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 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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Stability of solar system

As far as I understand, the stability of the Solar system means that planets do not collide and will not in near future. The only thing that is stated on Wikipedia is that scientists are concerned ...
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Stability analysis: small perturbations vs second derivative test

In a mechanical system with some equilibrium point $r_0$, one can do an analysis in order to check if such point is stable or unstable, i.e. the motion of a particle around of it is bounded or ...
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Is physics qualitatively stable if we let Planck's constant tend to zero?

I realise that we can't meaningfully answer the quesition "what is Planck's constant were zero" because it would break out physical models beyond recognition. However, if we let Planck's constant ...
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Pendulum with friction: La Sall's Invariance Theorem

I am trying to understand la Sall's Invariance Theorem, which is used to proove that a system is aysmptotically stable. Can someone help me to understand it, by making an example of how to use it. ...
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Sinking of Cage with weights on one side

If there is a cage with weights strapped on one side, will it always sink towards the weighted side face down? Will the cage rotate so the center of mass is facing downward?
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About the Stability of hydrogen Isotopes

Shouldn't tritium be more stable than a hydrogen atom with no neutrons? Why does tritium do alpha decay but not hydrogen atom with no neutrons? I suppose that when the number of neutrons increases the ...
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Why is it so much easier to fall when walking down a slope?

When I walk uphill on an icey road, I almost never slip/fall. But if I walk downhill or even on a relatively flat road, I slip/fall frequently. What is the physics reason behind this, and are there ...
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Nonlinear stability question

I am looking for a simple example where a system is linearly unstable, but nonlinearly unstable or stable, depending on the sign of the initial perturbation. For instance, assume the linear normal ...
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Decay of hydrogen nucleus?

Very naive question. Nuclear decay is associated to more complex nuclei and explained through radiation. What about hydrogen and less complex nuclei? Will these nuclei eventually break apart? Or is it ...
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Stability of potassium (fermipressure)

I have an exercise to calculate the pressure of the fermigas inside a potassium (bcc, $a = 0.525 \,$nm) crystal. The formula is given with: $p_0 = \frac{2}{5} \, \frac{N}{V} \, E_f(0)$ The result ...
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Is a Niven ring in the atmosphere of Uranus stable? [closed]

For my science fiction universe, I need to mine a lot of Deuterium and Helium-3. I have 10,000 intake fans each capable of 3,000 gigaliters an hour pushing atmosphere through 5 billion diffusers. ...
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Questioning Stability

Today in class my professor was teaching about Einstein's coefficients and in the talk of excited states in spontaneous emission, he was explaining about meta stability of an atom. This made me ...
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Why are the Lagrangian points $L_1$, $L_2$ & $L_3$ unstable?

Why are the Lagrangian points $L_1$, $L_2$ & $L_3$ unstable? I am doing a physics presentation in front of my class and I am just confirming this is correct, and if it isn't, could somebody ...
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Plausibility of a Dyson sphere [duplicate]

So Dyson spheres are generally considered implausible for two main reasons. One, it would an incredible amount (and type) of resources to build one. And two, a Dyson sphere would be unstable because ...
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Moon's orbital plane inclination causes Moon to fall

I read somewhere that if Moon's orbital plane would be perpendicular to the Earth's orbital plane - Moon will fall on Earth within 4 years (given today's position) Can this be shown analytically ...
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When would Earth's Moon's gravity take over? [closed]

At which point would an object stop being pulled from Earth and towards the moon? Could a light weight rope be tethered to the moon with the object over on Earth's gravity's side? Can it be done and ...
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Righting moment for object submerged in water

I am looking to determine the lateral angle at which an underwater camera system will no longer right itself. When on the ocean floor it is $-24.30~\text{kg}$ buoyant with the difference between its ...
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Stability on a bus

I ride the bus from home to school and vice versa approximately 3-4 times per week for an hour each time. The bus is either bi- or tri-articulated, and it can accelerate to speeds up to 80km/h. Most ...
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Why do modern bicycles have curved front wheel forks?

I can't help but wonder how the design might affect the stability of the the bicycle. How would it make a difference if they were straight, or curved much more than they usually are?
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Why do rope walkers always carry a long stick with them?

I saw in the film (based on a true story) "The walk" a guy who tried (and succeeded) to go from one high building to another via a rope. He even succeeded in going from one the (then still existing) ...
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How to determine the overturning moment on a stand alone, uncovered bean pole tipi [closed]

I will preface this by saying I am a highschool student who has not yet had a physics class. I engineered and built a hexagonal shaped, open bottomed, planter to hold soil that would contain pole ...
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Would it be correct to state that all the forms of everyday matter (mountains, tables, buildings, people, etc.) are in a metastable state?

We had a fire going in the backyard of a friends house this weekend, and after thinking about the chemical reactions occurring in the wood (and anything else we threw into the pit), I started to ...
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Question about a Attractors in Non-linear Systems

I've recently been reading up on non-linear dynamics and came across the concept of attractors. I'd like to ask if the concept of attractors can be used for pedestrian egress from a room? Since ...

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