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May
18
comment Existence and uniqueness of Stokes flow
Don't pin me down on it, but I believe the situation is only unsolvable if the far-field is unbounded
May
18
answered Existence and uniqueness of Stokes flow
May
13
awarded  Caucus
May
4
awarded  Citizen Patrol
May
3
revised Inaccuracy in numerical calculation of arclength of part of an ellipse
deleted 111 characters in body
May
3
accepted Inaccuracy in numerical calculation of arclength of part of an ellipse
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
ok, this is pretty embarrassing. The mistake was in a function call where I had swapped the parameters of 2 ellipses. So I got the shape-plot for 1 ellipse (with b=2.5) while I got the integral for a different one (with b=0.52). Anyway, it's solved. Thanks for the effort and sorry about the dumb mistake
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
Ah ok, so I am at least getting the same number. So maybe the error is already somewhere earlier: in the value of $\phi_s$. I will look into it and come back here when I sorted things out. Thanks for the help!! It's much appreciated
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
You're right, they both are the same (I was missing a bracket), but still I get a much higher value. What I noticed by the way is that you use b=2.5 while I have b=0.52. What do you get with that smaller b?
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
mmm that's odd. I found this for the integrand: $$a b \sqrt{\frac{b^4 \cos^2\phi+a^4 \sin^2\phi}{(b^2\cos^2\phi+a^2\sin^2\phi)^3}}$$ which is supposed to be the same according to ($\cos^2\phi+\sin^2\phi=1$) but apparently it is not????
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
By the way: I agree that a different parametrization would be better. The thing is that I also need the polar angle so I will have to do a bit of work connecting the parametrization you suggest with the polar angle
May
3
revised Inaccuracy in numerical calculation of arclength of part of an ellipse
added 111 characters in body
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
yeah, I see that now. Do you have a symbolic answer to the integrand? Then at least I can start looking for my mistake from there! Anyways, Thanks for the quick help!!
May
3
comment Inaccuracy in numerical calculation of arclength of part of an ellipse
@your first comment: sorry I wrote down the value in degrees instead of radian, I fixed it in the post. The relative distance comes from the fact that I know where the tip of the ellipse and the point $\phi_s$ are ---- your second comment: So you are saying that the problem is most likely caused by the parametrization in combination with round-off errors?
May
3
revised Inaccuracy in numerical calculation of arclength of part of an ellipse
added some clarification
May
3
revised Inaccuracy in numerical calculation of arclength of part of an ellipse
fixed mistake in integral
May
3
asked Inaccuracy in numerical calculation of arclength of part of an ellipse
Apr
29
comment Wisdom of the crowd in estimative calculation
@joriki yes, I think it is safe to assume that the estimates for the individual quantities are normally distributed
Apr
29
asked Wisdom of the crowd in estimative calculation
Apr
20
accepted Incomplete elliptic integral of the second kind and the arc length of an ellipse - does a `simple` relation exist?