THREE MAGNETS (N-dipole-body problem)

[Vdtta]

Three bar magnets are sitting on a frictionless table. They are pinned down through their centers, they can not translate, only rotate, again without any friction - it is a 2D situation, like this:

[S- x -N]

                      [N- x -S]


       [S- x -N]

INPUT: initial angles and coordinates
OUTPUT: new angles after system stabilizes

Is there a singe stable solution or could this system oscillate indefinitely?
Is there a way to calculate at what orientation would they stabilize, if any?

 

[R Power]

I am not too sure but may be this is the way system stabilizes...
imagine a triangle... and on each vertex imagine your magnets...3 on 3 vertex...
now the magnets will arrange as north of each faces south of other...like this:something like this imagine...I'm not sure

 

[Sobeita]

I'm certain there's a stable solution. Each magnet should seek an equilibrium and slope to it. Given the conditions you mentioned, especially "no friction", you could expect the magnets to vibrate indefinitely from the point of equilibrium, but that's negligible. (For a minute, I imagined it almost like a center of gravity problem, so that all three point toward the triangular center, but that's dead wrong, that would produce maximum repulsion.) I imagine that the closest two magnets would orient themselves in NSNS or SNSN format, which naturally provides the least resistance, and that the third, more distant magnet would partially displace both rotations slightly. I don't have a formulaic approach to solve your problem.

For any experts who happen to come across this page, is it possible that each magnet would orient itself perpendicular to the triangular center so that every magnet faces clockwise (or counterclockwise)? That sounds reasonable to me in an equilateral formation, but impossible in cases like a 10-10-160 degree triangle.

It definitely has to do with the distance between each magnet. That has to be part of any approach to solving this.

 

[Vdtta]

Thank you both for input.

Let me just say that I'm looking to solve this for more than a year now, and I still have no idea if there is one, many or some oscillating solution to this problem. I suppose I should just go and buy some magnets, pin them on a table and see what will happen, but I have no idea where I can buy magnets like this, nor where can I pull them from. So, if anyone can make experimental setup like this with real magnets, please do let us know what happens.

Any input is greatly appreciated.Reward for equations that can solve this: $250 (dead or alive)

 

[Sobeita]

Yeah, I'm pretty sure I'm not going to be able to help you. Here's the dipole-dipole procedure:

http://en.wikipedia.org/wiki/Magnetic_dipole-dipole_interaction

I also found this, it has a lot of relevant equations in it.

astrowww.phys.uvic.ca/~tatum/elmag/em3.pdf

I recommend you get a very cheap set of bar magnets, plastic medicine cups (from cough syrup, Pepto Bismol, etc.), three toothpicks, a shallow basin, and some clay, and try this:

1. Take the clay and mold it into three balls. Squash them into the bottom of a basin where you want the magnets to end up.
3. Push one toothpick into each of the clay shapes in the basin and pinch the clay around the skewer. If the toothpick is loose, try to reinforce it with a little extra clay. Again, try to make sure the tops of the toothpicks are all level with each other.
4. Fill the basin with water so that the water level is taller than the toothpicks but not as tall as the toothpicks plus the height of the cup.
5. Take each cup and tip it sideways. Partially submerge it in water, then tip it over the top of one toothpick. (The goal is to achieve partial buoyancy when the weight of the magnet is added to the cups.) Now repeat this for each of the toothpick.
6. Place one magnet on top of each cup. The cup should not rest on the top of the toothpick but float just above it. This way the toothpick will not interfere with the rotation of the cup, but will constrain it to the local area. If the cup is too high or too low, you can remove the magnet, lift the cup up off of the toothpick, and repeat this step.

This is the best solution I could think of with cheap and common materials.