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Natural Science Forum / Physics / Relativity / January 2009THREE MAGNETS (N-dipole-body problem)
--- THREE MAGNETS (N-dipole-body problem) --- imagine 3 bar magnets sitting on a table randomly spaced. they are fixed and can not translate, only rotate around their centers , it is 2D situation. there is no gravity, no friction and only forces are magnetic forces. here is a picture where "x" is the point of rotation and coordinate center of each magnet: ------------------------------------------------ [S- x -N] [N- x -S] [S- x -N] ------------------------------------------------ INPUT: initial angles and coordinates OUTPUT: new angles after system stabilizes 1.) is there a "general solution"? or it must be integrated step by step? 2.) is there a singe solution? is solution stable, chaotic or oscillating? basically, how to simulate this simple situation? unfortunately it does not end there. this is only simplified situation and "real algorithm" is the one that can handle situations in 3D with any number of "free floating" magnetic dipoles. it will need to handle both angular and linear acceleration. however, even if this is possible the ultimate question is still how to compare it with the real-world and make sure it works as it should... given the four situations, DO MAGNETS ATTRACT OBJECTS IN A STRAIGHT LINE? a.) magnet dipole - magnet dipole b.) magnet dipole - electric charge c.) magnet dipole - metal molecule d.) magnet dipole - charged metal molecule > --- THREE MAGNETS (N-dipole-body problem) --- > [quoted text clipped - 35 lines] > c.) magnet dipole - metal molecule > d.) magnet dipole - charged metal molecule http://www.research.ibm.com/grape/grape_ewald.htm Sue... thanks, i dont get it really. i do not see how it fits to this case. do your fridge magnets spiral on the way to your fridge door, or go straight line? > thanks, > > i dont get it really. i do not see how it fits to this case. > > do your fridge magnets spiral on the way to your fridge door, or go > straight line? with out the extension of the effective magnetic length of 3 bar magnets sitting on a table randomly spaced with the replacement of the axial coordinate z by the phase angle j of dipole, the effective magnetic rotation angle Dj can be defined as follows, , (1) where B1(j) is the amplitude of the dipole field at the angle j(z) with the definition of j(z=0) = 0, and B10 = B1(j=0) = B1(z=0) is the amplitude of dipole field at the center, and L is the effective magnetic length. According to this definition, it means that the magnetic field of the region where dj/dz = 0 does not contribute to the effective magnetic rotation angle. > thanks, > > i dont get it really. i do not see how it fits to this case. > > do your fridge magnets spiral on the way to your fridge door, or go > straight line? So far I have never had a thrown fridge magnet get repulsive as it nears the fridge door so I remain of the opinion that induced dipoles have real effects and molecular dynamics like Ewald sums are a pretty good way to model them. http://www.chem.purdue.edu/gchelp/liquids/inddip.html http://www.research.ibm.com/grape/grape_ewald.htm http://en.wikipedia.org/wiki/Van_der_Waals_force http://en.wikipedia.org/wiki/Multiple_integral#Some_practical_applications The Origin of Gravity --C. P. Kouropoulos http://arxiv.org/abs/physics/0107015 http://arxiv.org/abs/physics/0107015v1 Sue... "The trouble ain't that there is too many fools, but that the lightning ain't distributed right" --Mark Twain > --- THREE MAGNETS (N-dipole-body problem) --- > imagine 3 bar magnets sitting on a table randomly spaced. they are [quoted text clipped - 11 lines] > INPUT: initial angles and coordinates > OUTPUT: new angles after system stabilizes With no friction, how do you expect it to "stabilize"? -- in general that requires some dissipative (energy loss) mechanism. I suppose there would be EM radiation, but that would be exceedingly small for macroscopic magnets, so I'll neglect it. Certainly for some ranges of initial conditions the rotations of the magnets could be localized (but not static). And for some carefully-tuned initial conditions there could be a static configuration. There certainly are a host of initial conditions for which the magnets simply spin forever. In general, this is too complex of a system with too little symmetry to be able to say much at all.... For the above system, I'd guess that there is a stable configuration if carefully arranged (or if there is friction): the lowest magnet puts N toward the mutual center, and the other two put S toward the center; there's another with poles reversed. this is probably not very strongly stable. Note that adding a fourth magnet would make a qualitative change -- for locations of the centers anywhere close to a circle there is most likely a stable configuration with the poles alternating toward the center. > 1.) is there a "general solution"? > or it must be integrated step by step? Clearly there is no general closed-form solution. For certain configurations with additional symmetry there are simple solutions. For instance, when all three magnets are fastened along a straight line, there will be two static configurations with the magnets all lined up with alternating pole tips, there will be configurations in which the magnets are approximately lined up but oscillate around their mean positions, and there are also a host of configurations in which the magnets spin; I believe that most of the non-static solutions are chaotic (perhaps the small oscillations are not chaotic, depending in detail on the spacing of the centers along the line and the initial conditions). > 2.) is there a singe solution? > is solution stable, chaotic or oscillating? There is no single solution that covers all possible magnet locations and initial conditions. I'm pretty sure that for most magnet locations and for most initial conditions the motion will be chaotic. > basically, how to simulate this simple situation? Do what one always does: write down the equations of motion and integrate them numerically over time. You'll find that writing a simulation program for this is not too difficult (compared to other common simulation programs), but interpreting the results will be quite challenging (chaotic systems are like that).... > [... the rest was to ambiguous for me to determine what you are trying to ask] Tom Roberts thank you all, > Do what one always does: write down the equations of motion and > integrate them numerically over time. i was unable to find equations of motion for spinning charges and their magnetic moments. i already have n-charge-body simulator that uses Coulomb and Lorentz equations: http://www.youtube.com/watch?v=DUNP4z-Vaac http://www.youtube.com/watch?v=JpI-klsq9nQ http://www.youtube.com/watch?v=aYBMrGM6IpM that seems to work, now i want electrons to spin, but i can not find any equations to account for spin magnetic moment. i can calculate rate of change in linear acceleration, but i have no idea on what factors angular acceleration would depend, not the one of spin, but the angular acceleration of orientation. i just don't see why would electron, with its dipole magnetic moment, not be able to re-orient instantaneously. basically, im failing to grasp angular inertia of magnetic dipoles. > thank you all, >> Do what one always does: write down the equations of motion and >> integrate them numerically over time. > > i was unable to find equations of motion for spinning charges and > their magnetic moments. For the case of N small bar magnets with fixed centers rotating in their mutual magnetic fields: Determine the expression for the energy of a magnet in an external magnetic field. Determine the expression for the external magnetic field of a magnet. Apply both of them to all of the magnets to get an expression for the potential (magnetic) energy of the system as a function of the orientations of all the magnets (this will be QUITE complicated). Then determine the expression for the kinetic energy of a rotating magnet. With these expressions you can write down the Lagrangian of the system, from which the equations of motion follow in the usual way. If you don't understand what I said, then you probably don't have the mathematical and physics background needed to simulate such a system. The algebra will be formidable.... Tom Roberts > If you don't understand what I said, then you probably don't have the > mathematical and physics background needed to simulate such a system. > The algebra will be formidable.... > > Tom Roberts I understand what you said, it does not make any sense. You have not given any equations of motion. You just say things like: "Determine the expression for", "Then determine the expression"... What in the world does that mean? I could have given you instructions to build an airplane like that: "Build left wing, then build right wing, then build engine..."; You advise is unusable and your worry about ability required to understand it is hence pathetic. By the way, the software I gave the links for is UNIQUE. No one in the world has even managed to implement electromagnetic interaction in 3D, even less taking both electric AND magnetic fields into account. Nothing similar exist, do you understand that? I'm now worried about your knowledge and ability to understand. Are you sure you know how magnets work? Perhaps, you could answer this simple question from everyday life: given the four situations, DO MAGNETS ATTRACT OBJECTS IN A STRAIGHT LINE? a.) magnet dipole - magnet dipole b.) magnet dipole - electric charge c.) magnet dipole - metal molecule d.) magnet dipole - charged metal molecule straight line or not... what say you? >> If you don't understand what I said, then you probably don't have the >> mathematical and physics background needed to simulate such a system. >> The algebra will be formidable.... > > I understand what you said, it does not make any sense. Then you don't really understand it, do you? Don't expect me to do your work for you. If you do not know how to look up the expressions I mentioned and derive the equations of motion from the Lagrangian, then as I said, you don't have the necessary background and knowledge to do this. Don't blame me for that. > No one in the > world has even managed to implement electromagnetic interaction in 3D, > even less taking both electric AND magnetic fields into account. This is rather indicative of your lack of knowledge and experience in this area. There are DOZENS of such programs; some are even freely available on the Internet (though they tend to be more difficult to use than commercial packages). Not to mention programs like Mathematica and Maple that help you solve specific problems.... Tom Roberts > Then you don't really understand it, do you? > > Don't expect me to do your work for you. If you do not know how to look > up the expressions I mentioned and derive the equations of motion from > the Lagrangian, then as I said, you don't have the necessary background > and knowledge to do this. Don't blame me for that. Hehehe, my simulators obviously work. I could also repeat how you have no idea what are you talking about, but it is now clear with your refusal to argument your statements. You could have just write down that equation, it would take much less typing effort. Stop blabbering... SHOW ME! > > No one in the > > world has even managed to implement electromagnetic interaction in 3D, [quoted text clipped - 7 lines] > > Tom Roberts Mathematica and Maple!? Stop insulting yourself, stupid! Why don't you try to argument what you just said, give me one link, JUST ONE. SHOW ME! ================================================= It is funny that with all your software and equations you imagine to know... ...with all that, you still can not say anything about this simple, everyday situations: for each of four given situations describe, DO MAGNETS ATTRACT OBJECTS IN A STRAIGHT LINE? a.) magnet dipole - magnet dipole b.) magnet dipole - electric charge c.) magnet dipole - metal molecule d.) magnet dipole - charged metal molecule straight line or not... Tom Roberts, what say you? > > Then you don't really understand it, do you? > [quoted text clipped - 48 lines] > > straight line or not... Tom Roberts, what say you? do mean, are the lines of fluxx straight in these situations Don't mind Tom, someone snuck some pepper into his Preparation H again :-). > > If you don't understand what I said, then you probably don't have the > > mathematical and physics background needed to simulate such a system. [quoted text clipped - 15 lines] > even less taking both electric AND magnetic fields into account. > Nothing similar exist, do you understand that? You might contact the people at ITER, (Fusion reactor), see if they can use it. > I'm now worried about your knowledge and ability to understand. Are > you sure you know how magnets work? Perhaps, you could answer this [quoted text clipped - 9 lines] > > straight line or not... what say you? If I had to solve that problem I'd use a computer. Regards Ken S. Tucker > > given the four situations, > > DO MAGNETS ATTRACT OBJECTS IN A STRAIGHT LINE? [quoted text clipped - 8 lines] > If I had to solve that problem I'd use a > computer. Ken S. Tucker, you are moron. You can not use computer to solve it since there is no such software. But the stupid part about your logic is that it would be much more 'ACCURATE' to test it in real-life. It is also stupid because the point of it all is to TEST the ALGORITHM. Didn't they teach you in school how magnets work? Does your fridge magnet spirals on the way to your fridge door or goes straight line? > > > given the four situations, > > > DO MAGNETS ATTRACT OBJECTS IN A STRAIGHT LINE? [quoted text clipped - 10 lines] > > You can not use computer to solve it since there is no such software. Well iterating n-bodies is a straightforward sim, but slow. What's your app? > Does your fridge magnet spirals on the way to your fridge door or goes > straight line? Is that your problem? Charges in B-fields are tougher. As a softwar pro, I can see your specs are fuzzy, try posting your specs and if we have time we'll comment on them. Regards Ken S. Tucker > Is that your problem? > Charges in B-fields are tougher. [quoted text clipped - 3 lines] > Regards > Ken S. Tucker Well, it is not just my problem. It is also a part of the Ultimate Question of Live, Universe and Everything... it concerns everyone. What spec? I already said what spec I have so far, I use Coulomb and Lorentz equations. I use formula like this: F= m*a = k * Q1*Q2/r^2, and all I ask is for similar formula that can take spinning magnetic moment into account as well. I need to calculate rate of change in angular momentum as well as rate of change in linear momentum. I have all sorted out for linear, and now I see there are no equations that can handle torque and linear acceleration in the same time. I'm asking simple questions. I want that equation Tom is talking about, unfortunately he can not write it down or point some link about it, at least. I also want simple description of everyday life experience about line of attraction between magnets and magnets/ charges/metals. > > Is that your problem? > > Charges in B-fields are tougher. [quoted text clipped - 8 lines] > > What spec? Why are you doing this study? > I already said what spec I have so far, I use Coulomb and Lorentz > equations. I use formula like this: F= m*a = k * Q1*Q2/r^2, and all I > ask is for similar formula that can take spinning magnetic moment into > account as well. I need to calculate rate of change in angular > momentum as well as rate of change in linear momentum. Then you'll need an angular inertial momentum spec, mass distributions on the dipole, or zero. >I have all > sorted out for linear, and now I see there are no equations that can > handle torque and linear acceleration in the same time. The math is there, the spec is still lacking. Are you dealing with a conserved system Regards Ken S. Tucker > > Is that your problem? > > Charges in B-fields are tougher. [quoted text clipped - 22 lines] > experience about line of attraction between magnets and magnets/ > charges/metals. Open up any E&M textbook, and using the material in there either look up or derive the force a dipole feels in a magnetic field, and work from there. Doing it by minimizing the energy of the system would be a better way. Same textbook - read it. > You can not use computer to solve it since there is no such software. Should we kowtow to you as you obviously are omniscient to know that no person on this planet wrote such software. Credibility score nearing negative infinity. Hey, that the number you I'm assigning to your filter! ================================================= Golden California Girls: > Should we kowtow to you as you obviously are omniscient to know that no person > on this planet wrote such software. No, you should prove me wrong. SHOW ME, you human! ================================================= Eric Gisse: > Open up any E&M textbook, and using the material in there either look > up or derive the force a dipole feels in a magnetic field, and work > from there. Bullshit. SHOW ME! ================================================= Ken S. Tuicker > The math is there, the spec is still lacking. You are moron. SPECS: charge-charge interaction in 3D. what part do you not understand? The math is there, eh? good... SHOW ME! > ================================================= > Golden California Girls: [quoted text clipped - 31 lines] > > SHOW ME! my fringe magnets wont work look! http://farm1.static.flickr.com/88/254588320_de32fc4269.jpg?v=0 ================================================= Golden California Girls: > Should we kowtow to you as you obviously are omniscient to know that no person > on this planet wrote such software. No, you should prove me wrong. SHOW ME, you human! ================================================= Eric Gisse: > Open up any E&M textbook, and using the material in there either look > up or derive the force a dipole feels in a magnetic field, and work > from there. Bullshit. SHOW ME! ================================================= Ken S. Tuicker > The math is there, the spec is still lacking. You are moron. SPECS: charge-charge interaction in 3D. what part do you not understand? The math is there, eh? good... SHOW ME! ================================================= Golden California Girls: > Should we kowtow to you as you obviously are omniscient to know that no person > on this planet wrote such software. No, you should prove me wrong. SHOW ME, you human! ================================================= Eric Gisse: > Open up any E&M textbook, and using the material in there either look > up or derive the force a dipole feels in a magnetic field, and work > from there. Bullshit. SHOW ME! ================================================= Ken S. Tuicker > The math is there, the spec is still lacking. You are moron. SPECS: charge-charge interaction in 3D. what part do you not understand? The math is there, eh? good... SHOW ME! > > The math is there, the spec is still lacking. > SPECS: charge-charge interaction in 3D. > > what part do you not understand? > > The math is there, eh? good... We're in the software marketing/consulting business, do you have a web-site link for your product? Have you had any sales yet ? Ken |
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