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pw
Posts:
14
Registered:
10/3/12


Re: Integrating over 3D vector
Posted:
Oct 11, 2012 2:24 AM


Hello,
I see what you are getting at. You have demonstrated the vector direction and force along the 3D wire path according to biotsavart.
I took the liberty of rewriting the code sections from the notebook you sent so that I could rearrange things and enter (iterate) more numbers.
This is very close to what I was looking for. I have not had much chance to do much more than look at your notes and rearrange your code into programmatic space.
I will attempt to rearrange the code to allow me to make a volumetric plot with a series of fixed distances from the wire.
What I hope is that I can ultimately step my way along equally spaced positions along the (any) path and iterate through a series of radial distances from those.
Peter
On 10/09/2012 05:09 PM, mathgroup wrote: > Here are 2 examples of a odd wire shape for 2D and 3D geometries...... > > I used the parameter 's' to define x,y,z of the wire......and than > performed an integration over the variable 's'.....assumed CCW current.... > > here are the results...I tested them with several locations along the x > and y axes that would tell me if my results were correct and they seem > correct.....I made the H vectors larger than the actual values to make > it easier to see the vectors.......unfortunately, I had to use > NIntegrate because dH was too complicated.... > > > jerry b..... > > Original Message From: pw > Sent: Monday, October 08, 2012 11:36 PM > To: mathgroup@smc.vnet.net > Subject: Re: Integrating over 3D vector > > Hello, > > The attachment is interesting in the linearity of the procedure > used to solve the problem. > > I am, however, thinking that it may be more efficient to simply > calculate a linear integral over the full calculated length > (straight length) of the wire, and then simply transform the > results into the direction and 3D position of each point > on the wire. Then simply perform integration of the 3D > results by position within the volume of the winding space. > > > Peter > > > > On 10/06/2012 08:52 AM, mathgroup wrote: >> I dont know you're background, so dont know if this is of value to you >> or not.... >> >> here are 2 examples of biot savart calculations for a triangle and a >> loop.....it's interesting that, unfortunately,in each case I had to use >> Integrate with GenerateConditions>False, otherwize it took forever to >> do the integrals...this often happens with definite integrals... >> >> >> jerry b >> >> Original Message From: pw >> Sent: Friday, October 05, 2012 1:48 AM >> To: mathgroup@smc.vnet.net >> Subject: Re: Integrating over 3D vector >> >> >> Hello, >> >> I think I need to do a line integral like NIntegrate[]. >> >> I think I may just need to collect single position integrals >> and then transform the integrals using the 3D coordinates... >> >> Thank you for mentioning the Classroom Assistant Palette, >> that was very useful. >> >> Current linux distro is Ubuntu PP . Mathematica distro is 8.04. >> >> I am looking to integrate magnetic flux along a series of curved >> windings. >> >> >> Peter >> >> >> On 10/04/2012 02:33 PM, mathgroup wrote: >>> several questions.... >>> >>> 1. of course, you can nest integrals....I personally use the Classroom >>> Assistant palette and put together the number of integrals I want.... >>> >>> 2. sometimes getting vector potential A is easier....etc.. >>> >>> 3. could you tell me exactly what the current distribution is.....I'm >>> assuming from what you say that there isnt any symmetry to break it down >>> into one integral only, e.g. circular loop.... >>> >>> >>> If you are interested, I can send you a double integral example to >>> calculate the force between a wire along the z axis and a square loop >>> positioned away from it....this involves double integrals.... >>> >>> jerry blimbaum >>> >>> Original Message From: pw >>> Sent: Wednesday, October 03, 2012 10:39 PM >>> To: mathgroup@smc.vnet.net >>> Subject: Integrating over 3D vector >>> >>> Hello, >>> >>> BiotSavart Law is used to calculate the magnetic field strength >>> at some vector location relative to the path of a conductor. >>> >>> The function of the law requires integration along the path of the >>> current in 3 dimensions which indicates 3D displacement. >>> >>> QUESTION: Is it possible to 'nest' a series of integrals >>> that follow the series of XYZ coordinates. >>> >>> ie: Integrate[{x1,x2,x3}, >>> Integrate[{y1,y2,y3}, >>> Integrate[{z1,z2,z3}, >>> .... >>> ] >>> ] >>> ]; >>> >>> >>> Thanks for any interest, >>> >>> Peter >>> >>>



