# Magnetic bound state in classical mechanics

• A
• H Ucar
In summary, the paper presents a new way to obtain a magnetic bound state by using angular motion. The interaction between the field based forces and inertial forces ensures stability and allows for the formation of a bound state.
H Ucar
TL;DR Summary
Is it legitimate to discuss magnetic bound state solutions in classical mechanics here?
Seven years ago, I wanted to share and discuss my experiments results there but it was not possible since there was no published peer review paper yet and apparently not fulfilling forum requirements. Now we have such a publication, but still not sure the subject can be discussed here. Anyway, magnetic bound state solutions are present in classical mechanics (http://doi.org/10.3390/sym13030442) and currently reproduced by students, amateur scientists and engineers all around the world. If you have questions, I will be happy to answer them. Thank you - Hamdi Ucar

Delta2
Welcome to PF.

A magnetic bound state in a general sense is keeping an entity or a formation localized by means of magnetic fields. In classical physics Earnshaw theorem forbids this to happen in a statical configuration where no force fields including gravity, electrostatic, magnetic field and any combinations of them can be used to obtain a static equilibrium.

However, dynamic equilibriums are possible and this way one can obtain a bound state through orbital mechanisms like a star/planets system based on gravitational interaction and atoms where electrons orbit the nucleus based electric field attraction.

On the other hand, this mechanism does not work with magnetic fields since an orbital motion can be only stable in a central force problem when the dependence of the central force to the distance is expressed by a power factor greater than the inverse cube (r−3). This factor is r−2 for gravitational and electrical forces but r−4 for magnetic forces since magnetic force should always be between dipoles but electrical forces can be between charges (monopoles).

So, in classical physics, the only known way to obtain a bound state was the orbital mechanism and this only works with gravitational and electrical fields providing the attraction. The orbital motion is a dynamic interaction where field based forces are balanced by the inertial forces and Earnshaw theorem does not apply.

The magnetic bound state scheme given on this paper is also based on interplay of force fields and inertial forces, but rather in angular terms as angular motion, torque and moment of inertia. Since the bounded object is only required to perform an angular motion around its center of mass, it can stay without translational motion in contrast to the orbital motion.

Actually this angular motion only serves to obtain stability in angular degrees of freedom keeping a dipole body in an antiparallel orientation within a magnetic field.

From basic experiences with magnets we know we cannot do it when we place two magnets close to each other in a repulsive orientation on a low friction/frictionless surface. However this can happen here by the help of a property of the harmonic motion.

In a harmonic motion, the displacement and the acting force are always in the opposite directions. In a driven harmonic motion which this effect is based, a magnetic dipole body is exposed to a rotating magnetic field. This interaction is highly nonlinear and lies between driven harmonic motion and parametric excitation.

Anyway, a harmonic oscillator can be associated with a natural frequency and in a driven harmonic motion this determines the phase of the driven motion with respect to the periodic driving motion at a given frequency. By excluding possible damping factors, this phase is zero when driving frequency is below the natural frequency and shifts to 180° above it. This phase factor is called phase lag and in order to obtain the antiparallel kind alignment mentioned above, phase lag should be 180°.

This way, it is possible to exert a force of a magnetic body having full degrees of freedom in the direction of the weak field. That is, a rotating dipole magnet can repel another dipole magnet having degrees of freedom. After this stage, it is possible to obtain a stable equilibrium between this repulsive interaction and an attractive field force allowing to establish a magnetic bound state.

It should be noted that the power factor of the repulsive interaction with respect to the distance between dipoles varies between r−7 to r−8, almost twice of the static forces between dipoles. This high power factor ensures the stability of the equilibrium where the interaction can be attractive at long distance and switch to repulsive when magnets get close.

We can also align the orientation of the driving dipole slightly off the rotation plane in order to create a virtual static dipole which can be used for the attraction factor. Therefore a dipole magnet attached to a rotor can lock another dipole magnet in air. While this interaction is explained by the angular oscillation of the free body, translational oscillations also present to some extent and contribute to the repulsive factor. This contribution can be also primary depending to configurations.

The channel [YouTube channel advertisement redacted by the Mentors] covers numerous experimental solutions on this principle which some also mentioned in the article. Details about shown experiments can be found in their description text.

Last edited by a moderator:
Delta2
Apart from the wall of text, MDPI was listed as a predatory publisher in the Beall list.

Delta2 and malawi_glenn
This is an interesting image from your paper. Can describe in just a few sentences what's going on?

In this experiment, three large rare Earth dipole magnets mounted in these drums, rotating in sync and poles orthogonal to their rotation axes generate a complex time varying field having local minimum which serve to trap another rare Earth dipole magnet in air. Under such a condition, a magnetic body tends to stay in a position where its kinetic energy is minimum. More accurately, this minimum energy level (potential well) can be expressed as Landau's "effective potential"[1]. This model is used to explain the Kapitza pendulum (the inverted pendulum having a vibrating arm). Kapitza pendulum"s equation of motion is a forced harmonic motion with parametric excitation and exemplified with "rotating saddle" effect. This equation in its linear form is known as the Mathieu equation where its stability can be evaluated by Ince–Strutt diagram.

Videos of these experiments and their configuration details can be found on the Sudanamaru channel.

Note that Kapitza pendulum can be also realized magnetically using a compass needle as the pendulum and an AC driven Helmholtz coil as the vibrator [2].

[1] L.D. Landau and E.M. Lifshitz, Mechanics (Pergamon, Oxford, 1960), pp. 93-95. DOI:10.1002/zamm.19610410910

[2] Lisovskii, F.V., Mansvetova, E.G. Analogue of the Kapitza pendulum based on a compass arrow in an oscillating magnetic field. Bull. Russ. Acad. Sci. Phys. 71, 1500–1502 (2007). DOI:10.3103/S1062873807110044

vanhees71 and bob012345
Thanks. Is this just of academic interest or do you have an application in mind you can talk about?

Potential applications specific to this scheme are non-invasive surgery, particle traps, endoscopy and magnetic tweezers. These applications should be based on electrically or electromagnetically generated alternating fields instead of mechanical methods.

vanhees71 and bob012345
Just saw this video and was curious if it had been discussed here at the forum. I was quite surprised to see this thread was posted by the discoverer himself, Hamdi Ucar.

Mar 26, 2023

Action Lab previously posted a video about the time the paper was published, but didn't mention the similarity with the strong force mentioned in the above video, which I find really interesting.

Jan 7, 2021

Hamdi's YouTube channel has videos dating back to 2016 which show this effect.

mattt and DrClaude
Isn't this already used in levitating globes etc.?

A.T. said:
Isn't this already used in levitating globes etc.?

I don't believe so. I've watched several videos regarding the levitating globe in your video and no one has disassembled one. But everyone claims they work via a feedback system.

I'm unable to find any reference to either Hamdi Ucar nor this effect anywhere in wikipedia. There is also very scant information anywhere on the internet outside of Mr. Ucar's pages and The Action Lab. Perhaps if I spoke Turkish, I'd have better luck.

OmCheeto said:
I don't believe so. I've watched several videos regarding the levitating globe in your video and no one has disassembled one. But everyone claims they work via a feedback system.
You mean an active controller that senses the the globe position somehow, and adjusts the electromagnets in the base? That's possible. But the levitron spinner, is just a spinning magnet, levitating above a permanent magnet. Seems similar to what is presented by Ucar and The Action Lab , with the only difference being which part is rotating:

A.T. said:
You mean an active controller that senses the the globe position somehow, and adjusts the electromagnets in the base?
Yes.
That's possible. But the levitron spinner, is just a spinning magnet, levitating above a permanent magnet. Seems similar to what is presented by Ucar and The Action Lab , with the only difference being which part is rotating:

I suspect if you picked up the base of one of these spinning top levitrons and turned it on its side that the top would not follow like the Ucar device. The Ucar device seems to generate something quite similar to flux pinning in superconductors.

OmCheeto said:
I suspect if you picked up the base of one of these spinning top levitrons and turned it on its side that the top would not follow like the Ucar device. The Ucar device seems to generate something quite similar to flux pinning in superconductors.
Ucar's device might be more stable, because it has the stronger/larger magnet spinning (rather than the small levitating one), and because the spin rate is orders of magnitude higher. It's not necessarily something fundamentally different, just a different configuration.

OmCheeto
The principle is different. I wrote it above. There is no gyroscopic effect there, only a consequence of the driven harmonic motion. See the yt video titled '"How passive radiator (and bassreflex) works - 960fps". Above the resonance frequency, the passive radiator is 180 degrees out of phase with the active radiator. This condition makes the displacement of a body in the opposite direction of the force it receives. In a rotational dynamics of the magnetic interaction this opposition forces the magnetic body to be oriented in a repulsive angle.

A.T. said:
Ucar's device might be more stable, because it has the stronger/larger magnet spinning (rather than the small levitating one), and because the spin rate is orders of magnitude higher. It's not necessarily something fundamentally different, just a different configuration.

H Ucar said:
The principle is different. I wrote it above. There is no gyroscopic effect there, ...
Indeed. The spinning top (levitron) uses gyroscopic effects to stabilize orientation.

Not sure about the levitating globe tough. Is there anything spinning fast at all in them? Or are the electromagnets in the base emulating a fast changing / rotating field?

## 1. What is a magnetic bound state in classical mechanics?

A magnetic bound state in classical mechanics refers to a system where a charged particle moves in a magnetic field and its motion is confined to a specific region of space due to the magnetic field. The particle's trajectory forms closed loops, hence the term "bound state."

## 2. How is a magnetic bound state different from an electric bound state?

In an electric bound state, a charged particle's motion is confined due to an electric field, whereas in a magnetic bound state, the confinement is due to a magnetic field. Electric bound states typically involve attraction or repulsion between opposite charges, while magnetic bound states arise from the particle's interaction with a magnetic field.

## 3. What factors influence the stability of a magnetic bound state?

The stability of a magnetic bound state is influenced by the strength of the magnetic field, the charge and mass of the particle, and the initial conditions of the particle's motion. A stronger magnetic field or a heavier particle can lead to a more stable bound state, while certain initial conditions may cause the particle to escape the magnetic confinement.

## 4. Can a magnetic bound state exist in a vacuum?

Yes, a magnetic bound state can exist in a vacuum as long as there is a magnetic field present to confine the charged particle's motion. The absence of other particles or external forces does not prevent the formation of a magnetic bound state in classical mechanics.

## 5. What are the practical applications of studying magnetic bound states in classical mechanics?

Studying magnetic bound states in classical mechanics can provide insights into the behavior of charged particles in magnetic fields, which is essential in various fields such as particle physics, plasma physics, and magnetic confinement fusion. Understanding magnetic bound states can also help in designing magnetic devices and optimizing magnetic field configurations for specific applications.

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