Timeline for Hamilton equations-Symplectic scheme [closed]
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Mar 12, 2021 at 12:26 | history | closed |
Stefan Waldmann Will Sawin Pedro Lauridsen Ribeiro Joonas Ilmavirta Ben McKay |
Not suitable for this site | |
| Mar 11, 2021 at 19:27 | history | edited | gmvh |
Added "na.numerical-analysis" tag, because the question is really about the symplectic Euler method
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| Mar 11, 2021 at 17:00 | vote | accept | Jokerp | ||
| Mar 11, 2021 at 13:22 | answer | added | gmvh | timeline score: 2 | |
| Mar 7, 2021 at 14:44 | comment | added | Jokerp | @RicardoBuring i trasnfered this question to math.stack exchange! math.stackexchange.com/questions/4052524/… | |
| Mar 7, 2021 at 14:21 | comment | added | Ricardo Buring | @BenMcKay The sets of equations define different numerical integrators: in the first case $(q_{i+1}, p_{i+1})$ directly in terms of $(q_i, p_i)$, and in the second case $q_{i+1}$ in terms of $(q_i,p_i)$, and $p_{i+1}$ in terms of $(q_{i+1},p_i)$. Anyway, the question seems to be more suited for Math.StackExchange. | |
| Mar 6, 2021 at 21:30 | comment | added | Ben McKay | ... If so, how would we know that these $Q,P$ from the second sentence, first or second clause, are equal to those in the first sentence, as their definition appears to be completely unrelated? | |
| Mar 6, 2021 at 21:29 | comment | added | Ben McKay | Maybe I should try again to clarify my confusion. In your first sentence, you define $Q,P$ to be the result of applying a Hamiltonian flow to some $q,p$. In your second sentence, you first define $Q,P$ to be certain functions of $q,p$ and $\Delta t$. In the second clause of the second sentence, you write down two equations involving variables called $Q,P$. Are the $Q,P$ in the first sentence intended to equal those in the second sentence, 1st clause? What about the second sentence second clause? | |
| Mar 6, 2021 at 20:17 | history | edited | Jokerp | CC BY-SA 4.0 |
edited body
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| Mar 6, 2021 at 19:47 | comment | added | Jokerp | @BenMcKay also the difference is that the second hamiltonian does not depend on q but Q | |
| Mar 6, 2021 at 19:46 | history | edited | Jokerp | CC BY-SA 4.0 |
edited body
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| Mar 6, 2021 at 19:31 | comment | added | Jokerp | @BenMcKay I am sorry to confuse you! This is supposed to be a transformation! And I want to know if it is symplectic or not | |
| Mar 6, 2021 at 19:14 | history | edited | Ben McKay | CC BY-SA 4.0 |
misspelling of symplectic as sympectic
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| Mar 6, 2021 at 18:03 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor Grammar improvement and formatting
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| Mar 6, 2021 at 17:56 | comment | added | Ben McKay | Assuming that you are asking that $Q,P$ be computed using a linear approximation, linear in $\Delta t$, then clearly both are symplectic, since one is the flow of $H$ and the other the flow of $-H$. | |
| Mar 6, 2021 at 17:55 | comment | added | Ben McKay | I am not clear what you are asking. How can you say both that $Q,P$ are $q,p$ at a later time step and also that they are given by the equations above? Surely if we wait for some amount of time $\Delta t$, the location of $Q,P$ will usually be a nonlinear function of the time step $\Delta t$. Are you asking that this holds up to higher order terms in $\Delta t$? If so, you can't choose which of the two expressions for $Q,P$ you get to use. | |
| Mar 6, 2021 at 17:50 | review | Close votes | |||
| Mar 12, 2021 at 12:26 | |||||
| Mar 6, 2021 at 17:28 | history | edited | Jokerp | CC BY-SA 4.0 |
edited title
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| Mar 6, 2021 at 17:22 | history | asked | Jokerp | CC BY-SA 4.0 |