Path Integral from n*n array
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I have an n * n array, which represents a scalar field. I wish to determine the path(line?) integral of a closed path around the centre of the array.
I think the values of the field change by angle rather than distance, so the distance from the centre of the array at which the closed path is measured should not be important, but I would like to confirm this too.
I have a number of questions
1) Must the path be "smooth"? Does it need to be a circle of radius (1/2n(*some fraction)) if the area of the path is critical which I need to determine) centred on the array
Or
2) Can I just sum the perimeter values of the array - i.e. the path is a square.
3) Is there a matlab function for this, or do I need to manually tell matlab which values of the array to sum?
4) Is this the correct methodology for a line integral (I have never calculated such a thing before)
thanks a lot!
7 comentarios
William White
el 24 de Jul. de 2017
Hi David, Thanks for that...You have jumped a few steps (or so it seems). I have a few questions if you don't mind...
1) These functions are for displacements, so why cannot I get the net displacement? I dont understand why the integration (summation) has already been done?
2) How did you come by those results?
3) I was under the impression that the total displacement at a point was the vector sum of the Ux and Uy displacements at that point?
4) The crux is, I have different formulae (from the literature) which appear to give different solutions (displacement fields); and I figured a sure-fire way to confirm the validity was to take a path around the origin, which, if correct, would equal b?
kind regards W
David Goodmanson
el 26 de Jul. de 2017
Hi William, Since this is not a Matlab topic this website is not the right forum, but if you want to discuss further feel free to contract me via my profile.
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