# Tagged Questions

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### Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
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### Noether Theorem and Energy conservation in classical mechanics

I have a problem deriving the conversation of energy from time translation invariance. The invariance of the Lagrangian under infinitesimal time displacements $t \rightarrow t' = t + \epsilon$ can be ...
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### Emmy Noether's theorem in simpler terms

I'd like to understand Noether's theorem and its contents as to what it implies in a bit simpler terms. I am familiar with mathematics unto Calculus 1,2,3 and some linear algebra and group theory. I ...
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### Deriving $p = mv$ from translational symmetry (momentum conservation law)?

"In classical mechanics, momentum is defined as the quantity which is conserved under global spatial translations or, alternatively, as the generator of spatial translations." (G.Parisi, ...
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### How do you know if a coordinate is cyclic if its generalized velocity is not present in the Lagrangian?

Goldstein's Classical Mechanics says that a cyclic coordinate is one that doesn't appear in the Lagrangian of the system, even though its generalized velocity may appear in it (emphasis mine). For ...
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### What's the importance of Noether's theorem in Physics

The Noether's theorem that I want to mention is the following: Noether's theorem. I know the importance of Noether's contribution to modern algebra. Can anyone write about Noether's theorem in ...
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### What symmetry causes the Runge-Lenz vector to be conserved?

Noether's theorem relates symmetries to conserved quantities. For a central potential $V \propto \frac{1}{r}$, the Laplace-Runge-Lenz vector is conserved. What is the symmetry associated with the ...
Often in textbooks Noether's theorem is stated with the assumption that the Lagrangian needs to be invariant $\delta L=0$. However, given a lagrangian $L$, we know that the Lagrangians $\alpha L$ ...