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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.

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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Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?

I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance. Am I correct? Veritasium/Minutephysics video on Youtube.
TBBT
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Why doesn't a nucleus-like body made up of just neutrons exist?

We know that neutrons exert short ranged nuclear forces over other nucleons in a nucleus, and these forces are only attractive in nature. Also this force is universal and doesn't differentiate between charged or uncharged bodies. So why doesn't a…
Mehul
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Why doesn't a bike/bicycle fall if going with a high speed?

Why does a bike/bicycle fall when its speed is very low or close to zero and is balanced when going with a high speed?
Ahmad Farid
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Why are $L_4$ and $L_5$ lagrangian points stable?

This diagram from wikipedia shows the gravitational potential energy of the sun-earth two body system, and demonstrates clearly the semi-stability of the $L_1$, $L_2$, and $L_3$ lagrangian points. The blue arrows indicate lower potential energy, red…
Ehryk
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Why does this object periodically turn itself?

See below gif image taken from here. Or see this Youtube video about 30 sec in. Is this a real effect? Why does it seem to turn periodically? Can it be explained by classical mechanics alone? Is there a simple equation that models this…
pacó
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Is it possible that every single isotope is radioactive, and isotopes which we call stable are actually unstable but have an extremely long half-life?

I've read that tellurium-128 has an half-life of $2.2 \times 10^{24}$ years, much bigger than the age of the universe. So I've thought that maybe every single isotope of every single atom are radioactive, and isotopes which we call "stable" are…
Quantum Force
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Why do most office chairs have 5 wheels?

(Inspired by Why are four legged chairs so common?) I've been wondering for a while... Why do most wheeled office chairs have 5 wheels? My guess would be that while stability vs. simplicity results in 4 legs, adding mobility to the equation may…
Rolazaro Azeveires
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Stability of rotation of a rectangular prism

I've noticed something curious about the rotation of a rectangular prism. If I take a box with height $\neq$ width $\neq$ depth and flip it into the air around different axes of rotation, some motions seem more stable than others. The 3 axes which…
Kyle Oman
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How can the unstable particles of the standard model be considered particles in their own right if they immediately decay into stable particles?

How can the unstable particles of the standard model be considered particles in their own right if they immediately decay into stable particles? It would appear to a layman such as myself that these heavier unstable particles are just transient…
Justin
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Where did Schrödinger solve the radiating problem of Bohr's model?

One of the problems with Bohr's theory to describe the hydrogen atom, was that the electron orbiting around the nucleus has an acceleration. Therefore it radiates and loses energy, until it would collapse with the nucleus. Now Schrödinger describes…
BNJMNDDNN
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What does it mean when an isotope is stable?

Does stable mean that an isotope has a very long half life, for example xenon-124 has a half life of 1.8 x 10^22 years, or does it mean that fissure is theoretically not possible, or does it mean that the isotope has a very long half life, but the…
inf3rno
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Gravity in other than 3 spatial dimensions and stable orbits

I have heard from here that stable orbits (ones that require a large amount of force to push it significantly out of it's elliptical path) can only exist in a three spatial dimensions because gravity would operate differently in a two or four…
PixelArtDragon
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Why certain rotations are unstable? (Euler Equations)

We have the Euler equations for a rotating body as follows $$I_1\dot\omega_1+\omega_2\omega_3(I_3-I_2)=0\\ I_2\dot\omega_2+\omega_1\omega_3(I_1-I_3)=0\\ I_3\dot\omega_3+\omega_2\omega_1(I_2-I_1)=0$$ Where $I_i$ are the moments of inertia about the…
John Doe
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Why does the weighing balance restore when tilted and released

I'm talking about a Weighing Balance shown in the figure: Press & Hold on onside of the horizontal beam and then release it. It makes some oscillations and comes back to equilibrium like shown in the figure. Both the pans are of equal equal masses.…
claws
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Confusion regarding the principle of least action in Landau & Lifshitz "The Classical Theory of Fields"

Edit: The previous title didn't really ask the same thing as the question (sorry about that), so I've changed it. To clarify, I understand that the action isn't always a minimum. My questions are in the points 1. and 2. below. I understand that…
Javier
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