4:26 PM
2

Context I would like to compute the torque that a razor thin disc applies onto a razor thin ring. Attempt I have defined a domain dom = ImplicitRegion[0 <= x <= 1 && -1 <= y <= 1, {x, y}]; and the Laplace operator op = -Laplacian[u[x, y], {x, theta, y}, "Cylindrical"]; I impose the edge...

I don't know if it's me, but there are a lot of things I don't understand. Among these things :
1) The geometry : " torque that a razor thin disc applies onto a razor thin ring" ???

May be I should remove this context and just state that I am interested in the gravitational potential generated by a ring and a disc?

2) "The outer box imposes a symmetry which is not in the sought solution" For, me the problem is symetric, but the boundary conditions at Infinity are not respected. So it's another problem

@andre point 2 is a typo. it now reads 0 <= x <= 1 && -1 <= y <= 1. But its not at infinity.

3) "This is imposing fixed potential on the disk not fixed density" I Don't understand. My background in mechanics is low, but not in electrostatics, and the problem should be the same. Is potential imposed at X<x<1/2 or is somthing else imposed ? In this caes what ?

4:26 PM
@andre I was not sure about this: is it really equivalent to fix the potential or the density? If so I ll remove this point from my question.
Hello and thanks for your time
do you think I should remove the mention of torquing?
My implicit question behind this question is how to impose boundary condition at infinity and use FEM?

@chris AhAh !!! Gravitational Potential ? For me Razor = "rasoir" (in french) !!

razor fin =disque infiniment fin

OK thanks. Concerning 1) I think you should write : "that I am interested in the gravitational potential generated by a ring and a disc?"

ok
I have put a cartoon to make it clearer.

Concerning "remove the mention of torquing" : For me "torquing " is related to "rotation", so it's not related to your question ???
I'm discovering the photos you have just added.
... I trying to understand ... (suspens !)

4:51 PM
Can you confirm that the disk and the ring are not coplanar ?

Well that's the idea but I think I know how to deal with this once I have the potential everywhere.

5:17 PM
Two misaligned discs or ring will torque each other (ils exercent un couple l un sur l autre)
for instance the alt azimuthal torque for a disc has this structure !Mathematica graphics

5:34 PM
I'm still trying to understant, but I must go.
I'll be back in 1 hour.
Here is a reminder (graphic 1):

5:53 PM
thanks: if they are co planar there is no torque;
but say in this configuration yes. !Mathematica graphics
or may be more clear here !Mathematica graphics

1 hour later…
7:01 PM
OK. Now my ideas are relatively clear. I'm thinking how to explain them concisely. But the conclusion is a little bit desappointing. It is : you don't need FEM. To obtain the gravity, it suffices to integrate the matter quantity over the space with the ponderation 1/distance^2

7:19 PM
(cf Newton, who is "new" only in his name)

3 hours later…
9:52 PM
While I agree in principle (and I do give the analytical result in my post), I am still interested technically in FEM being able to reproduce this result. Thanks for your help anyway.