Unanswered Questions
1,541 questions with no upvoted or accepted answers
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Are all canonical transformations either a point transformation, gauge transformation or a combination of them?
It's regularly argued that in the Hamiltonian formalism, we have more freedom to choose our coordinates and that this is arguably its most important advantage.
To quote from two popular textbooks:
[S]...
CommunityBot
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How can one define a covariant rate of change of rest mass for an extended body?
For a point mass I can define a covariant rate of change of its rest mass as $\frac{d}{d\tau}m_0$ where $\tau$ is the proper time. How can I also define a covariant rate of change of rest mass for an ...
- 2,015
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2
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What properties must a smoothly spinning toy top have?
It would seem that there is some open source software that would allow you to create objects of a certain volume, even with arbitrary shape (I'm thinking blender and some of it's addons.)
Now, I know ...
- 9,765
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Why do the orbit equations have to be symmetric about two axes even the orbit is not bounded?
In the book of Classical Mechanics by Goldstein, at page 88, it is given that:
$$
\frac{d^{2} u}{d t^{2}}+u=-\frac{m}{l^{2}} \frac{d}{d u} V\left(\frac{1}{u}\right) .
$$
The preceding equation is such ...
CommunityBot
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Using action-angle variables in non-periodic system
I'm a little confused by the discussion in the last section $\S 50$ of Landau and Lifshitz's (Classical) Mechanics (1960, first English ed.). Here, they consider finite motion of a system whose ...
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Gauge freedom in Lagrangian corresponds to canonical transformation of Hamiltonian
I want to show that the gauge transformation
$$L(q,\dot{q},t)\mapsto L^\prime(q,\dot{q},t):=L(q,\dot{q},t)+\frac{d}{dt}f(q, t)$$
corresponds to a canonical transformation of the Hamiltonian $H(p, q, ...
- 207k
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How can I derive the stress tensor for a Newtonian fluid in more physical terms?
The question is quite fundamental and more on a beginner's level (not sure if good in this high-level-forum, but I try): I have big problems in understanding the stress tensor for Newtonian fluids in ...
CommunityBot
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3
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1
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Wave equation on Air- Solid interaction
Suppose that there is, due to an explosion $h$ meters above the ground, a wave in the air with high density, velocity and pressure, capable of inducing an elastic wave on the earth's surface. How does ...
- 4,185
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How are action variables linked to first integrals of a Hamiltonian?
Suppose I have an integrable Hamiltonian system $H(q_{1}, p_{1},..., q_{n}, p_{n})$, with first integrals $F_{1} = H, F_{2},..., F_{n}$. Excluding certain singular level sets (i.e. separatrices), one ...
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Question about the applications of Gauss's principle of least constraint
Recently i've learned the formulation of Gauss's principle of least constraints, which states that the motion of a system of material points is in maximal accordance with free motion, or under least ...
- 207k
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Is there is an entropy cost of moving an object?
Is there an entropy cost associated with moving an object from one point to another, even if all forces involved are conservative? Or, is there some condition on what kind of move has an entropy cost?
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Generating function of point transformation
I am asked to show that the generating function corresponding to a point transformation in Lagrangian mechanics can be taken as null.
The point transformation consists of
$$
Q_i=Q_i(q,t),
$$
and ...
- 207k
3
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Minimal value of angular momentum in a close binary
I just noticed something interesting with the angular momentum of a close stellar binary. This question is somewhat related to another question of mine, but the question here is clearly different :
...
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Physical origin of gradient-like system with nonautonomous damping term
I am in mathematics major, and I am considering the equation $$\ddot u(t) + \gamma(t) \dot u(t) + \nabla \phi (u(t)) = g(t), $$
where $\phi: \mathbb{R}^n \to \mathbb{R}$ is of class $C^1$, convex and ...
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Is the process of quantization a total postulate?
In QFT, we transform a classical lagrangian into a quantum one by transforming our scalar fields into quantum operators. To do so we chose an ordering (Weyl or normal ordering for example), and we ...
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