All Questions
Tagged with mathematical-physics classical-mechanics
125
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Holonomic constraints as a limit of the motion under potential
In Mathematical Methods of Classical Mechanics, Arnold states the following theorem without proof in pages 75-76:
Let $\gamma$ be a smooth plane curve, and let $q_1, q_2$ be local coordinates where
$...
- 133
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123
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What does it mean for classical mechanics to be based on the category of sets?
It is quite common[1][2] in the study of physics in the context of category theory to say that one of the fundamental difference between classical mechanics and quantum mechanics is that classical ...
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$C^{\ast}$-algebra approach to classical mechanics
Can someone please help me understand how classical mechanics (for example in terms of Hamiltonian formalism) can be described in terms of $C^{\ast}$-algebras? I read usually that in this case the ...
- 159
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154
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What is the most general transformation between Lagrangians which give the same equation of motion?
This question is made up from 5 (including the main titular question) very closely related questions, so I didn't bother to ask them as different/followup questions one after another. On trying to ...
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Pre-requisites for V.I. Arnold's mathematical methods for classical mechanics
I am an undergraduate, studying physics. I have studied maths courses like Groups, Linear Algebra, Real analysis, Differential geometry and probability. I wish to get into mathematical physics, ...
4
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2
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137
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Gauge Symmetry of the Lagrangian
My teacher told the following statement to me during office hours. Is it correct and if so, how could one go about proving it?
Given a material system subject to holonomic and smooth constraints ...
- 402
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Prove: Conformal map $w(z)$ transforms a trajectory in potential $U(z)=|dw/dz|^2$ to one in potential $V(z)=-|dz/dw|^2$
This is a conclusion given without proof in the Chinese version of Arnold's Methematical Methods in Classical Mechancs.
Contents related to this conclusion are missing from the English version (I ...
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Two questions regarding Spivak's Configuration Space
The following is from the fifth Chapter Rigid Bodies of Spivak's Physics for Mathematicians. The post consists of a statement Spivak makes -with no proof- that I do not understand. For clarity, I've ...
- 379
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2
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446
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It is possible to have a drag force which is non-Lipschitz?
When working with the Drag Force is typical used on classical mechanics systems the following:
For high speeds it is used the Drag equation which says the drag is proportional to the squared of the ...
- 93
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413
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Is a reasonable assumption to consider that the contact point of the Euler's Disk (with stationary center of mass) trace this finite bounded spiral?
Is a reasonable assumption to consider that the contact point of the Euler's Disk (with stationary center of mass) trace this finite bounded spiral?
This question is highly related to working with the ...
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Perturbation Method: What is the acceptable method to terminate expansion
I am using the book Classical Dynamics of Particles and Systems by STEPHEN T. THORNTON, JERRY B. MARION, page: 67 and they use perturbation method to approximate:
\begin{equation} T = \frac{kV + g}{...
- 283
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532
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Angular momentum and precession in classical Hamiltonian (symplectic) mechanics
In Hamiltonian mechanics, angular momentum is a certain momentum map and a component of the angular momentum is the generator function of the action of a one-parameter subgroup of the rotation group $...
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13
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408
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Anticommutation of variation $\delta$ and differential $d$
In Quantum Fields and Strings: A Course for Mathematicians, it is said that variation $\delta$ and differential $d$ anticommute (this is only classical mechanics), which is very strange to me. This is ...
8
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What is an intuitive way of understanding Ostrogradsky instability?
Is there a way of explaining why no differential equations in physics exceed order two without delving into Lagrangian and Hamiltonian mechanics - i.e. from Newtonian mechanics? Moreover, is there ...
2
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43
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Resonant and non-resonant tori density in non-degenerate system
I'm following the discussion on the page 290 of Mathematical Methods of Classical Mechanics by V. I. Arnol'd (you can download it here), and I've encountered the fact that in a nondegenerate system, ...
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