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Re: Integrating over 3D vector

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128348] Re: Integrating over 3D vector
  • From: pw <p.willis at telus.net>
  • Date: Tue, 9 Oct 2012 00:36:27 -0400 (EDT)
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  • References: <20121004033915.2CDC06871@smc.vnet.net> <513F5F84AADF427991A95D687F8E5492@JEROMEPC> <20121005064847.53C5C6858@smc.vnet.net> <DD5AE69A35CE44D89F02E6C12507EC1D@JEROMEPC>

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 don?t know you're background, so don?t 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 at 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 at smc.vnet.net
>> Subject: Integrating over 3D vector
>>
>> Hello,
>>
>> Biot?Savart 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
>>
>>




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