИτlk 15:13, 12 January 2014 (UTC)

diagrams
i find your diagrams to be great. isaac newton would be thrilled with the succinct, yet descriptive, portrayal of the relationship between geometry and calculus. sorry for not signing in when i posted this (didn't realize), but the poster was me (saw you left a comment on my IP page, switch it over if possible plz? ;> want my IP page to remain blank) — Preceding unsigned comment added by I3roly (talk • contribs)


 * Hi, yes. Thanks again for your kind comments.


 * Please do sign in (it's happened to me before by accident). Please sign your posts on a talk page using four tildes at the end like this: ~.


 * Did you make this silly and pointless edit at Talk:University of Cambridge? If so, please not again.


 * I'm not going to blank your IP page, it's up to a user to manage their own user and user talk pages. M&and;Ŝc2ħεИτlk 19:38, 15 January 2014 (UTC)

Nice work in Matrix multiplication
Hi Maschen,

Just wanted to say that I like the additions you've made to Matrix multiplication. Making these concepts more concrete will help those trying to understand it for the first time. Regards, --Mark viking (talk) 00:21, 15 January 2014 (UTC)


 * Not sure if the index notation makes things harder to read though, seemed clearer without, but also the properties can be verified in a single line. Anyway, thanks, as always. ^_^ M&and;Ŝc2ħεИτlk 19:38, 15 January 2014 (UTC)

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A beer for you!

 * ... OK, these came from nowhere. Thanks, but I drink coffee instead of alcohol. M&and;Ŝc2ħεИτlk 10:10, 26 January 2014 (UTC)

A cup of coffee for you!
Don't worry! My post on WP physics basically repeated what others said, which is why I decided to removed it. Nevertheless thanks, as always. ^_^ M&and;Ŝc2ħεИτlk 10:35, 26 January 2014 (UTC)

March 2014
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File:N-vector.svg
I might be wrong, but to me it looks like the cycles on the faces of the parallelogram are the wrong way around. It seems to me that if u,v,w are positively oriented then the surface of the parallelepiped they determine should have a counterclockwise orientation wrt the outward normal (that is, in a "right-handed" sense). Obviously this is a matter of convention, but the one used in the image now seems to go against what I would expect. Can you confirm? Sławomir Biały (talk) 12:20, 1 April 2014 (UTC)


 * I thought the orientation of the plane element follows the directions of the vectors in the exterior product, so in u&and;v, the "tail" of v is placed at the "tip" of u, and the orientation follows. The diagram does not place vectors tail to tip to show the vectors span a parallelepiped. At the time the source I used was Misner, Thorne, Wheeler's Gravitation 1973, p. 100 shows a parallelogram and p. 365 shows a cube.


 * It also matches the diagrams drawn for the outer product of two vectors in geometric algebra, e.g. Doran and Lasenby's Geometric Algebra for Physicists 2003 p. 13, and 1999 New Foundations for Classical Mechanics (early in the book, forgot the page number).


 * I presumed for higher dimensional parallelotopes the same orientation occurs on the surfaces, and in such a way the orientations are oppositely directed at the edges. Admittedly I haven't diagrams for this outside of MTW.


 * Now that you mentioned the outward normal, I'll try and fix the diagrams later today. Thanks, M&and;Ŝc2ħεИτlk 14:12, 1 April 2014 (UTC)


 * I would caution against incorporating any convention such as right-handedness in this diagram, which in any event would become excessively confusing in other dimensions, and seek rather to establish a consistent pattern over all dimensions. Geometric algebra is, after all, utterly agnostic to handedness. In every dimension, adding the wedge product of a vector should leave the previous indication of orientation on the boundary of the new figure in a consistent fashion. We then have two choices: (a) Is the vector added as a wedge product to the left or to the right of the previous expression, and (b) Is the surface at which the boundary is considered to be at the root or the tip of the new vector in the product? These choices should be made consistent with the "obvious" choices in dimensions 0, 1 and 2. This requires some thought. An orientation in 0D (scalars) is a sign (+ or −) associated with a point.  So let's say we would use a + to indicate the direction of a line segment by associating it with the point boundary of the line segment that we'd associate with the tip of the new vector, which suggests an answer to (b) as the old indication lives at the tip of the new vector (which seems to fit with the outward direction).  If we then decide u∧v is to be represented as v following u around a parallelogram, we see that we must interpret u as the new vector to remain consistent.  This suggests that the new vector must be the one at the left of the expression (v gives the orientation around the boundary of the surface at the tip of u, i.e. where u is an outward direction).  Taking this to the next dimension, the circular orientation on u∧v∧w given by v∧w should be on the surface at the tip of u. This seems to agree, using a completely different approach, with Sławomir's preference.  My presumptions and logic should be checked, of course. —Quondum 15:15, 1 April 2014 (UTC)


 * I don't think "handedness" is at all the issue. The real issue may be whether the manifold under consideration is orientable. Things like Klein bottles, and Möbius strips aren't, other things, like Lie groups, are (modulo my failing memory). I don't know anything about GA, but Q's description lends some support to the idea that consistent description (= orientability) should have the drivers seat. YohanN7 (talk) 16:03, 1 April 2014 (UTC)

Apart from the colouring quirk with the ellipsoids in the SVG versions (which I'll fix after, we'll have to cope with PNG for now), does this satisfy everyone's concern (orientations, etc.)? The positive orientation on a parallelpiped (cube in MTW) is indeed as Sławomir described, and my original diagrams had the wrong orientation. M&and;Ŝc2ħεИτlk 20:54, 1 April 2014 (UTC)


 * You appear to have switched the u and v vectors in the negative orientation ellipsoid depiction; otherwise it looks good. Though I'm not convinced that having a diagram dedicated to negative orientation is needed, at least not directly mirroring (forgive the pun) the one defining orientations. —Quondum 21:35, 1 April 2014 (UTC)


 * Sorry, fixed. I drew the negative orientation diagram in case it would be needed or useful for someone. M&and;Ŝc2ħεИτlk 21:44, 1 April 2014 (UTC)


 * As of the the latest version (I haven't kept track of any changes that might have transpired in the mean time), the above diagram now looks more like what I would expect. I like Quondum's explanation as well.  It would be great if something like this appeared in the literature; then we could reference it ;-)   Sławomir Biały  (talk) 22:44, 1 April 2014 (UTC)


 * Penrose uses the idea of oriented boundaries in The Road to Reality, which is where I got much of the idea. When I get an opportunity, I'll check whether he develops it in sufficient detail to piece together the "consistent" picture. —Quondum 23:00, 1 April 2014 (UTC)
 * Penrose illustrates (pp. 235–6) how the boundary of a compact oriented (not necessarily connected) p+1-dimensional region is a compact oriented (not necessarily connected, possibly empty) p-dimensional region without boundary, all the way down to p=0. He does not specifically relate it to the exterior product, though he does relate a volume element to the exterior product. This gives a framework to which one could directly relate my picture of orientation across dimensions using the concept of an interior and boundary of a region, but the connection is perhaps not direct enough to allow us to use Penrose directly as a reference for our my description. Penrose's separation of manifolds (in which geometric figures exist) and tangent spaces (in which exterior products exist) is rigorously more correct; we're conflating them. —Quondum 02:46, 2 April 2014 (UTC)
 * I think this is more in line with the way I was thinking of the picture. An orientation on a region is an orientation on the boundary together with a notion of "outwards".  But as you say, this doesn't directly involve the exterior product, so it's a little tricky to say how the orientation arises naturally if someone hands you three vectors and asks you to orient their parallelepiped.  The explanation you gave above seems to fill that gap.   Sławomir Biały  (talk) 11:26, 2 April 2014 (UTC)

Thanks to everyone for the helpful comments, which do seem to confirm the orientations on surfaces can be found in the literature, but rarely in the context of the exterior product. I tried to tweak the caption for coherency along the suggested lines. M&and;Ŝc2ħεИτlk 07:15, 3 April 2014 (UTC)

A minor point, does anyone know the name of the n-dimensional analogue of an ellipsoid? M&and;Ŝc2ħεИτlk 07:34, 3 April 2014 (UTC)

Introduction to smooth manifolds by John M. Lee has a big chapter on orientability and orientations, including rigorous definitions of things like "handedness" (and exterior products are present). YohanN7 (talk) 12:55, 3 April 2014 (UTC) One quirk though, exterior products are used (in his book) exclusively for co-vectors (elements of the co-tangent spaces or higher tensor powers) rather than vectors. YohanN7 (talk) 13:19, 3 April 2014 (UTC)


 * If you have that reference and have the time to provide a referenced summary, that would be helpful. I've reworded the caption a bit to avoid unnecessary concepts (the orientation of an exterior product is independent of the quadratic form of the space, but the outward normal isn't, "right-handed" should be avoided, and "positive" at best applies to 0-d and I might argue not even then ). An interesting point is the orientation of p-forms vs. that of p-vectors, but are related (they both are oriented, and their orientations can presumably be related), but this should wait for a more rigorous definition. —Quondum 15:03, 3 April 2014 (UTC)


 * I have the reference, but real-life issues are probably going to stand in the way. I'm quite sure orientations in terms of p-forms and p-vectors are canonically related, just don't know exactly how. (A p-form (p-covector) is, in Lee's world, a multilinear function of p 1-vectors. P-form fields naturally extend the concepts.) I'll need to read up, and this might take some time. YohanN7 (talk) 16:00, 3 April 2014 (UTC)


 * I have managed to get a look at the reference (the recent 2nd edition, chapter 15). While it goes into the orientation on a manifold in some detail, and defines "consistently oriented" on a vector space, it does not appear to give anything that would support my description above. It seems to do only the same as Penrose: it relates the interior side of a bounded region (alternately a nowhere-tangent vector field on the boundary) to a relationship between the orientation in the region to an orientation on the boundary. It relates the orientation of a volume-form to that of a manifold, but still this is too indirect. Thanks for the reference, but I don't think it will be suitable for what Sławomir (and I) would have liked. —Quondum 18:44, 3 April 2014 (UTC)


 * In Lee's reference, there are no diagrams (or worded descriptions of them) like here?
 * In any case, I don't see what the quirk is, the diagrams are similar for exterior products of vectors and covectors (in the latter they are "meshes" of level surfaces to coordinate curves, but the orientation must surely be the same). M&and;Ŝc2ħεИτlk 20:30, 3 April 2014 (UTC)


 * I see no p-vector/p-from orientation issue, if that's what you mean by the quirk. Lee does relate the two to each other, at least in top dimension.
 * Lee's diagrams are few and not that helpful for pure vectors (no regions). The best is one on two dimensions of a rotation arrow between two basis vectors, and then in three dimensions a third basis vector is simply added, something that could be related to a spinning top model. This is not a picture that generalizes to higher dimensions easily. Lee goes abstract, basically talking about ordered bases and the determinant of the transformation, so not much help there. —Quondum 21:13, 3 April 2014 (UTC)
 * Just expanding on that a little: just like Penrose, the emphasis and most of the diagrams relate to orientation on manifolds and their boundaries. The problem with this is that it does not help so much if we want a picture that can be built using only the exterior product on a vector space, without considering a manifold (which is considerably more structure). —Quondum 00:04, 4 April 2014 (UTC)

Seems for now the diagrams will be referenceless, not that's it's an immediate problem. M&and;Ŝc2ħεИτlk 12:30, 4 April 2014 (UTC)


 * Perhaps some notable author will use them as inspiration, then we'll have our reference ;-) —Quondum 14:45, 4 April 2014 (UTC)


 * I've seen a friend's book published from the open university actually adapt a diagram from WP (in a computing topic, no memory of the author or title). If a professional physicist or mathematician actually used one of mine in their book, that would be something...
 * Shall we replace the latest version in the relevant articles, or are the other suggestions? M&and;Ŝc2ħεИτlk 18:18, 5 April 2014 (UTC)
 * I have no further suggestions at this point. Feel free to replace. —Quondum 18:48, 5 April 2014 (UTC)

This looks very good now. One thing that is obviously missing is a decent description over at the (arguably mistitled) orientation (vector space) page. Perhaps these lovely images can be adapted to that article as well? Sławomir Biały (talk) 11:35, 6 April 2014 (UTC)


 * Looking at Orientation (geometry), we need to be careful to avoid confusing two independent concepts: the orientation (meaning direction), and the orientation (meaning handedness). I'd say that the existing picture showing the latter is misplaced in that article. This juxtaposition may help in thinking of an renaming. I see there is also the related article Orientability, but that's not much help here. —Quondum 15:22, 6 April 2014 (UTC)


 * I'm guessing the best place in the orientation (vector space) article is the section Multilinear algebra or Geometric algebra? If not please say. As to adapting, aside from changing notation to match the text, is there anything else? M&and;Ŝc2ħεИτlk 08:13, 7 April 2014 (UTC)


 * Not an easy question to answer. It doesn't seem to belong specifically in any one, but for now I'd put it in the Multilinear algebra subsection (which might be more specifically named Exterior algebra). I think the possible implication of a link with the quadratic form of a geometric algebra should be avoided.  This kind of picture really does belong in this article. Once a suitably abstracted non-manifold version is found (as well as a source for the concept), it would go with a separate section on the association of orientation between dimensions. —Quondum 23:07, 10 April 2014 (UTC)

File:GA parallel and perpendicular vectors.svg
I'm not sure this diagram is right, especially the top (antisymmetric) part.

Surely if a and b correspond to particular vectors, then they ought be shown as the same vectors both on the left and the right hand side; whereas in your pic they seem to suffer rotations of 90°, so that a and b on the left do not represent the same vectors as a and b on the right.

Also, I'm not sure that the equations follow particularly intuitively.

Can I suggest instead bringing the equations on in the opposite order, ie

$$\begin{align}\mathbf{a} \perp \mathbf{b} & \Leftrightarrow \mathbf{a}\mathbf{b} = \mathbf{a} \wedge \mathbf{b} \\ & \Leftrightarrow \mathbf{a}\mathbf{b} = - \mathbf{b} \mathbf{a}\end{align}$$

and

$$\begin{align}\mathbf{a} \parallel \mathbf{b} & \Leftrightarrow \mathbf{a}\mathbf{b} = \mathbf{a}. \mathbf{b} \\ & \Leftrightarrow \mathbf{a}\mathbf{b} = \mathbf{b} \mathbf{a}\end{align}$$

with, in the right hand side of the antisymmetric example, -ba shown with a green "-b" extending downwards, and a blue "a" extending horizontally rightwards, to define an bivector equal to the ab shown on the right.

I just think that might be clearer. Jheald (talk) 19:04, 6 April 2014 (UTC)


 * Sorry, this is easy to fix (and has been). Let me know if anything else. Best, M&and;Ŝc2ħεИτlk 08:13, 7 April 2014 (UTC)


 * Many thanks for this. On second thoughts, probably the "-b" should be blue after all, with the "a" in green.  I had thought maybe to use the colours to show which vector was first in the product; but looking at it now I don't think that really conveys itself.


 * Sorry for this small change of mind, and thanks again for all the pics!  All best,  Jheald (talk) 11:00, 9 April 2014 (UTC)


 * I was a bit confused at your proposal of the colours, but decided to go along with the suggestion anyway. Cheers, M&and;Ŝc2ħεИτlk 11:10, 9 April 2014 (UTC)

How stuff rotates (again)
First, I'll quote myself from your earlier thread: "My almost embarrassing confusion between spin and tensor order stems from my having learned this the old-fashioned way and the paucity of modern-style GA references to translate it to the GA language for me. Pretty much all of the references deal with spin 0, 1/2, or 1, which in my view are the trivial cases. I can't really find anything that deals with the lowest order non-trivial cases, spin 3/2 and spin 2. It would be very nice to see a paper that deals with these to let the reader see the generalization or better yet to see a paper that deals with the general case."

Lo and behold… Brought to my attention today is the paper that solves the problem of rotation for general spin. Try translating the j=3/2 and j=2 examples to GA. It should be a fun (and hopefully straightforward) exercise for you. Teply (talk) 00:10, 10 April 2014 (UTC)


 * You might like this too:, The unitary representations of the Poincaré group in any spacetime dimension. YohanN7 (talk) 13:03, 10 April 2014 (UTC)


 * Thanks both for the papers! Will read and digest. M&and;Ŝc2ħεИτlk 18:57, 10 April 2014 (UTC)


 * The first section (of five or something) is pretty much exactly chapter 2 in Weinberg vol 1, but with more detail in some respects.
 * The other paper, I'm surprised they could do so much in closed from. I knew about some of this qualitatively, but didn't think it was possible to find anything near neat expressions. Nice. YohanN7 (talk) 00:32, 11 April 2014 (UTC)

Mysterious gamma matrices
Remember the high-order gamma matrices we wondered about when working on the Bargmann-Wigner equations? Turn out we have an article on them (I think, not sure yet, busy with other stuff). YohanN7 (talk) 06:06, 12 April 2014 (UTC)

Photon wave vector space diagram
Would you be interested in looking at updating File:Light cone colour.svg? As you'll see from the caption, the axes are mislabelled. I would suggest the following changes: This diagram is used in Photon, which is a featured article, so it is worth fixing confusing elements such as this. —Quondum 21:58, 27 April 2014 (UTC)
 * Most important: the axes must be relabelled to something like "frequency" (vertically) and "wavenumber" (horizontally).
 * The vertical axis should not emphasize one direction (have arrow points both ways or remove embellishments); the distinction is only of chirality.
 * It makes sense to show two space axes.


 * There's nothing wrong with the diagram per se, it is the light cone of an event in spacetime. The text coming with the diagram is highly confused though, and I understand what Q is getting at. It might be supposed to illustrate the solutions of the energy-momentum relation in terms of 4-momentum split up into time (energy) and space (3-momentum) parts. But frequency (energy) is always positive (as opposed to the time coordinate in a light cone diagram). [This has to do with the fact that a photon is its own anti-particle. You can either throw away the negative frequency solutions, or impose additional conditions on the wave equation.] It is the 3-d wave vector (or 3-momentum) that can be plus/minus whatever satisfies the energy-momentum relation. Chirality has nothing to do with this. YohanN7 (talk) 23:07, 27 April 2014 (UTC)


 * Read the text in the section. It is not meant to be a cone in Minkowski spacetime at all. It was added by Incnis, and is meant to be the space of possible wave four-vectors (for plane-wave photons of know frequency, I suppose). It is clearly meant to fit into an equation describing the circularly polarized wave given only the wave 4-vector. He even added a hidden comment into the caption (still there) to the effect that he wasn't sure which half-cone mapped to which chirality. He was depicting something reasonable, though I have not yet produced the solution equation that he intended the vector to fit into, so I'm not sure that he got it exactly right. The red dot at the centre is meant to suggest that the apex of the cone is not a possible wave vector. —Quondum 00:17, 28 April 2014 (UTC)


 * Wave 4-vectors&mdash;yes. The wave 4-vector is the same as momentum 4-vectors modulo a constant (even identical to it in natural units). I never said that the diagram was meant to be a cone in Minkowski spacetime, but it is a (past and future) cone in Minkowski spacetime. Chirality&mdash;no. Circular polarization or any other polarization&mdash;no. The term chirality isn't used for massless particles. They term would be helicity, and helicity is another degree of freedom independent of 4-momentum. Four-momentum (or wave 4-vector if you prefer) does not give any information about polarization, which is a (complex) linear combination of positive and negative helicity eigenstates. You need to look at the vierbeins (roughly, spin 4-vectors) used in the quantization, two of which are linearly independent, to talk about polarization. (The situation is different for electrons. They have definite chirality, due to maximal parity violation, in the lab frame in which they are created, but this is not Lorentz invariant.)
 * You seem to think that the diagram is related to the sentences in the article with references 18 and 19? Perhaps User:Incnis Mrsi thought so too, we'd have to ask. YohanN7 (talk) 07:03, 28 April 2014 (UTC)


 * Better described this way: To each wave 4-vector $|Ψ\rangle$, there is a 2-dimensional complex continuum $|Ψ_{1}\rangle$ of polarizations, subject to normalization $|Ψ_{2}\rangle$. YohanN7 (talk) 08:38, 28 April 2014 (UTC)

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Graphic request
Hi Maschen, I noticed that plate trick has no graphical illustration, but one is sorely needed. I thought this might be up your alley. I have been editing the lead of the spinor article, and I also hope to include a graphic there. Best, Sławomir Biały  (talk) 12:19, 15 August 2014 (UTC)


 * Hi, sorry to keep you for so long, just noticed this now.
 * For plate trick I'll try and get something done in the next few days, and still haven't forgotten the diagram for orientation (vector space) above and will get to that too.
 * Best, M&and;Ŝc2ħεИτlk 06:57, 19 August 2014 (UTC)

welcome back!
Just noticed some of your activity on userpages I'm watching, and I gather you had an official break. Welcome back! Rschwieb (talk) 17:37, 19 August 2014 (UTC)


 * Not an "official" wikibreak - the reason was because I had final exams at the time, etc. . Thanks for the comment, nice to see you. M&and;Ŝc2ħεИτlk 23:43, 23 August 2014 (UTC)

Update
Congrats, and welcome to the jungle! &mdash;&thinsp; H HHIPPO  17:45, 19 August 2014 (UTC)


 * Many thanks, good to see you as well. M&and;Ŝc2ħεИτlk 23:43, 23 August 2014 (UTC)

Response re: gravitomagenetism
I responded to you on my talk page. Fresheneesz (talk) 21:58, 29 August 2014 (UTC)

Plea for support in calming things down
Belated "welcome back"! If you were inclined, you could take a look at the kerfuffle at Talk:Rotation_matrix and second my plea for cool-down. I fear an obstreperous contributor needs reminding of WP:TE or WP:NOTGETTINGIT. The issue is a triviality, but I am not sure I don't see an edit war in the making there.... Cuzkatzimhut (talk) 14:16, 4 September 2014 (UTC)


 * My belated reply: thanks, very nice to see you. For now my contributions will be very scrimp. It seems you have already handled the situation fine, there appears to be no contributions since the 4th september. Cheers, M&and;Ŝc2ħεИτlk 23:47, 5 September 2014 (UTC)


 * Thanks, that one worked, but I asked for protection of Wave packet now. It looks like obstreperous actors are loose... Pardon the "whining"... Cuzkatzimhut (talk) 20:26, 24 October 2014 (UTC)

Generalized coordinates image
Hi, I just read the Lagrangian mechanics article and got confused by your. I think that the caption text of this image (which appears in multiple articles) is actually incorrect. Generalized coordinates are supposed to uniquely define the configuration of the system (as also mentioned on the 2nd sentence of the generalized coordinates article); but in this image, only the arc length parameterization (bottom right) satisfies this properties. For the other choices, there are multiple points on the complicated path that are mapped to the same generalized coordinate value. Am I missing something? Could you fix the image (as it is already used in multiple article)? My suggestions are either to get rid of all examples except the arc length; or if you want to still illustrate other possibilities, use a less complicated path which then would allow the 1d-projection to still be injective. Actually, I just realized that somebody else had already made this comment here for example. Simon Lacoste-Julien (talk) 16:15, 30 November 2014 (UTC)


 * Hi, yes, I have been meaning to fix those images for a while, as with many numerous others. I'll try and sort something out by today, please hang on for longer. Sorry to keep you and everyone else waiting.
 * By the way, anyone is free to delete incorrect/misleading images from articles as they please... M&and;Ŝc2ħεИτlk 15:17, 3 December 2014 (UTC)

Here are some I made now:

It would be better to draw some simple mechanical examples (pullys, blocks and inclined planes, pendulums and the like) and label generalized coordinates on those, I'll get to those soon for a physical perspective. The ones drawn here should be fine for a more mathematical visualizaton. Best, M&and;Ŝc2ħεИτlk 22:09, 3 December 2014 (UTC)


 * Rather than keep the incorrect image File:Generalized coordinates 1df.svg, I'll replace this with the last two. M&and;Ŝc2ħεИτlk 23:38, 6 December 2014 (UTC)

What's up?
Long time no see.

Exams?

YohanN7 (talk) 13:28, 1 December 2014 (UTC)


 * Not exams, did those last June. No postgraduate work either, didn't get through the PHD offers (survived the interviews but other students must have had superior transcripts than I have, admittedly it was only a scrape past the 2.1 class)... Only study for me now is self-study with graduate-level books (those savings were worth spending on the dover and other books). Just stuck with a crappy job for now while reaching for worthwhile ones. Nice to see you and others are making productive contributions. Best regards. M&and;Ŝc2ħεИτlk 15:17, 3 December 2014 (UTC)

"actually"
I have made some remarks about "actually" and footnotes here.Chjoaygame (talk) 16:26, 6 December 2014 (UTC)


 * Thanks for feedback, Chjoaygame. I like the helpful edits you made to the lead to sharpen it up as well. Good job! ^_^ M&and;Ŝc2ħεИτlk 23:29, 6 December 2014 (UTC)

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