Unanswered Questions
1,536 questions with no upvoted or accepted answers
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Is there some notion of classical uncertainty which quantizes to quantum uncertainty?
I would like to know if there is some notion of classical uncertainty which quantizes to give quantum uncertainty?
For instance, suppose we have a classical system whose phase space is given by a ...
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What is the geometric interpretation of a general 'state space' in classical mechanics?
Let $\pmb{q}\in\mathbb{R}^n$ be some n generalized coordinates for the system (say, a double pendulum). Then the 'state space' is often examined using either the 'Lagrangian variables', $(\pmb{q},\dot{...
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Spectral statistics and integrability
It is commonly believed that the energy level spacings of integrable systems follow a Poisson distribution, while those of classically chaotic systems follow Wigner-Dyson statistics instead. Someone ...
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What frame of refernce to select in statistical mechanics?
Suppose we have a solid particle suspended inside a fluid such as an ideal gas, as shown in the following picture:
Our system is the solid particle and the environment is the gas (which acts as a ...
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Untwisting Strands of a Rope
Statement:: Topoisomerases help in relieving strain in the DNA ahead of the replication fork caused by the untwisting of the double helix (Topoisomerases are enzymes that participate in the over ...
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Minimum Potential energy required to behave like a turning point in relativistic case?
Inspired by this question a normal extension would be to ask:
What is the minimum potential energy required (to behave as a turning point) for an elastic collision between $2$ point particles $A$ and $...
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What curve does a rod form when bent to intersect 3 or more points?
Suppose that we have a sufficiently thin, flexible cylindrical rod of length $L$ made from a homogeneous, isotropic material, and that initially [at rest?] the central axis of the rod is a straight ...
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About the equation $\frac {d^2} {dt^2}\vec x(t) = \nabla \times \vec F(x(t))$. Motion in a curl vector field
I was wondering if there is a physical interpretation of ODEs of the form
$$\frac d{dt}\vec x(t)=\vec y(t)$$
$$ \frac d{dt} \vec y(t) = \nabla \times \vec F(x(t))$$
(or equivalently $\frac {d^2} {dt^2}...
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Kinematics of a rolling disk on a static disk (variation of the Euler disk)
I'm puzzled by the following problem. Consider a simple tilted disk $\mathcal{D}$ of radius 1 (in any unit) rolling without sliding on top of a static horizontal disk $\mathcal{S}$. The normal $\...
CommunityBot
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Particle in "external potential" VS particle on "curved surface": equivalence?
Let's consider a non-relativistic particle - its position is $x(t)\in \mathbb{R}^n$ - in an external potential $\phi$, with Lagrangian $$L=\dot{x}^i \eta_{ij}\dot{x}^j/2 - \phi(x),\tag{1}$$
where $\...
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Help with Newton's 3rd law
I am using the book Classical Dynamics of Particles and Systems by STEPHEN T. THORNTON, JERRY B. MARION and they say that Newton's 3rd law only applies when forces are $\textbf{central forces}$, ...
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Time dependent canonical transformations (a problem in Arnold's classical mechanics textbook)
I am stuck on a problem on page 242 of Arnold's book "Mathematical Methods of Classical Mechanics". The problem statement is as follows:
Let $g(t): \mathbb{R}^{2 n} \rightarrow \mathbb{R}^{...
CommunityBot
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Intuitive explanation on why velocity = 0 for a inverted pendulum on a wheel system
I believe I have solved below problem. I am not looking for help on problem-solving per se. I am just looking for an intuitive explanation.
Problem statement: wheel mass = $m_1$, even mass rod BC mass ...
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How does coarse-graining lead to irreversibility?
This is how I used to understand how coarse-graining leads to irreversibility.
Suppose that we start with a coarse-grained phase space and two initial conditions belonging to two different phase cells....
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How to compute classical probability distribution for 1D harmonic oscillator with $K/x$ (central force) potential energy?
I am trying to find, or derive, the probability distribution function for a classical 1D harmonic oscillator with a $K/x$ potential energy (from a $K/x^2$ central force). I am familiar with the ...
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