THREE MAGNETS (N-dipole-body problem)
abaraba
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
abaraba
Sue...
abaraba
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?
RustyJames
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.
Sue...
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
Tom Roberts
> --- 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
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
abaraba
> 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.
xxein
xxein: I can provide only a simple answer to the initial setup (in
general).
If the ascii represents coordinates and bar length, and no perpetual
motion can be achieved, the solution is static.
The leftmost N will be swung to the bottom S due to strength of the
field and vv. The right N magnet will point to the bottom S. Where
else? It is the closest opposite polar influence.
Why don't you try it for yourself? It is simple enough to do, isn't
it?
abaraba
> field and vv. The right N magnet will point to the bottom S. Where
> else? It is the closest opposite polar influence.
>
> Why don't you try it for yourself? It is simple enough to do, isn't
> it?
I find it very complicated, but I'm glad its a simple matter for you.
Can you please tell me if magnets attract objects in straight line or
they spiral on the way?
RustyJames
as The leftmost N will be swung to the bottom S due to strength of the
> > field and vv the Lorentz Force Law HINDERS AND MORE angular acceleration OR orientation AND A STALL WILL OCCURE
THUS SAYITH RUSTY JAMES AND SO IT IS TRUE
RustyJames
wrote:
I mean any more more angular acceleration or orientation a stall in
angular acceleration or orientation magnetic null will occur
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.
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
abaraba
> 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?
Tom Roberts
> Tom Roberts wrote:
>> 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....
>
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
Ken S. Tucker
into his Preparation H again :-).
On Jan 20, 1:44 pm, abaraba <zelko...@gmail.com> wrote:
> > 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?
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
> 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 I had to solve that problem I'd use a
computer.
Regards
Ken S. Tucker
abaraba
>
> 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,
> > 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
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?
RustyJames
do mean, are the lines of fluxx straight in these situations
abaraba
> > 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 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?
Ken S. Tucker
> > > 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 I had to solve that problem I'd use a
> > computer.
>
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
abaraba
> 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
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.
Ken S. Tucker
> > 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
>
> 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?
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
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.
Doing it by minimizing the energy of the system would be a better way.
Same textbook - read it.
Golden California Girls
> 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!
abaraba
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!
abaraba
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.
abaraba
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.
rustyj...@gmail.com
my fringe magnets wont work look!
http://farm1.static.flickr.com/88/254588320_de32fc4269.jpg?v=0
Ken S. Tucker
> > 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