


Thu Nov 27, 2008 9:35 am 
Post subject: 
Harvey Major Contributor
Joined: 16 Jan 2008 Posts: 1927




jcmax wrote:  Harvey wrote: 
From this can begin new mathematical models that treat the poles as separate single spherical point sources of force of a magnetude* that follows the inverse cube rule. The subsequent interactions between these spheres becomes as simple as modeling the interaction of jelly balls

I might as well throw this one over the transom, then:
http://jcmax.pbwiki.com/SpinningDipoles 
You done some good work there
As far as tossing it overboard, well, I don't know. You already have the Z component available in the force formulae although its unused in your example. If we could add the third dimension to the magnatude equations and pass that on to the force equations I think your work would offer the force and magnetude of any desired point spatially with reference to the point pole. I know there is some disagreement with regards to the inverse square rule and a truly accurate model would actually follow the real toroidal shape of the dipole field which normalizes to an inverse cube as the field becomes spherical. But for approximations your equations are probably the same as those used by FEMM and therefore could be plugged into korkscrews program without any Z needed.
But for a better analysis we need the Z, and for an accurate analysis we need the forces present inside the catenoid (still looking for a better term than catenoid) region where some of the interactions occur. That's the area that moves all around the inverse square and is sensitive to the actual surface shape of the magnet.
So I started thinking about where this is going. We want to visualize the field interactions. How do we calculate all of the force vectors, set the points, connect the dots and then render the image in real time? By layering each sphere as a density gradient that can be selected by the viewer and only rendering that level of detail. With the right calculations and physics modeling we could be viewing 3D field interactions in a short period of time. It's just something I foresee, certainly not an absolute and it does not nullify existing equations, just changes how we look at them.
Thanks for sharing your work on this 

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Thu Nov 27, 2008 3:34 pm 
Post subject: 
korkskrew Regular Contributor
Joined: 25 Jan 2008 Posts: 106 Location: Longmont, CO




Damn! Thanks!
Didn't know a math genius was watching. 

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Thu Nov 27, 2008 11:37 pm 
Post subject: 
alsetalokin Site Admin
Joined: 14 Apr 2007 Posts: 640 Location: Sol III




transom?
Sounds like a zahada clue.
Could either be that little decklike thing on the back of a skiboat,
or
the little window above the doorframe, not often seen in modern construction in the USA.
Toss over the first, and it's tossing out. Toss over the second, and it's tossing in.
Impressive toss, regardless.
(An early alsetalokin axiom: If the model involves partial differential equations or matrix algebra, it is by definition too complex for me to understand. Application of this axiom, or rather an heuristic suggested by it, has saved me a lot of time over the years. I simply scan the document for certain key symbols, and if they appear, I feign stupidity, excuse myself and run for the door.) _________________ "Abandon hope, all ye who enter here..." 

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Fri Nov 28, 2008 8:53 am 
Post subject: 
Harvey Major Contributor
Joined: 16 Jan 2008 Posts: 1927




alsetalokin wrote: 
... I feign stupidity, excuse myself and run for the door ...

LOL, I have a much more strategic approach. I use written statements that prove I'm not feigning Then they excuse me and show me to the door It's true! Just ask Nova
Zahada, yeah I gotta get back to that  stopped on 50b and took a break. I think RB was on 72
When I looked up transom it seemed like the business structure that made up the stern of a ship. So I figured that's where you toss the stuff that you want to say goodbye to.
Yeah, I was going over some of that matrix stuff on the MIT site. I'm sure glad I have two boys with Calculus under their belt and all three with a good handle on Algebra. That way they can pull their old man out of the quick sand when he needs it 

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