Unanswered Questions
1,535 questions with no upvoted or accepted answers
28
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741
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Extended Born relativity, Nambu 3-form and ternary ($n$-ary) symmetry
Background: Classical Mechanics is based on the Poincare-Cartan two-form
$$\omega_2=dx\wedge dp$$
where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. On the other hand, the ...
- 1,066
15
votes
2
answers
511
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Regularization: What is so special about the Coulomb/Newtonian and harmonic potential?
I wanted to know if the procedure for regularization of the Coulomb potential outlined in Celletti (2003): Basics of regularization theory could be generalized to arbitrary polynomial potentials. So ...
CommunityBot
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13
votes
1
answer
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The role of the virtual work principle
Lanczos' masterpiece "The Variational Principle of Mechanics" has, on page 76, the following statement:
Postulate A (virtual work): The virtual work of the forces of reaction is always zero for any ...
CommunityBot
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13
votes
1
answer
732
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Trying to solve 2D Toda Lattice Equation with Lax Pair Approach
I am working on this Hamiltonian:
$$ H = \frac{p_1^2 + p_2^2}{2m} + e^{q_2-q_1} + e^{q_2} + e^{-q_1} -3 $$
Thank you for the hint that it is a modification of the Toda Lattice Equation.
Let me sketch ...
CommunityBot
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9
votes
0
answers
293
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What exactly is the relationship between the symplectic 2-form and the frequency of leaves of integrable systems in classical mechanics?
In classical mechanics we equip a differential manifold with a closed symplectic 2-form $\omega$. The symplectic leaves of integrable systems also have a unique frequency, in literature denoted $\...
CommunityBot
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8
votes
0
answers
335
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Euler-Lagrange equations for chain fountain
Most of us are familiar with chain fountains.
I was wondering how this phenomenon is explained in the Lagrangian mechanics. I mean do we know how the Euler-Lagrange equations look like for this system?...
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7
votes
3
answers
315
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How to think about magnetic wells?
From classical mechanics we have the basic credo that a system chooses to minimize its energy. Since the energy is given by $$ E = T + V $$ where $T$ is the kinetic energy (usually $T=P^2$ for non-...
CommunityBot
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7
votes
0
answers
105
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Beam stiffening when twisted
For a particular cylindrical beam that is bent and twisted, its bending stiffness is found to increase with twist. I have a limited knowledge of continuum mechanics. Can the theory explain this, ...
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7
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135
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Variational principle with $\delta I \neq 0$
In Covariant Phase Space with Boundaries D. Harlow allows boundary terms in the variation of the action. If we have some action $I[\Phi]$ on some spacetime $M$ with boundary $\partial M = \Gamma \cup \...
- 36.3k
7
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591
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Hamiltonian formulation of the semiclassical Model of electrons
I'm currently reading the book Solid State Physics by Neil W. Ashcroft and N. David Mermin. In Chapter 12 they introduce the "Semiclassical Model of Electron Dynamics". In short: After having solved ...
7
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Animating the Bosonic String
I am interested in studying the classical solutions to the Bosonic string in flat 3+1 dim. spacetime by having them rendered a moving picture on a computer. This is partly for fun, and partly to ...
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6
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What does it mean for classical mechanics to be based on the category of sets?
It is quite common[1][2] in the study of physics in the context of category theory to say that one of the fundamental difference between classical mechanics and quantum mechanics is that classical ...
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410
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Is there a modified Least Action Principle for nonholonomic systems?
We know that one can treat nonholonimic (but differential) constraints in the same manner as holonimic constraints. With a given Lagrange Function $L$, the equations of motion for a holonomic ...
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5
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Group theoretical approach to conservation laws in classical mechanics
I'm doing some major procrastination instead of studying for my exam, but I wanted to share my thought just to confirm if I'm right.
Suppose that the action, $S(\mathcal{L})$ forms the basis of a ...
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In statistical mechanics, why is one "allowed" to treat classical systems probabilistically?
Is the essential argument that these systems are microscopically chaotic enough that we can approximate their evolution as random (vastly simplifying calculations) and still make accurate experimental ...
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