# Tagged Questions

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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### For how long must a molecule remain stable to be considered “stable”?

In the Star Trek: Voyager episode The Omega Directive, Seven of Nine says that the Borg synthesized a molecule which was "kept [] stable for one trillionth of a nanosecond before it destabilized". ...
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### Will Cone standing on its tip, without any other force other than gravity topple?

A cone standing on its tip is considered to be in unstable equilibrium as a slightest force could topple it. So, if the cone is stood on its tip with no other force other than gravity (and the ...
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### 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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### Gravitational potential outside Lagrangian points or Lagrange points

The diagram in Why are L4 and L5 lagrangian points stable? shows that the gravitational potential decreases outside the ring of Lagrange points — this image shows it even more clearly: If I ...
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### Effect of water on wobble of rotating structure

If we have a structure that rotates to create artificial gravity, then if the mass isn't perfectly distributed along the circumference the CM will be offset from the geometric center so there will be ...
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### Staying in orbit - but doesn't any perturbation start a positive feedback?

I am not a physicist; I am a software engineer. While trying to fall asleep recently, I started thinking about the following. There are many explanations online of how any object stays in orbit. The ...
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### 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 ...
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### Gravity in other dimensions than 3 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 ...
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### 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 ...
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### Deviation from Earth's orbit

How much orbital deviation is required for the Earth to get knocked out from current orbit so it either moves away from Sun or towards the Sun?
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### James Webb Space Telescope's halo orbit at Lagrange point L2

The James Webb Space Telescope (JWST) is expected to be launched in 2018 and operate in the L2 vicinity, about 1.5 million km from Earth. It will be placed in a halo orbit around the unstable L2 ...
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### Why is Larry Niven's Ringworld Unstable?

In his 1970 science fiction novel Ringworld, author Larry Niven describes the eponymous Ringworld, a gigantic structure shaped as a ring with a radius of around 1 AU, rotating around a star in the ...
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### Is Dyson Sphere a stable construction?

Suppose that a star is encompassed by a Dyson Sphere. Do we need a position control system for the Dyson Sphere to keep its origin always aligned with the center of the star? Will it stay aligned ...
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### Why are L4 and L5 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 L1, L2, and L3 lagrangian points. The blue ...
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### 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 ...
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### What is a “Center Of Mass” issue of a Gorillapod?

I read somewhere that a Gorillapod may have "Center Of Mass" issues when used with the long lenses. So, I wish to understand what is a "Center Of Mass" issue? I have to clarify that I am NOT a ...
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### 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: http://www....
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### 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 ...
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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? ...
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### Is mid-water bouyancy a classic example of a balanced but unstable system?

I came to this thought experiment as I was pondering good teaching examples of stable and unstable systems. It occurred to me that stable systems are really quite abundant. For a shoot-from-the-hip ...
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### How does the distance between two rails effect the speed of a steel ball bearing?

As part of a school science project, I constructed a Rollercoaster using Polyurethane tubing as rails for a steel ball bearing to rest on. In the process of building the coaster I observed that ...
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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 ...
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### Two planets in same orbit - not planets?

Let us pretend for a moment that there are two identical planets that are exactly opposite their star from each other and are the same distance from said star. (This would make them, at all times, ...
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### 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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### Why do they store gold bars with the narrow side down? [closed]

I watched on TV as they where showing gold bars stored in bank vaults and I noticed that they always stack them with the narrow side down and the wide side up. Like this: So there has to be a ...
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### What are the ideal centers of mass and rotation for a steadicam?

For those who don't know what a steadicam is, I'll explain it in two points to give a basic idea. If you know what a steadicam is, skip to point 3. 1) A steadicam is a stabilizing mount for a motion ...
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### Question on the stability of the solar system

One of the pertinent questions about many body systems that causes me much wonder is why the solar system is so stable for billions of years. I came across the idea of "resonance" and albeit an useful ...
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### 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 ...
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### 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 ...
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### How fast do you have to spin an egg to have it standing?

If you take a hardboiled egg and put it on a table and start to spin it, if you spin it fast enough it will start to spin in an upright position. What is the angular velocity needed for this ...
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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?