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Hamiltonian's latest activity
Hamiltonian
reacted to
haushofer's post
in the thread
Why are Physicists so informal with mathematics?
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What you want reminds me of a painter who first wants to understand the exact chemical structure of his paint before painting. That...
Mar 28, 2024
Hamiltonian
reacted to
kuruman's post
in the thread
Why are Physicists so informal with mathematics?
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There is a joke that dates back to the days when college dances were chaperoned. A group of ladies in a room are lined up against one...
Mar 28, 2024
Hamiltonian
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martinbn's post
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How Can Parents and Teachers Identify a Student's Potential for a Maths Degree?
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Once they asked a mathematician if he will insist that his children follow his footsteps in choosing a career. He said: "No, no, of...
Mar 19, 2024
Hamiltonian
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Orodruin's post
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Verifying that Newton's Equations are equivalent to the EL equations
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Yes, in essence. As long as you are doing curvilinear coordinates on a Euclidean space only reading up to 2.3.2 will suffice for what...
Mar 18, 2024
Hamiltonian
replied to the thread
Verifying that Newton's Equations are equivalent to the EL equations
.
ok so for the LHS of the EL equation, we have, $$\frac{d}{dt}\left (\frac{\partial\mathcal{L}}{\partial\dot{\phi}^a}...
Mar 18, 2024
Hamiltonian
reacted to
Orodruin's post
in the thread
Verifying that Newton's Equations are equivalent to the EL equations
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In general, the metric components are functions of the coordinates ##\phi^a## so $$ \frac{d}{dt} g_{ab} = \frac{d\phi^c}{dt}...
Mar 18, 2024
Hamiltonian
replied to the thread
Verifying that Newton's Equations are equivalent to the EL equations
.
Ok, so since ##g_{ab}## is not generally constant I will have on the LHS of my EL equation, $$\frac{d}{dt}\left...
Mar 18, 2024
Hamiltonian
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pinball1970's post
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Random Photos
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Thought I had lost this.
Mar 18, 2024
Hamiltonian
replied to the thread
Verifying that Newton's Equations are equivalent to the EL equations
.
ok so in Einstein summation convention, my final equation reads, $$g_{ab}\ddot{\phi}^b=-\frac{\partial}{\partial \phi^a}\left...
Mar 18, 2024
Hamiltonian
replied to the thread
Verifying that Newton's Equations are equivalent to the EL equations
.
$$\frac{\partial\mathcal{L}}{\partial\dot{\phi}^1}=g_{11}\dot{\phi}^1+g_{12}\dot{\phi}^2$$...
Mar 17, 2024
Hamiltonian
reacted to
Hill's post
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Verifying that Newton's Equations are equivalent to the EL equations
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I think it is straightforward. Take the first equation...
Mar 17, 2024
Hamiltonian
replied to the thread
Verifying that Newton's Equations are equivalent to the EL equations
.
ok, I see the mistake. $$\frac{\partial\mathcal{L}}{\partial\dot{\phi}^1}=g_{11}\dot{\phi}_1+g_{12}\dot{\phi}_2$$...
Mar 17, 2024
Hamiltonian
replied to the thread
Verifying that Newton's Equations are equivalent to the EL equations
.
they do in the ##2\times 2## case right? $$\sum_{a=1}^{2} g_{1a}\dot{\phi}^a = g_{11}\dot{\phi}_1+g_{12}\dot{\phi}_2$$ or are you trying...
Mar 17, 2024
Hamiltonian
posted the thread
Verifying that Newton's Equations are equivalent to the EL equations
in
Introductory Physics Homework Help
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In the past, I have shown relatively easily that if we have a lagrangian of the form...
Mar 17, 2024
Hamiltonian
replied to the thread
Deriving ODEs for straight lines in polar coordinates for a given Lagrangian
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I was originally thinking that once we derive the two ODEs from the EL equation we must somehow prove that the solutions to these ODEs...
Mar 17, 2024
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