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 can we determine stable and unstable equilibrium points from a potential energy versus displacement graph?

In this question, how can we comment on the position of stable/unstable equilibrium if we don't know the total energy of the system? We know force is zero at points 'a', 'b', 'c' and 'd' but there ...
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Can planets orbiting a binary star trace out an orbit in the form of an 8 (or $\infty$-sign)? [duplicate]

In this article there is a lot explained about planets orbiting a binary star. It is said that a planet orbits the binary star around the CM of both stars. I couldn't find anything about planetary ...
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Stability of Photon Orbits

In the context of general relativity the photonsphere occurs in $r = 3M$ (schwarzschild), and it is a saddle (unstable) fixed point on the phase space. Is it possible for a saddle point to be an ...
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Stability, unstability (and metastability) in liquid-gas phase transition: unstable in regards to what?

I have a question about the stability, unstability (and extra questin about metastability, between the spinodal lines if you have time), when we are having a liquid gas phase transition. Here, a ...
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Will an isolated Helium atom decay if all electrons are removed?

I’m not about a plasma with the possibility of reassembling of the lost electrons. How long a He-nucleus (aka. an alpha particle) will be stable without electrons? Stimulation for my question was ...
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A question about the tennis racket theorem with degenerate eigenvalues $I_1, I_2 , I_3$

If a rigid body has a symmetry such that two of the principal moments of inertia are equals, i.e. $$I_1=I_2> I_3 \qquad{\rm or}\qquad I_1>I_2=I_3.$$ Are the rotations around the principal axes ...
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Explain why a stationary object on an inclined plane may start moving after a random time? [duplicate]

An object (such as a mug of coffee, expensive phone, laptop) is placed on an inclined plane and remains stationary due to friction. After an interval (observed as random) it will begin to move (and ...
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Wheel rolling leaned against a vertical wall

I'm new with rigid problems about. I'm trying to solve this: A massive circular disk of mass m, radius R, and negligible thickness is leaned against a vertical wall, slanting by 45 . In the ...
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Stability of a matrix with complex coefficients

while solving a physical problem of an optical beam propagating through a periodic media, I have obtained the following system of coupled differential equations \begin{gather} \frac{d}{dz}\begin{...
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What is the state of the equilibrium for a second derivative equal to zero?

Considering a potential energy of $U$, and a displacement of $x$, the force is given by $F=-\frac{\partial U}{\partial x}$. Since equilibrium is defined as the point at which $F=0$, we can express ...
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Situation of Stable, Neutral and Unstable Equilibrium

Recently, I was reading about stability of equilibrium. I came across the definitions for different types of equilibrium. Neutral Equilibrium: The kind of equilibrium of a body so placed that when ...
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Why do (short) strands of hair keep a horizontal position while falling?

When I drop a short (5 to 10 cm) strand of hair, it tends to end up falling slowly down at a horizontal position. I would expect a uniform cylinder to fall through air neutrally (at a arbitrary ...
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“Dynamically Stable” vs. “Elastically Stable”?

I am studying a group of materials using density functional theory. I am able to calculate elastic constants, phonon densities of states, and formation energies. The results imply that the materials ...
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thermodynamics and stability

Suppose this three processes, at same T and P, each of them on thermodynamical equilibrium: atoms -->molecule 1 atoms --> molecule 2 atomsdifferent --> molecule 3 Where atoms are infinitely ...
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What is the physical interpretation of Rayleigh's inflection point theorem?

Let $\boldsymbol{u} = U(z)\,\mathbf{e}_x$ be the velocity profile of an inviscid parallel flow. Rayleigh's inflection point theorem states that this flow may be linearly unstable to perturbations only ...
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Is this system in stable or unstable equilibrium? [closed]

6 positive, identical charges $+q$ are placed in a hexagon. A negative charge whose value I want to determine is placed at the center to keep the system in equilibrium. Which means $dU/dr = 0$. But ...
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Regularization: What is so special about the Coulomb/Newtonian and harmonic potential?

I wanted to know if the procedure for regularization of the Coulomb potential outlined in Celletti (2003): Basics of regularization theory could be generalized to arbitrary polynomial potentials. So ...
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Periodicity of the Kelvin-Helmholtz Instability

Why is the Kelvin-Helmholtz Instability so regular across space? If any perturbations anywhere in the boundary can lead to instability, why doesn't the pattern appear randomly across the boundary? ...
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Dzhanibekov effect in quantum systems

Dzhanibekov- or Tennis racket effect is what happens when an object with three diferent moments of inertia doesnt spin around the axis with highest or lowest moment of inertia. The object starts to ...
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Conservative central force and stable orbits

I saw a question a few days ago which referred to Bertrand's theorem. So, I now know that stable, closed orbits only occur when the potential function is $\frac{-k}{r}$ or $\tfrac{1}{2}kr^2$. If ...
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Smallest relative velocity driving a two-stream instability

The physical picture is a two-stream system of cold electrons and ions (i.e. $T_i=T_e=0$) with realtive velocities $V_i$ and $V_e$. The dispersion relation obtained is $$D(\omega)=1-\frac{\omega_{pi}^...
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Are electroweak particles stable?

Photons that [are associated with] the electromagnetic force are stable; while the W and Z bosons that [are associated with] the weak force are short lived. I guess that the high temperate electroweak ...
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Tipping point on fence panels? [closed]

I deal in temporary fence panels - and my concern is the tipping point of our product out in the field. Panels are 6' tall x 12' long (63#) Stands are 23" long x 6" wide We use sand bags (30#-40#) ...
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Why is that a system with a concave-up entropy-energy graph cannot have a stable thermal equilibrium?

This is from Schroeder's An Introduction to Thermal Physics: Let A and B be a system both with a concave-up entropy-energy graph. The systems will achieve thermal equilibrium when they are at the ...
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Binding Energy and Instability

I believe that I am correct in saying that: (1) a nucleus constitutes a preferred configuration for nucleons as compared to a disassembled array of nucleons; and (2) nuclei decay so as to achieve more ...
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Is it possible to have stable orbits around Lagrange point $L_1$?

Is it possible to have stable orbits around Lagrange point $L_1$? If yes, is there an upper limit to the mass of a body on such an orbit?
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Is there a connection between Bertrands theorem and Chaos theory?

Bertrand's theorem states Among central force potentials with bound orbits, there are only two types of central force potentials with the property that all bound orbits are also closed orbits, ...
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(No) imaginary frequency particle oscillations

Suppose we have two scalar fields $\varphi, \kappa$. Next, suppose there is a region in space where they are mix with each other, i.e., we have a lagrangian $$ \tag 1 L_{\text{int}} = A \varphi \kappa ...
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Understanding how the quartic Higgs coupling turns negative at high energies

How is the conclusion that the Higgs quartic coupling becomes negative at high energies ($\sim 10^{10}$) GeV inferred? I'm looking for a reference that has the necessary idea and calculations to ...
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How does Earnshaw's Theorem make passive magnetic bearings impractical?

I have only learned high-school physics but would like to gain insight into how Earnshaw's Theorem makes stable bearings that use magnetic levitation from permanent magnets impossible or impractical. ...
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How to find the frequency of small oscillation of a particle in a given potential? [closed]

A particle of mass $m$ is in a potential $$V(x)=-\frac12ax^2+\frac14bx^4$$ where $a$ and $b$ are positive constants. The equilibrium points occur when the potential $V$ is either minimum or maximum, i....
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Stability of Electromagnetic Waves

Is there currently any theory or set of equations which describe the stability of electromagnetic waves in gravity wells of compact objects such as neutron star or a white dwarf star . Weather the ...
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Why are stationary rotations of a rigid body about the largest principal axis not Liapunov stable?

In Arnold's Mathematical Methods of Classical Mechanics, 2nd ed., p. 145, he considers a rigid body with no external torque rotating about a fixed point O. He shows that the stationary solutions of ...
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Exotic Matter: Stabilizing Wormholes

Background I know wormholes are still hypothetical but this is pertaining to exotic matter and it's effect on wormholes. Reading through various sources, they all specify that if wormholes exist, ...
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Why are lower energy systems stable?

Apart form the practical evidence that the systems that exist in nature try to attain lowest energy possible and hence, maximum stability, and atoms forms bonds to attain low potential energy but do ...
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Phase portrait Hamiltonian system

I have the Hamiltonian: $$H(x,p)=\frac{p^2}{2m}+\frac{x^4}{4}$$ When I find the critical points associatted with the system $\dot{x}=\frac{p}{m}$ and $\dot{p}=-kx^3$, I find only one critical point ...
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How does center of mass correlate to stability?

"If an object is tilted it will topple over if a vertical line from its centre of gravity falls outside its base" http://www.schoolphysics.co.uk/age11-14/Mechanics/Statics/text/Stability_/index.html ...
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The stability of an atom

I've read about different models of atom proposed in 18$^{th}$ and 19$^{th}$ centuries, of which the most vital were JJ Thomson's model, followed by Rutherford's nuclear model and then Bohr's quantum ...
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Finding the stability from the eigenvalues of two second-order DEs

I'm analysing the stability of a double physical pendulum, and have determined the dimensionless system of equations to be \begin{align} \label{eq:dimensionless} \begin{aligned} & \ddot{\...
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Multiple star system, stable orbits?

Inspired by worldbuilding SE, I know that there are relatively stable star systems with two or three suns, but any more than that and they start to become very unstable (e.g. trapezium systems), but I'...
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Why are superfluid vortex lattices stable?

Both (a) neutral superfluids that are externally rotated, and (b) type-II superconductors (i.e. charged superfluids) under applied magnetic fields between the critical fields $h_{c1}$ and $h_{c2}$, ...
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Thermodynamic stable equilibrium conditions

If I understand correctly (which I clearly don't) the condition of stable equilibrium of a closed system at constant $(P,T)$ is that $G$ is minimum. That implies that $dG=0$ and $d^2G≥0$. Since $dG=...
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What is linear / eigenvalue buckling analysis?

I need some simple and clear explanation of what is called linear buckling analysis and why it is also called eigenvalue buckling analysis? In other words how natural vibration frequency or ...
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How the solar system just stay around the Sun and sSun itself?

I know that each and every planet stay with the solar system because of sun's gravitational field. What object has the gravity to hold our solar system while the boundless universe is all around the ...
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How to calculate precision of Pound-Drever-Hall technique?

When I read the fifth section (Noise and fundamental limits: how well can you do?) of Eric's article, I have question. In this section(page 85 and 86), Eric discussed the shot noise, and gave the ...
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Schrödinger equation solutions: stability and oscillations

What is known about Stability of solutions of time-independent Schrödinger equation (TISE)? Existence of time dependent but oscillatory solutions (of Schrödinger equation)? Stability of oscillatory ...
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On the stability of black holes

Vera Rubin just passed (RIP) and recent News reviving the theory that the dark matter might be due to (small?) black holes; the idea that smaller black holes may be more prevalent than thought (then ...
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overstability vs resonance: what is the difference?

Reading about discs, I encountered the word 'overstability' that its difference with resonance is not clear to me. Does anyone know the difference?
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Is there a prediction when our solar system would fall apart?

Within a few billion years our Sun would become a red giant and destroying Mercury and Venus and perhaps even the Earth. But nevertheless our solar system will still have some planets like Jupiter and ...
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Why are all mesons unstable?

My question is: why are all mesons unstable? Shouldn't the lightest mesons like the pion be stable because they are made from the lightest quarks (and anti-quarks)? Or could the they annihilate (the ...

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