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

• Sione
In summary, the three magnets on a table are randomly spaced. There is no gravity, no friction, and only magnetic forces are acting on the magnets. The top magnet, the middle magnet, and the bottom magnet are represented by "x", "y", and "z" coordinates, respectively. The initial angles and new coordinates after the system has stabilized are shown.
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:
Code:
[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

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.

Loren Booda said:
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?

## 1. Is interaction between three magnets a unique solution?

Yes, the interaction between three magnets is a unique solution. This means that the final outcome of the interaction is dependent on the initial positions and strengths of the magnets, and there is no other set of initial conditions that will result in the same outcome.

## 2. Does the interaction between three magnets result in an oscillatory solution?

It depends on the initial conditions. The interaction between three magnets can result in an oscillatory solution, where the magnets exhibit periodic motion around each other. However, this is not always the case and the magnets can also reach a stable equilibrium or exhibit chaotic behavior.

## 3. Can the interaction between three magnets result in a chaotic solution?

Yes, the interaction between three magnets can result in a chaotic solution. This means that the motion of the magnets is highly sensitive to their initial conditions and even small changes in the initial positions and strengths can result in vastly different outcomes.

## 4. Is there a mathematical equation that can accurately model the interaction between three magnets?

Yes, there are mathematical equations, such as the Lorentz force equations, that can accurately model the interaction between three magnets. However, the complexity of the equations increases with the number of magnets and it becomes difficult to predict the exact behavior of the system.

## 5. Can the interaction between three magnets be used in any practical applications?

Yes, the interaction between three magnets has many practical applications, such as in magnetic levitation systems, electric motors, and magnetic resonance imaging machines. Understanding the behavior of three magnets can also provide insights into the behavior of larger systems with multiple interacting components.

• Electromagnetism
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
666
• Electromagnetism
Replies
2
Views
855
• Introductory Physics Homework Help
Replies
7
Views
532
• Electromagnetism
Replies
4
Views
2K
• Electromagnetism
Replies
3
Views
2K
• Electromagnetism
Replies
6
Views
2K
• Introductory Physics Homework Help
Replies
25
Views
538
• Electromagnetism
Replies
23
Views
3K
• Electromagnetism
Replies
5
Views
2K