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2answers
94 views

Stability of equilibrium points

For a spinning top, the linearised equation in the angle $\theta$ when the top is spinning about its axis of symmetry, which is vertical, is of the form ...
3
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1answer
166 views

Why does the metastable form of Technetium-95 have a longer half-life than its most stable state?

I was looking at the isotopes of technetium page on Wikipedia recently, and it seems that the metastable ${^{95m}Tc}$ has a substantially longer half-life (61d) than its most stable state of ...
3
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1answer
265 views

Can stable nuclei theoretically fission through quantum tunneling?

As I understand it, an unstable nucleus is going to randomly fission because the forces binding it together are momentarily weaker than the electrostatic repulsion of the protons. Given that some ...
3
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1answer
56 views

Earth-Sun Lagrange points L4/L5 existence

Why do Lagrange points L4 and L5 exist at all? Consider the mass of Jupiter equals 320 Earth masses, and distance from Lagrange point to Jupiter is about 4-6 A.U. We get that the gravity of Jupiter ...
3
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1answer
102 views

Stability of square of masses on strings under rotation

Imagine we have a square of masses, $m$, connected by light inextensible strings, length $l$, rotating around it's centre at angular speed, $\omega$. It's easy enough to show that there must be a ...
3
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1answer
229 views

Vacuum stability in quantum field theory

What exactly do people mean when they talk about the scale dependence of the effective potential ($V$)? I explain the motivation for my question (and hence my confusion) below. Please correct me as ...
3
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1answer
102 views

Possibility of stable muonic structures?

In an analogy to the neutron, which decays rapidly as a free particle, but when bound in a nucleus it is stable, would it be possible to crease a structure that permits the stability of muons - be it ...
3
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0answers
38 views

Stability of D-Branes and Coupling to Fields

I've been brushing up on my string theory using Becker, Becker, Schwarz (p. 208 in particular). They state that some D-branes can couple to R-R fields from closed string excitations. They then go on ...
3
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0answers
28 views

Stability condition for AdS background (when gravity coupled to matter fields)

In finding the stability condition for AdS background (when gravity coupled to matter fields), why the conserved energy should be positive?
3
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2answers
151 views

Rayleigh-Taylor Instability dependence on acceleration direction

I'm trying to bolster my understanding of the Rayleigh-Taylor instability, and I've gotten stuck on the point of which fluid (more or less dense) is being accelerated into the other. Cases of uniform ...
2
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4answers
248 views

How does the position of lift affect the stability of the lifted object?

Consider this example: Treat G as 10. The blue blocks provide lift of 10N, or -1KG. The red block has a weight of 20N, or 2KG. The black bar has no weight. All have their center of gravity in ...
2
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3answers
210 views

Unstable equilibrium in a pendulum

Consider a pendulum with a bob and a massless, rigid, hinged rod attached to the bob. The bob is at rest at the bottom most position. Neglecting friction, is it possible to impart such a velocity ...
2
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3answers
139 views

How to do linear stability analysis on this system of ODEs?

I was trying to do linear stability analysis of spring pendulum. I arrived at the differential equations which describe the system. But I am unable to proceed to linear stability analysis. Is it ...
2
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2answers
147 views

How “unnatural” is the universe? [closed]

Looking to read up on the impact the discovery of Higgs boson has on the String Theory I came upon these two paragraphs in an article about the Higgs boson Nobel Prize: One possibility has been ...
2
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1answer
417 views

Radioactive decay / binding energies

If my understanding is correct, the binding energy determines a nucleus' stability and the greater the binding energy, the more stable the nucleus (e.g iron-56). The mass of the sum of nucleons that ...
2
votes
1answer
42 views

Why should slope of pressure versus volume always be negative?

I read that the slope of the pressure, ($P$), versus volume ($V$) graph should always be negative for thermodynamic stability, but there was no further explanation in the text. Could someone give an ...
2
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1answer
181 views

Importance of periodic orbits

In the study of dynamical systems, one often talks about solutions that repeat themselves after a certain time, hence their name of "periodic orbits". Then one moves to the distinction of "stable" ...
2
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1answer
637 views

How does light get into a stable optical cavity in the first place?

It is supposedly possible to trap a beam of light bouncing back and fourth between two mirrors in a stable configuration. As I understand it, this means the configuration will prevent further spread ...
2
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2answers
1k views

Countersteering a motorcycle

Everyone knows the story about countersteering. For those who don't I will explain it below and after the explanation i will ask my question. You can watch this short video as a beginning: ...
2
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2answers
1k views

Mech stability through gyroscope

I recently read up about gyroscopes, angular momentum and mechs (the big Cockpit controlled robots) and was wondering if it would be possible to get a stable walking mech (only as example, not meant ...
2
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1answer
117 views

Is there always an equilibrium point in space for gravity?

For instance, for a two-body system, there will always be a point in-between the two in which the forces of gravity completely cancel, and if I were there then I would experience no net force. I ...
2
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1answer
74 views

Why is plasma confinement on the NIF called inertial confinement when it appears to be confined by pressure?

I've heard that unlike Tokamaks that use magnetic confinement of the plasma, the NIF project uses 'inertial' confinement. What's inertial about it? Do they spin the plasma to use angular momentum like ...
2
votes
2answers
100 views

Stability of planet-enclosing shell supported by atmosphere

I understand that a hollow spherical shell of uniform density gives net zero gravitational attraction to objects inside it. So in vacuum, a ball at the centre of a spherical shell would not be stable ...
2
votes
1answer
180 views

Earnshaw's theorem and springs

Earnshaw's theorem states that the Laplacian of the potential energy of a small charge moving through a landscape full of static negative and/or positive charges (and gravity) is zero. Thus you can't ...
2
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1answer
252 views

Why are there some inconsistencies with the underlying principle of center of gravity and rotational inertia?

COG: The lower the center of gravity, the more stable and object is. Rotational Inertia: The farther the concentration of mass from the defined axis of rotation, the more resistance the object has to ...
2
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1answer
335 views

Complex valued energy

I'm working on a 2D He superfluid system with vortices. I was asked to calculate the kinetic energy of vortex-(anti-)vortex pairs and compare the two situations. One finds in literature that the ...
2
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1answer
30 views

Coexistence at Lagrange points

I was wondering how precise the location of an object in a Lagrange point needs to be to maintain stability, since it seems that several natural objects (asteroids) exists together in some of these ...
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1answer
79 views

Classifying regions of Van der Waal like gas

Given the equation of state $$p+a\left(\frac{N}{V}\right)=\frac{Nk_BT}{V-bN} \tag 1$$ Taking into account of the fact that a realistic model requires $p \geq 0, V \geq Nb, N>0$ classify the ...
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2answers
762 views

Why a mono-atomic crystal layer (2D) can't be stable?

According to Peierls and Landau, 2D crystals were thermodynamically unstable. They can't exist! Of course, this theory was disapproved in 2004 (example: graphene). What is the general definition of ...
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2answers
193 views

How does particles gain electrical charges and repel each others? (electrostatic stabilization)

When I study electrostatic stabilization, I understand that the particles have same charge and thus repel others, this is how colloid is stabilize. But how does particles gain electrical charges and ...
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1answer
161 views

Why does graphene exist?

I started to read some articles on graphene and almost all say that graphene was discovered late because physicists thought it would be unstable. Despite this, I didn't found a clear explanation of ...
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1answer
545 views

Stability and lifetime of soap bubbles formed with light gases like helium or hydrogen?

A friend asked me if it would be possible to make soap bubbles out of a gas like hydrogen and if you did, would they float higher, faster. Due to the lower mass of light gases (compared to the air) I ...
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2answers
227 views

Saturn ring stabilization

The rings of Saturn are the most extensive planetary ring system of any planet in the Solar System. I'm wondering, what power is primarily responsible for that stability? © Public Image by NASA ...
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1answer
436 views

Upper equilibrium point of a pendulum with small perturbations

I remember the following fact about a rigid pendulum: The point when the pendulum weight is lowest is a stable equilibrium while the point where the pendulum weight is highest is an unstable one. ...
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2answers
31 views

Notions of “confined” and “metastable” states?

What is the exact definition of terms "confined state" and "metastable state", in the context of quantum mechanics? Can we also have a "confined metastable state"? Can we somehow easily link these ...
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0answers
15 views

why can noise induce multistability, particularly in (bio)chemical systems

There are several instances that people claim that a system is monostable in a deterministic model, but when they consider stochastic models, from either master equations or Fokker-Planck equations, ...
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0answers
10 views

Recursion relations and stability analysis

I have a recursion relation in the form of the following two equations: $X_{t+1} = X_t + V_{t+1} \\ V_{t+1} = wV_t + cy(g-X_t)$ I want to write these two equations into a matrix form so that I can ...
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0answers
41 views

Measure of stability

Is there a measure of stability of different systems? What I mean by stability is the ability of a system to return to its original position, even when inputted with high amounts of energy. The more ...
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1answer
22 views

Examining the presence of persistent domain from time series data

There are three variables, $X_t$, $Y_t$, and $Z_t$ that are dependent of each other, and I have the time series data of those variables from replicated experiments. The stochastic dynamics look quite ...
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0answers
35 views

What is the criterion of stability of thick-walled spherical shell?

Is there the formula (if someone already has discovered it) or what is the algorithm (if a particular formula was not deduced), to calculate the critical pressure of thick-walled spherical shell $−$ ...
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0answers
479 views

How would the solar system change if Earth was to just disappear? [closed]

Having just finished Arthur C. Clarke's "Childhood's End", my question is, what exactly will happen to the stability and configuration of our solar system if our planet Earth was to just disappear? I ...
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2answers
637 views

How, exactly, does a reaction wheel work?

Reaction wheels, mounted on spacecrafts and satellites, are used for precision attitude control. It is not clear to me how they can do this, though. My best guess is that when a motor accelerates a ...
0
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2answers
119 views

Why is there a limited range of possible soap bubble size?

Soap bubbles are never "too small" or "too large". What defines the range of possible diameters of a soap bubble? Related questions: Why do steam bubbles increase in size as they rise, Why is the ...
0
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3answers
90 views

What makes an orbit stable or unstable?

I have an assignement, where I have a given central potential $V(x)=-\frac{K}{6r^6}$ and object with an angular momentum $L$. I've calculate the radius of a circular orbit, which I've done by ...
0
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3answers
162 views

Why doesn't an orbiting body keep accelerating?

As a physics newbie I'm trying to get a grip on basic orbital mechanics. I think I'm beginning to get grasp on how bodies interact with each other. When a body approaches another body it accelerates ...
0
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1answer
96 views

Classical Mechanics - Potential Energy Function [closed]

Question The potential energy function of a particle of mass $m$ is: $$V(x) = \frac{cx}{x^2+a^2}$$ where c and a are positive constants. Qualitatively sketch $V$ as a function of $x$. Find two ...
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0answers
44 views

How stable is a tablespoon of neutrons once removed from a neutron star? [duplicate]

I've often heard public lectures describing the degenerate, exotic matter left behind after a star collapses but fails to go supernova; one that has found its way to become a neutron star. The speaker ...
0
votes
1answer
41 views

Is an elastic, gravitating object stable?

As I understand, an object can contract under its own gravitantional pull. Then as it does so, different parts of the object must move with some velocity. This in turn means that their relativistic ...
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1answer
31 views

2D room with electron-point-charges (stability)

Is there a fast way to find out stable #"point charges" & constellation for this kind of Simulation. The 2D repeating itselve in each direction till infinity, so i've a kind of symetrie here. ...
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1answer
62 views

Temporal properties of a photon

Naively, one can attempt to consider the (impossible) light-speed inertial frame. From there you arrive at nonsense conclusions like 'the universe is flattened in the direction of travel' which must ...