# Questions tagged [stability]

Stability theory addresses the stability of potentials, solutions of differential equations, and of trajectories of dynamical systems under small perturbations of initial conditions.

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### Why don't motorcycles have as good a turning radius as bicycles? [closed]

The question is about why are motorcycles not manufactured with handlebars that can turn to great degrees like a bicycle. In most motorcycles, you hardly have a steering angle of about 20-30 degrees, ...
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### Why are vortices stable?

Vortices persist over time, but change their shape. I am used to a structure that persists being “stable” as in it is robust against small perturbations. How can one define stability of a Vortex? For ...
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### How do you check the stability of a kink solution?

I am reading a nice introductory note by Hugo Laurell (http://uu.diva-portal.org/smash/get/diva2:935529/FULLTEXT01.pdf) but got confused on section 3.2. He claims the stability of kink by expanding a ...
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### Is passive magnetic levitation without moving parts possible without the use of diamagnets?

So, I looked at the Wikipedia page on magnetic levitation and it described lots of ways of levitating things magnetically, but they were all stabilized by either electronic feed-back loops, ...
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### Has any one seen an application of the virial theorem (say with magnetic fields) for non-self gravitating system?

Here is the version of the theorem I am most familiar with - consider an ideal magneto-fluid with density $\rho$, bulk velocity field $\mathbf v$, with magnetic field $\mathbf B$ and (isotropic gas) ...
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### Will a platform only supported by a column in the center fall? (Excluding weather)

My friend told me that without wind, a building with a platform that only has a column supporting it would be balanced and not fall, given that there is no wind. I said that the platform would fall ...
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### Clarification in the definition of stable and unstable equilibrium

I am studying about types of equilibrium which are stable, unstable and neutral. In the definitions of these equilibriums they used the term "position of equilibrium". Like in stable ...
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### Extrema in the Table of Nuclides [closed]

Symbolic picture of a nuclid chart: I would like to know for which $Z$ the area in the nuclide map has the greatest width and for which $N$ and the greatest height. Does anyone know? Note: I don't ...
594 views

### Why is the number of isotopes of an element bounded?

Is there a known reason why any given element has finitely many isotopes? Here I mean both stable and unstable isotopes. If we know this, do we have a reason why, for a given element, are the isotopes ...
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### Is classical Kaluza Klein theory stable or not?

Set Up In the original classical Kaluza Klein theory, you have a $d+1$ dimensional manifold where one space dimension is a circle $S^1$. In the "low energy limit," none of the metric ...
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### Is $\phi^4$ theory unstable?

I tried to write a simulation of a $\phi^4$ theory for 2+1 dimensions. But whatever values I gave for the coupling constant it always seems to blow up. i.e. a wave-like equation with a mass and ...
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### Stability analysis of ODEs containing non-linear terms

I am currently reading this lecture notes on non-linear dynamics. If you look at equation (7) it is easy to write the ODEs, $\dot{x} = y$ and $\dot{y} = -x$ into a matrix form $\dot{\vec{x}}=A\vec{x}$...
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### If radioactive decay is measured by halflife does it mean that few atoms of a radioactive material are practically stable?

If radioactive decay is measured by halflife does it mean that few atoms of a radioactive material can be considered practically stable? If we try to measure the time when 0,1% of the atoms of the ...
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### Moment Of Inertia and Stability of Rotation [duplicate]

https://youtu.be/uyU25DdONjo In the last 10 seconds of the video,the guy says that the rotation is unstable, the the moment of inertia is intermediate, why is this so? Is it as rotation from the other ...
299 views

### Why higher the binding energy per nucleon, more stable the nucleus is.?

Binding energy per nucleon is a measure of how stable the nucleaus is. is this true.? I looked at few answers on this site but there is no clear agreement on it.
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### Linear stability analysis of a 2-cycle

In a discrete $N$-dimensional Hamiltonian map $\mathbf{X}^{(n+1)}=f(\mathbf{X}^{(n)})$, we often find a 2-cycle which shows oscillation between two points in phase space. In such a Hamiltonian map we ...
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### Could the hypothetic water bodies on Mars be 'stable' only if they were large like Earth's oceans?

Could the hypothetic water bodies on Mars be 'stable' only if they were large like Earth's oceans which needs macroscopic basins? Are possible rivers and lakes enough to ,mantain all the water.As ...
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### Fixed point of non-linear system: infinite eigenvector

I've come across a $2d$ non-linear dynamical system (autonomous) the stability properties of which I would like to understand better. Computing the stability matrix, its eigenvalues and eigenvectors, ...
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### Radiation of EM waves by revolving electron

If accelerating charges produce electromagnetic waves, what makes Bohr's model of the atom so different from Rutherford's? Rutherford's model had a drawback that due to the constant acceleration of ...
45 views

### Physics history — the Ultraviolet Catastrophe [duplicate]

I will ask my question in a way that's all handwaving and no math, and I will welcome handwaving answers. I'm interested in visualizing the concepts. We had an idea about the atom as a massive nucleus ...
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### Does Earnshaw's theorem apply to electrostatic + gravitational systems?

I've been learning about particle traps and Earnshaw's theorem. When dealing purely with electrostatic forces the theorem makes intuitive sense to me. But does it really apply to systems involving ...
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### Island of Stability in Astronomical Surveys

To the segment of nuclear physicists that predict that there is indeed an “Island of Stability” in super-heavy transuranic elements, where these atoms shouldn’t suffer the effects of radioactive ...
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### Stability analysis of a cubic characteristic polynomial

I have the following cubic characteristic polynomial describing some dynamical system: f(\lambda, b) = \lambda^{3} + 3\left(\frac{1}{2} + i \right)\lambda^{2} + \left( 3i-3b-\frac{1}{4} \right)\...
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### Stability of A Driven Pendulum [closed]

I am having confusion with regards to the proof of my problem. This involves a pendulum with harmonically driven pivot and the task is to show that the pendulum is stable in the inverted position when ...
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### Necessary and Sufficient Conditions for an Equilibrium to be Stable

In the 4th section The condition that convection be absent of the book Fluid Mechanics by Landau and Lifshitz, they give the following statement: For the (mechanical) equilibrium to be stable, it is ...
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### Mathematical Theory (Static and Dynamics) for multiple charges in space:

Which treatable general theory or mathematical tool is best suited to deal with multiple electrical charges in 2D and 3D spaces in terms of static analysis and in equilibrium condition and also its ...
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### Stability of a bicycle - analysis of eigenvalues

I am interested in bicycle stability and found this article (RG) on it. It seems that they calculate the roots of the characteristic polynom after using an exponential-ansatz (page 1969, (b)). I fail ...
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### Lagrange with Higher Derivatives (Ostrogradsky instability) [duplicate]

In class our teacher told us that, if a Lagrangian contain $\ddot{q_i}$ (i.e., $L(q_i, \dot{q_i}, \ddot{q_i}, t)$) the energy will be unbounded from below and it can take any lower values (in other ...
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### Does a positron go into decay process like some other elementary particles ? Electron, it's counterpart is stable and has a long half life

Can a positron decay? Or is it a stable particle like its counterpart the electron? (Reference: https://physics.aps.org/articles/v8/s138)
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### Why are Charge Density Waves (CDWs) sensitive to quenched disorder?

Just wondering if there is a simple answer for why CDW are unstable under quenched disorder? I would guess something about the nesting condition gets spoiled but then I read that Pair Density Waves ...
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### Why is helium-3 stable?

Why is helium-3 stable? Besides hydrogen, helium-3 is the only isotope that has a neutron-to-proton ratio less than 1. Why is it not radioactive?
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### Objects falling from table

It is an everyday experience: You have placed an object a tiny little bit too much over the edge of a table and it falls down. This is the case when the center of gravity is above the floor and not ...
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### Do laser filaments propagate in a straight line over long distances?

In so-called filament propagation, a powerful laser beam can propagate through a medium without diffraction. This occurs because the beam focuses itself through non-linear optical effects. Self-...
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### Binding Energy and Stability in Nuclear fission

I've read that particles in nuclear fission disintegrates into two particles with higher binding energy, and in this process energy is released. Now I am just trying to understand this by common sense,...
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### What would happen if the attractive force at work in the nucleus had been equal in magnitude to the repulsive electrostatic force between the protons?

I am just starting with radioactivity and I came upon this statement: "Since the nucleus is stable, this means that there is some attractive force at work in the nucleus and that its magnitude ...
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### Stable number of neutrons for a given nucleus with $Z$ protons [closed]

I have been trying to derive an expression for the stable number of neutrons using the semi-empirical mass formula. I tried to derive it by dividing the Ma by total number of nucleons and then ...
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### How weighing balance works and can balance itself?

i am new in this community and i was not able to answer in a similar post "how does a weighing balance that has 2 identical mass on both sides is capable of balancing after being tilted". i ...
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### Balance of an non-homogeneous object

Would a pencil balanced on its tip, remain balanced if the the tip was made of a material twice as heavy than the rest of the pencil?
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### Why does exchange occur between electrons having same spin in “degenerate orbitals”?

I am a high schooler and I read in my chemistry book that half filled degenerate orbitals are stable because electrons with the same spin in those degenerate orbitals exchange their positions and this ...
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### What actually makes a Bohr's radius stable?

I was told that Bohr introduced the concept of Stationary orbits in which electrons were stable in my school but I never got the reason behind this stability. So can someone explain why is Bohr's ...
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### How to show that an atomic Hamiltonian spectrum is lower-bounded?

I'm looking for a proof that the spectrum of an atomic (or molecular) Hamiltonian is lower-bounded. Right now, the closest I've got is the proof in [1] that the spectrum of a second-order elliptic PDE ...
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### Can a position variable have an infintesimal in it?

I've been pondering unstable systems, such as a perfectly round rock atop a smooth hill. At the top of the hill is a metastable point where the rock could roll either way after an arbitrary amount of ...
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### What is an intuitive way of understanding Ostrogradsky instability?

Is there a way of explaining why no differential equations in physics exceed order two without delving into Lagrangian and Hamiltonian mechanics - i.e. from Newtonian mechanics? Moreover, is there ...
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### Nature of stability in a conservative system

In CM, a conservative system can be described by a potential energy function, $V(x)$ The states of the system which will be in equilibrium will be found at the extrema of this potential where: \$\frac{...
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### Stability analysis basics

I would like to see a rigorous treatment of stability analysis. For example, a lot of high-school level texts give examples like this: https://courses.lumenlearning.com/physics/chapter/9-3-stability/ ...
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### Planetary model of the atom

Wherever I look about the early planetary model of the atom, it says the electron must lose energy while revolving around the nucleus. And therefore fall into the nucleus. Thus, the atom is unstable. ...
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### What is the intuition behind a high Froude number causing instability in uniform flow?

Uniform flow in an inclined plane becomes unstable for high froude numbers. I can follow the spectral analysis, but I am curious why I would expect high froude numbers to cause instability. What is ...
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### Why does uniform flow become unstable when the Seddon celerity is greater than the Lagrangian celerity?

Uniform flow down an inclined open channel becomes unsteady under certain conditions. Vedernikov's number > 1 is a generally accepted necessary condition for this type of instability. Vedernikov's ...