hey, thanks a lot! that does indeed sound like it.
now, i have to admit i have no idea how to apply it. let me rephrase the problem slightly so that hopefully we can derive some formula that can be plugged in computer....
lets image only 3 bar magnets sitting on a table randomly spaced. they can not move, but can only rotate around its center, it is 2D situation. there is no friction of any kind, no gravity and the 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.) any idea how to derive equations to fit this case?
2.) for every initial position is there only one solution, even in 3D and with more magnets?
3.) gravity and magneto-electric fields act instantaneously on distance, right? so, is there any way to find out how quick reaction will be - how strong is rotational acceleration each instant for each magnet and how does it depend on distance?
4.) imagine now these magnets float in 3D space freely, and lets consider the middle magnet. it has a "choice" to be repelled to the right or to rotate its south pole to the left. will it rotate or will it translate? in other words, how to split acceleration to translation and rotation, what will it depend on if there is no friction and magnets are point particles with magnetic dipole moment?
cheers