THREE MAGNETS - is interaction unique, oscilatory or chaotic solution?

[Sione]

--- 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, we have "top" magnet, "middle" magnet and "bottom", like this:

[S- x -N]                                topMag: a=90, x=7, y=25

                  [N- x -S]              midMag: a=270, x=18, y=19


      [S- x -N]                          botMag: a=90, x=12, y=4

- input are 3 initial angles and 3 pairs of (x,y) coordinates
- output are the new angles after system stabilize


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 there are no bugs. here's simple question from every day 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

 

[Loren Booda]

Have you considered that the magnets as stated might oscillate ad infinitum, most likely chaotically? An interesting problem - simple to state, but hardly trivial. You need to write code, and a powerful computer to crunch it, step-by-step. You may first want to peruse the three-body problem.

 

[Sione]

Have you considered that the magnets as stated might oscillate ad infinitum, most likely chaotically? An interesting problem - simple to state, but hardly trivial. You need to write code, and a powerful computer to crunch it, step-by-step. You may first want to peruse the three-body problem.

an echo, eh?