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I would like to compute the torque that a  (thin) disc applies onto a ring. I.e. I would like to try to understand what is the impact of this outer ring on the inner disc in the simulation below.

For this I would like to compute the gravitational potentiapotentiall generated by a (razor) thin disc and a ring. So the abstraction is the following (seen from 9 different angles)

Once I know how to compute the potential it becomesshould become straightforward to compute the torque one feature applies on the other. IHere I want to use FEM here for flexibility, which I will use when I will account for a more realistic abstraction of the problem. (e.g. exponential surface density profile in disc).

I would like to compute the torque that a  (thin) disc applies onto a ring. I.e. I try to understand what is the impact of this outer ring on the inner disc in the simulation below.

For this I would like to compute the gravitational potential generated by a (razor) thin disc and a ring. So the abstraction is the following (seen from 9 different angles)

Once I know how to compute the potential it becomes straightforward to compute the torque one feature applies on the other. I want to use FEM here for flexibility when I will account for a more realistic abstraction of the problem.

I would like to compute the torque that a (thin) disc applies onto a ring. I.e. I would like to try to understand what is the impact of this outer ring on the inner disc in the simulation below.

For this I would like to compute the gravitational potential generated by a (razor) thin disc and a ring. So the abstraction is the following (seen from 9 different angles)

Once I know how to compute the potential it should become straightforward to compute the torque one feature applies on the other. Here I want to use FEM here for flexibility, which I will use when I will account for a more realistic abstraction of the problem. (e.g. exponential surface density profile in disc).

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edge = {DirichletCondition[u[x, y] == 1, 0 <= x <= 1/2 && y == 0};0];
StreamPlot[-{D[#, x], D[#, y]} &@uD[x, y] // Evaluate, {x, y} \[Element] dom]dom,AspectRatio->2]

Mathematica graphicsMathematica graphics

edge = {DirichletCondition[u[x, y] == 1, 0 <= x <= 1/2 && y == 0};
StreamPlot[-{D[#, x], D[#, y]} &@uD[x, y] // Evaluate, {x, y} \[Element] dom]

Mathematica graphics

edge = DirichletCondition[u[x, y] == 1, 0 <= x <= 1/2 && y == 0];
StreamPlot[-{D[#, x], D[#, y]} &@uD[x, y] // Evaluate, {x, y} \[Element] dom,AspectRatio->2]

Mathematica graphics

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