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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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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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 maths 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 ...
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On Planets orbiting binary stars

Several years ago a discovery was made of planet orbiting a star of a binary system (two stars orbiting each other). Since binary star systems are plentiful in our galaxy, I presume we will be ...
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Why is the cone shaped space capsule free fall through the atmosphere bottom forward the stable orientation?

It seems the stable orientation of the cone shaped space capsule while free falling through the atmosphere is having the bottom point towards the translational velocity relative to the atmosphere. Can ...
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Would a Dyson sphere face physical limits faced by white dwarves?

During a recent online discussion, one of the participants made the claim that a Dyson sphere would be limited in mass by the Chandrasekhar limit. Attempts to solicit evidence for this claim were ...
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Thermodynamic Stability - Convexity - Concavity of Thermodynamical potential

The thermodynamic stability principle requires convexity of the internal energy upon all of its independent variables. When we pass through the Legendre transforms to build all the other ...
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What would happen if we had a crystal structure but only gravitational interactions?

The idea is simple. Let's say we arrange similar bodies (call them planets, ions, anything) in an infinite crystal structure, but the only possible interactions are gravitational interactions. A ...
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Electrostatics fundamentals

Suppose a charge is kept at the centre of a square frame and the vertices of the frame have four more charges fixed to the frame which are identical to each other but not necessary that these four are ...
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Stability of a falling object

Suppose there is a falling object that has flaps around it providing resistance to the non-contact force of gravity. How would the vehicle theoretically not flip over? From my understanding, the ...
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What can I investigate concerning the stability of bikes? [closed]

I'm in high school, and I'm doing an Extended Essay for IB? I only have 1 bicycle and no fancy tools or measurement equipment, so it has be a pretty simple experiment, but complex enough that I can ...
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Why particles of thermodynamic systems have a preference for low energy levels?

While reading Ken Dill's Molecular Driving Force, I noticed this paragraph when the author is trying to explain the Boltzmann distribution. Particles don’t have an intrinsic preference for lower ...
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2 answers
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Why exactly is Neutronium-4 unstable and how to explain Marqués' experimental results?

Wikipedia states: A tetraneutron is a hypothetical stable cluster of four neutrons. The existence of this cluster of particles is not supported by current models of nuclear forces. There is some ...
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What analysis should I make when there is toppling question without specified axis? [closed]

For example - What maximum weight can be put on a table of 20 kg and radius 1 m with massless leg which are symmetrically placed on circumference so, it doesn't topple? Here, I don't know how to ...
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How can one construct a phase space for the time evolution trajectories in Hamiltonian?

I was wondering if conjugate momenta and position can be the variables of the phase space or not. I have $\frac{\mathrm{d}x_1}{\mathrm{d}t}$, $\frac{\mathrm{d}x_2}{\mathrm{d}t}$, $\frac{\mathrm{d}...
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4 votes
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Does mass affect how likely an object is to topple over?

I was at work recently pulling around some pallets when I had a thought. I wanted to know if the mass of the pallet had any influence on how likely it is for the pallet to topple over when going ...
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1 vote
1 answer
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Equilibria and conserved quantities in a superposition of central potentials

I have a Lagrangian made up of a superposition of $k$ central repulsive potentials centered at $(a_k,b_k)$. Each potential is somewhat strange - they take the form $V(r)=-\ln\left(r\right)$. The whole ...
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Earnshaw's theorem and stability of charge inside a hollowed cavity of conductor

When a positive charge q is placed in the center of a spherical cavity of a spherical neutral conductor, it induces a negative charge $q$ to line the inner wall of the conductor, and a positive charge ...
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What is a quasistationary approximation

I was reading an article which states : The linear-stability analysis for this system can be performed in complete generality; but it will be best for purposes of this review to go directly to ...
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3 answers
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Is Lyapunov function the ultimate method to assess the stability analysis of a system?

I have migrated from physics to electrical engineering and I'm seeing people in control admire Lyapunov methodology and control designs as if there is no other solutions and they consider it very sane ...
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