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3
votes
1answer
27 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 ...
0
votes
2answers
69 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
votes
0answers
21 views

Calculations to Determine Force Required for Gyroscopic Stabalization

I am currently undertaking a project involving gyroscopes, the aim of which is to stabilize a large object. I have read that gyroscopes work because of conservation of angular momentum, and if you ...
0
votes
0answers
8 views

Argument for stability of journal bearing via inertial and viscous forces?

As I understand a journal bearing, a rotor is levitated by hydraulic forces from the lubricant. While these are lots of studies on this subject, I can't manage to find a paper that coherently breaks ...
0
votes
1answer
56 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 ...
0
votes
0answers
34 views

Stability of a system

What do we mean by "stability of a system " in a Lagrangian of a model? Let's say that we have a very simple model like this $$L=\frac{1}{2}K_{ij}\dot{q}_i\dot{q}_j-\frac{1}{2}F_{ij}q_iq_j,$$ where ...
2
votes
1answer
86 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 ...
1
vote
1answer
111 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 ...
10
votes
0answers
101 views

Does anyone know the mechanism behind this double helix cloud formation?

This looks like m=2 swirling instability mode of the axisymmetric jet, but how could an axisymmetric jet form up in the sky like that?
0
votes
2answers
82 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 ...
2
votes
1answer
117 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" ...
4
votes
2answers
180 views

Understanding the Jacobian Matrix

Taking the example of a two dimensional system, desribred by the following ODE's: \begin{align} \frac{dx_1}{dt}&=f_1(x_1,x_2)\\ \frac{dx_2}{dt}&=f_2(x_1,x_2) \end{align} The Jacobian Matrix ...
2
votes
1answer
46 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
88 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
3answers
118 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 ...
7
votes
2answers
142 views

Stable muon density inside a white dwarf star?

It occurs to me (though I'm hardly the first) that the decay $$ \mu^- \to e^- + \bar \nu_e + \nu_\mu $$ should be forbidden in electron-degenerate matter, since there must be an empty state available ...
2
votes
3answers
88 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 ...
7
votes
1answer
110 views

Why Are Normal Shock Waves Unstable in a Converging Channel?

While learning about shock waves in an introductory Gas Dynamics course, it was revealed that normal shocks are unstable if formed in a converging channel. Even if the local conditions ostensibly ...
4
votes
1answer
117 views

Deducing instability growth rates from the Hamiltonian for the nonlinear schrodinger equation

Consider the following nonlinear Schrodinger equation (NLSE): $$A_t+iA_{xx}+i|A|^2A = 0$$ where $A$ is a complex valued function of $(x,t)$. A solution to this equation is $A=a_oe^{-ia_o^2t}$. We ...
2
votes
1answer
130 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 ...
4
votes
2answers
137 views

Changes in planetary orbit?

Forgive a novice and her naive curiosity, but I was wondering about planetary orbit and the aging of planets. As a planet ages, does its transit around its sun/star decrease or increase in speed? ...
2
votes
0answers
29 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 ...
2
votes
2answers
124 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 ...
4
votes
1answer
145 views

How to simulate rotational instability?

I'm trying to simulate (for an educational game) the well-known effect that rotating objects with three nonequal moments of inertia are unstable when rotated around the middle axis. Some explanations ...
0
votes
3answers
104 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 ...
3
votes
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?
12
votes
3answers
2k views

Why do all elements above $\require{mhchem}\ce{Fe}$ not decay to $\ce{Fe}$?

OK, so $\ce{Fe}$ is the most 'stable element'. As such, why do all elements above it not decay into $\ce{Fe}$? In all cases, would it not lead to an increase in binding energy and therefore energy ...
1
vote
1answer
21 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 ...
7
votes
3answers
1k views

Is it possible that black holes are also neutron stars, but so dark that we cannot see them?

Since the concept of the singularity in a black hole leads to infinite densities, I wonder if it is really certain that black holes exist? Is there a possibility that massive objects (which are ...
1
vote
0answers
31 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 $−$ ...
0
votes
2answers
113 views

Centre of mass and objects tipping [closed]

In this picture if the only parts of an object in contact with a surface are the lines AB and CD am I right in saying that the centre of mass has to be in the area enclosed by ABCD (as shown). I ...
1
vote
2answers
471 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 ...
7
votes
1answer
81 views

Why does the heaviest point on a spinning ball tend to become the topmost pole? [duplicate]

I have a mostly hollow, small clear plastic ball. Inside the ball is a weight stuck to the edge but the weight is smaller than the ball so the ball will always come to rest with the weight at the ...
5
votes
3answers
264 views

Why aren't there more natural satellites orbiting the Earth than just the Moon?

Considering that there's a lot of debris in space and that impacts fling out rocks into space all the time, why do we only have one large natural satellite - the Moon? Shouldn't there be all kinds of ...
0
votes
0answers
29 views

What will change if we have another Earth in the space near Earth? [duplicate]

If a new Earth came and orbit our Earth within 300,000 km to Earth? I just did not know. thanks.
1
vote
2answers
144 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 ...
10
votes
1answer
236 views

The most stable way of standing in a bus

Here's what's bugging me for quite a long time. Imagine the every day situation, that you are standing in a bus with your back on wall having only limited space on the floor and no handle to hold. You ...
2
votes
1answer
162 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 ...
5
votes
0answers
216 views

Why is the orbital resonance of the Galilean moons stable?

It is well known that the orbits of Ganymede, Europa and Io are in a 4:2:1 resonance. Most online sources (including but not limited to Wikipedia) say that such an orbital resonance, along with the ...
3
votes
1answer
87 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 ...
2
votes
1answer
95 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
votes
1answer
304 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 ...
3
votes
1answer
78 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 ...
4
votes
6answers
455 views

Why a system should be at its lowest energy state for its stability?

Every possible reaction in chemistry is to attain stability. In physics, the alignment of an electric dipole in an external electric field and in all other physical systems (at least those I study in ...
5
votes
1answer
76 views

Stability theory [closed]

I'm studying stability theory recently and met a lot of phrases like linear stability and nonlinear instability. After searching on Google, I became more confused. Thus I wonder if there is any ...
3
votes
2answers
172 views

Linearized equations

What is $V_{\alpha\beta}$? And what is a symmetric, positive definite potential energy matrix? And why is there a linearized equation like this?
5
votes
1answer
116 views

Do all celestial objects have stationary orbit?

Do all celestial bodies of sufficient mass such big asteroids, moon, planets etc. have orbit such that the period of revolution is same as the sidereal period of that object (such as geostationary ...
5
votes
2answers
228 views

Will a wheel rolling down a hill ever fall over?

Say I have a detached bicycle wheel and I roll it down an infinite, flat, asphalt inclined plane, in air (ie there will be a terminal velocity). When, if ever, will the wheel fall over? I've been ...
2
votes
2answers
85 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 ...
1
vote
0answers
400 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 ...