All Questions
Tagged with equilibrium stability
63
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Doubt regarding proof of Earnshaw's Theorem using Gauss's theorem
While proving Earnshaw's theorem using Gauss's theorem, we consider a small sphere surrounding our test charge, and apply Gauss law on this sphere, stating that field from all external charges must ...
- 428
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96
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Why is the surface of a static liquid always perpendicular to the direction of net force acting on the liquid as a whole? [duplicate]
In a, let's say rectangular container, the water surface always aligns itself perpendicular to the direction of net force acting on it. Why exactly does it happen?
(For example when this container is ...
- 55
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2
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146
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Weight distribution and support polygon
I was working on a problem of supporting an object with sticks and wondering about some use cases that would fail.
My approach is to place the n-sticks (for example 4) under an object with mass m ...
- 13
1
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Doubt: Arnold's "Mathematical Methods of Classical Mechanics", pg. 18
I am having trouble understanding the following diagram from pg. 18 of Arnold's book:
I am unable to see why local maxima of the potential energy correspond to unstable equilibria (and, reciprocally, ...
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3
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428
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How can two black holes merge without violating No Hair? [duplicate]
Before two black holes merge, their individual event horizons must be perfectly spherical due to the No Hair theorem. If they weren't they'd be betraying information about the inside. After merging, ...
- 79
3
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Why is a star unstable if it's adiabatic exponents are less than 4/3?
In "Introduction to Stellar Structure" by Walter J. Maciel at page 76 it is said that for a partially ionized non degenerate hydrogen gas, the star is unstable if the adiabatic exponents are ...
3
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2
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157
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Time for pendulum to leave unstable equilibrium is logarithmic
I would like to show that the time it takes for a pendulum to leave the unstable equilibrium at the top is logarithmic; i.e. if the starting position of the mass is $\theta_0 = \delta$ for some small $...
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To prove mathematically that a tip standing vertically will fall exponentially as soon as it deviates from its original position. (Homework Problem) [closed]
This is one of my questions from Homework for Quantum Mechanics. I know the answer quantitatively but cannot find any mathematical explanation.
Question: Consider a thin needle of total mass m and ...
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3
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2k
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Clarification in the definition of stable and unstable equilibrium
I am studying about types of equilibrium which are stable, unstable and neutral.
In the definitions of these equilibriums they used the term "position of equilibrium". Like in stable ...
- 111
2
votes
2
answers
825
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Necessary and Sufficient Conditions for an Equilibrium to be Stable
In the 4th section The condition that convection be absent of the book Fluid Mechanics by Landau and Lifshitz, they give the following statement:
For the (mechanical) equilibrium to be stable, it is ...
- 41
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5
answers
1k
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Objects falling from table
It is an everyday experience:
You have placed an object a tiny little bit too much over the edge of a table and it falls down. This is the case when the center of gravity is above the floor and not ...
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1
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Balance of an non-homogeneous object
Would a pencil balanced on its tip, remain balanced if the the tip was made of a material twice as heavy than the rest of the pencil?
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110
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Nature of stability in a conservative system
In CM, a conservative system can be described by a potential energy function, $V(x)$
The states of the system which will be in equilibrium will be found at the extrema of this potential where:
$\frac{...
- 187
1
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3
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191
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Stability analysis basics
I would like to see a rigorous treatment of stability analysis.
For example, a lot of high-school level texts give examples like this: https://courses.lumenlearning.com/physics/chapter/9-3-stability/
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8
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5
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Crystals and Earnshaw's theorem
Earnshaw's theorem states that there can be no stable equilibrium in an electrostatic field. Now consider an ion in a cubic lattice, eg, a sodium ion in NaCl. That ion is certainly in stable ...
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