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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How much water to put in cup for maximum stability? [on hold]

I found this problem in ‘200 puzzling physics problems’ An empty cylindrical beaker of mass 100 g, radius 30 mm and negligible wall thickness, has its center of gravity 100 mm above its base. To ...
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Arnold's Mathematical Methods of Classical Mechanics and Lyapunov stability

In Arnold's Classical Mechanics of Classical Mechanics, he refers to Lyapunov stability in many of the problems in the second chapter. E.g. on page 20: "Problem: Consider a periodic motion along the ...
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Apparent contradictions in stability conditions for diamagnetic materials

I was looking at Herbert B Callen's book on thermodynamics, specially Chapter 8 on the Stability of Thermodynamic systems. In it, he states that for a system to be in a stable thermodynamical ...
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Can a Gyroscope be Used to Stop a Spinning Cable?

The scenario here is a helicopter attempting to hoist someone vertically into the air. When the person leaves the ground they begin to spin (sometimes slowly, other times quite fast if not stabilized ...
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How is Schrodinger's model of atom consistent with reference to Maxwell's Theory of Electromagnetic Radiation? [duplicate]

When Rutherford proposed his model of atom, he mentioned that "Nucleus is surrounded by electrons that move around the nucleus with very high speed in circular paths called orbits. James Maxwell ...
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Vorticity of Fourier Expanded Velocity

I have been reading some papers which find all three components of the vorticity vector for a Fourier expanded (perturbation) velocity field i.e $\mathbf{u'}(x,y,z,t)=\int\mathbf{\hat{u}}(x,y,t)e^{...
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Stability of a dipole magnet undergoing eddy current braking in a cylindrical tube

Consider a cylindrical dipole magnet with strength $B$ undergoing eddy current braking in a conductive cylindrical tube with the axis of the magnet aligned with the axis of the tube. The magnet ...
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Finding stable superheavy elements

Finding new stable superheavy elements is big interests in nuclear physics. Nuclides with $Z>92$ are not found in nature, but can be made artificially. Usually these nuclides become more unstable ...
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How can we deduce that a hydrogen atom is stable in relativistic QED?

Consider relativistic quantum electrodynamics (QED) with three quantum fields: the electromagnetic field $A_\mu$, one fermion field $\psi$ for electrons/positrons, and one fermion field $\psi'$ for ...
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Is flipping a coin is a stable rotation?

If I rotate a coin with dimensions: 10X10X1 about 1 of the big axes(10) in space, where there is no torque, will the rotation will be stable just like a frisbee or a football regular rotations are? ...
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Plum-pudding atomic physics in higher dimensions?

It is established that "normal" electron orbitals are not stable in more than 3 spatial dimensions, as the available energy levels become unbounded from below. However, this result only applies given ...
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What is causing plasma confinement instability according to Erik Witalis?

Erik Witalis mentions problems with traditional plasma confinement like the one in tokamaks and particle beams. Instead he mentioned a different technique. What is the problem with plasma confinement ...
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Chua's Circuit: an inequality ensuring that the equilibrium is not stable

According to Kennedy's Robust op-amp realization of Chua's circuit(1992), the differential equations satisfied by several physical quantities in Chua's circuit are $$\begin{aligned} C_{1} \frac{d v_{...
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Chua's circuit: Is $x=y=z=0$ a stable equilibrium?

According to this wikipedia page, the differential equations satisfied by several physical quantities in Chua's circuit is (What each letter represents doesn't matter that much in this question) For ...
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Why doesn't the Lagrangian depend on higher-order derivatives of position?

This isn't a duplicate of already-answered questions, but rather a follow-up of this answer. The author presents a field-theoretical argument whereby a problematic run-away particle creation is ...
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What does the Ostrogradsky instability have to do with stability?

Ostrogradsky's instability theorem says that under some conditions, a system governed by a Lagrangian which depends on time derivatives beyond the first is "unstable". In the proof, one computes the ...
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Stability/decay, are they boolean or not, or does QM probabilities overrule this?

This is not a duplicate, I am not asking whether the proton is a stable particle, or why it is. I am asking about the definition of stability/decay whether it is boolean or not. I have read this ...
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Spiral galaxy stability

Is there a limit of baryonic masses $M_{B}$ ($M_{B}=M_{\star}+M_{g}$), beyond which a spiral galaxy is no longer rotationally supported? Like for example: Could spiral galaxies of baryonic masses $M_{...
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Is Brandt-Neri-Coleman stability analysis valid?

My question is related to the problem of stability of magnetic monopoles in Yang-Mills-Higgs theories. I have read "The Magnetic Monopole 50 years later" from Coleman and, in section 3.5, he discusses ...
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Why does a force divide equally on multiple supports/legs?

Imagine a bridge spanning across two pillars/supports with a weight of $80N$. {Any external forces affecting the system are assumed to be negligible.} We know that the force exerted on these 2 ...
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Orbital stability and inverse square law

It is well-known that orbits are stable under an inverse square law gravitational attraction. My question is, how far could gravitational attraction deviate from an exact inverse square law without ...
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Jupiter & Saturn

In his prog. on Jupiter, Brian Cox stated that the complex gravitational interplay, between Jupiter & Saturn, prevented Jupiter from drifting through the Asteroid Belt, and approaching our part of ...
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Railroad train on tracks [closed]

What keeps the railroad trains on the tracks? P.S: It is not the flanges, as already remarked by Dr. Richard Feynman. I want a detailed explanation of this question, if possible. Thanks.
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Why are so few inclined circumbinary planets known?

For a research project I'm studying the orbits of circumbinary planets, most of these planets orbits are coplanar. However I was wondering if orbits with a high inclination could be stable. I made a ...
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Is this wire-melting phenomenon a manifestation of the Plateau–Rayleigh instability; have I done my math right?

In LECTURE 5: Fluid jets from MIT's 1.63J/2.26J Advanced Fluid Dynamics equation 23 is $$\omega^2 =\frac{\sigma}{\rho R_0^3} k R_0 \frac{I_1(k R_0)}{I_0(k R_0)}\left(1 - k^2 R_0^2 \right)$$ and is ...
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Stability of Schwarzschild and Reissner-Nordstrom spacetimes

I am interested to know what is the best we can say about stability of Schwarzschild and Reissner-Nordstrom black holes. I found some who study the behavior of perturbations that satisfy the ...
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What physics describe the way a waiter/ waitress is balancing his/her serving tray?

A waitress in order to balance his/her tray is continuously moving this tray up and down. Similarly if you want to balance a pencil by its tip on your hand, you move your hand up and down. Does ...
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Why is the orbit of the Earth around the Sun very intricate?

The movement of the earth around the sun is very Goldilocky. Did it happen over the years as the orbit of earth averaged out into how it is now? Is there any chance of it (orbit) changing by itself in ...
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Why is the isotope of lead-206 stable against alpha decay?

The mass of Lead-206 is larger than that of Mercury-202 + Helium-4. Why is then Lead-206 stable against alpha decay? I have heard that the beta-decay can stabilize a nucleus against alpha decay, and ...
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Why do unstable nuclei form?

Why do unstable nuclei form? Is it that we simply find unstable nuclei in nature and understand what these nuclei do in order to become more stable? I feel like textbooks gloss over this question ...
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Why symmetry leads to stability?

In the whole course of physics I observed a very common thing present around us which is symmetry. Symmetry leads to stability everywhere. For example:-Pauli's Exclusion principle tends to make the ...
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Why are orbits $1.5r_{s} < r < 3r_{s}$ unstable around a Schwarzschild black hole?

The "Orbital motion" section of the Wikipedia entry corresponding to Schwarzschild metric reads: A particle orbiting in the Schwarzschild metric can have a stable circular orbit with $r > 3r_s$. ...
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Stability condition of a finite difference algorithm

While studying finite difference methods of TDSE I found myself stuck on a reasoning step: The largest possible spatial curvature for the wave function, $\frac{\partial^{2}}{\partial x^{2}} \Psi(x, ...
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Poincaré Map (Quasi-periodicity; Stability)

In a Poincaré map, when quasi-periodicity is exhibited by the dynamical system, what does it mean in terms of stability for the dynamical system?. Why is it so that as Maximum Lyapunov exponent (MLE) ...
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Why does stability come from binding energy and not mass

The mass of a nucleus is given by: $$ Mc^2=n M_n c^2+zM_pc^2-B(z,n) $$ And we were told that nuclei want to maximise the binding energy per nucleon. However, I don't see why they don't want to ...
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Model Rocket Stabilisation

I am designing a model rocket and am using 3 B6-4 Engines. Inevitably there will be perturbation of its trajectory by wind and engine/thrust inconsistencies. The way that I currently understand the ...
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Earnshaw's Theorem in Chemical Bonds

Earnshaw's theorem says that: A collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. I also know ...
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Is there an analogue of Earnshaw’s theorem for inverse cube force laws?

Earnshaw’s theorem states that point charges cannot be held in electrostatic equilibrium by an electric field. Is there an analogue of this for inverse cube force laws?
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How can I prove that a state of equilibrium is unstable?

In the particular problem I encountered, an electric field was zero at the origin and we were meant to prove that a particle at the origin was in an unstable state of equilibrium. Is it enough to ...
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Earnshaw’s Theorem and Ring of Charge

A classic problem in determining the motion of a negative charge when displaced from a positively charged ring shows that the charge oscillates. However, Earnshaw’s theorem states that (quoting ...
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Increased Stability of Vortex Rings by Pushing it

I've noticed in playing around with smoke rings that they are substantially more stable in their axial motion if pushed from behind by a hand, as can be seen in various Youtube videos. I was wondering ...
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Strong force and radioactivity [duplicate]

Why does adding more neutrons to an atom unstabilise it? Won’t adding more neutrons increase the strong force and thus knit the nucleus more tightly? Or is it because it’s being added in a particular ...
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What if $\omega =0$, which is the frequency of the perturbation term?

In analytic mechanics, when we found a equilibrium position of the system, to determine the stability of that configuration, we apply $q \to q_0 + \epsilon \eta$ with $|\eta| \ll 1$ s.t $q_0$ is the ...
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What is the “special time dependence” that develops in an Ostrogradskian instability?

I've been reading papers that deal with Lagrangians containing second- and higher- order derivatives of field variables. In this paper in Section 3.1, I found this very interesting quote: The ...
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Why does the $\phi$-cubed theory have no ground state?

In the book of Sredinicki's, he claimed that the $\phi^3$ theory has no ground state, hence this is not a physical theory. My question is that I can't see why this system has no ground state. And I ...
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Large mass body on Lagrange point L4/5

Lagrange points L4 and L5 are stable for a test particle. But what happens if instead the body at L4/5 (let's call it C) has a mass significant enough that its gravitational pull on the other two (let'...
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Why Don't All Heavy Elements Decay into $^{62}\rm Ni$?

I read the question If we assume that protons don't decay, then will all matter ultimately decay into Iron-56 or into nickel-62?, but I have a different question concerning the decay that has ...
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Stability in Nuclear Shell Model

As far as I understand , a particular sub-shell is filled with either protons or neutrons, $2*(2l+1)$ number of them, and never both together since protons and neutrons fill up levels separately in ...
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Why is it that a stationary bike will fall but a moving one won't? [duplicate]

No matter how much I think about this I can't come up with a reason to me there is no difference In the forces acting against the tilting of the bike in both the cases as mothion is in the ...
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Stability of circular orbit in attractive inverse cube central force field

Considering a motion of a body under an attractive inverse cube central force, $\textbf{F}(\textbf{r}) = -\frac{k}{r^3} \hspace{1mm}\hat{\textbf{r}}$ with $k>0$. Is it possible for a body to move ...