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What part of [equation] don't I understand? Most of it.
July 5, 2010 4:04 PM   Subscribe

Help me understand my hard-to-understand calculus shirt.

I've had this for a while now; it's a similar design to the image here, although the typography is different. The equation is identical, though, and it seems to be something out of physics, judging by the overdots (for derivatives, I assume) and multiple integrals. So what is this the equation for? I'm not scared of math, so feel free to be as technical as you want.
posted by wanderingmind to Science & Nature (9 answers total) 2 users marked this as a favorite
 
Those are Maxwell's equations!
posted by mayhap at 4:29 PM on July 5, 2010


Well, I'm not sure, but I think this is a nonsense equation.

I don't recognise the combination of symbols as belonging to any field of physics. It also looks sort of wrong in other ways: why is the second integral on the top line a volume integral but only over dx? That doesn't make sense.
posted by atrazine at 4:36 PM on July 5, 2010


I would go with what atrazine thinks too. They certainly don't resemble Maxwell's equations.
posted by edd at 4:39 PM on July 5, 2010


mayhap,

that was my first thought too, because of the loop integrals because Maxwell's are the most commonly seen equations using them (that a T-shirt maker might want to use). I don't see any symbols that could represent an electric field, charge, or current, and where have all those volume integrals come from?
posted by atrazine at 4:42 PM on July 5, 2010


The shirt is being sold here. Their newer versions use Maxwell's equations, so I'm guessing that they chose an actual equation for the new version after people complained that this earlier one was nonsensical.
posted by Paragon at 4:42 PM on July 5, 2010


Ah, shoot, should have looked at the link before answering! In which case, yes, the version with the nonsense equation (?!) is very silly.
posted by mayhap at 4:49 PM on July 5, 2010


The second volume integral contains a grouping of acceleration terms (with small omega representing angular velocity, and cross products miswritten as x; r-double-dot also represents acceleration), multiplied by density (rho) and integrated over volume (but with an incorrect differential term, as atrazine notes). The last term includes the time derivative of velocity.

All in all, it looks like a somewhat-shuffled sum of forces in integral form, intended for maximum abstruseness. The most likely origin is fluid mechanics or particle dynamics.
posted by Mapes at 6:00 PM on July 5, 2010


I don't think it's complete nonsense, though I wouldn't vouch for its being error-free. The equation looks kind of like an integral formulation of the Navier-Stokes equation for an inviscid (i.e., non-viscous) fluid in a rotating frame.
posted by hat at 6:59 PM on July 5, 2010


The second volume integral looks like it came out of a transformation to a rotating reference frame; the integrals on the right side of the equation look like they came from the integral formulation of conservation of momentum. Agreed that the dx (at least!) is a typo.
posted by roystgnr at 11:44 AM on July 6, 2010


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