abaraba
Jan20-09, 06:00 AM
--- 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]
[N- x -S]
[S- x -N]
-------------------------------
- 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.
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
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]
[N- x -S]
[S- x -N]
-------------------------------
- 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.
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