Timeline for Example in motivation for Lagrangian formalism
Current License: CC BY-SA 4.0
28 events
| when toggle format | what | by | license | comment | |
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| Apr 13 at 14:09 | comment | added | freecharly | @Cleonis Thank you for pointing out this very insightful exposition of yours! | |
| Mar 6 at 23:03 | history | edited | Cleonis | CC BY-SA 4.0 |
deleted 4 characters in body
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| Mar 6 at 21:27 | history | edited | Cleonis | CC BY-SA 4.0 |
Added mention that the answer is derived from material that is available on my own website, with mention that a link to my website is available on my stackexchange profile
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| Mar 6 at 21:11 | history | edited | Cleonis | CC BY-SA 4.0 |
Removed superfluous section with a derivation. Additionally, some paragraphs were rewritten
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| Jun 9, 2023 at 2:55 | history | edited | Cleonis | CC BY-SA 4.0 |
Removed a section of the answer that involved a sign error. The sign error had no impact on the answer as a whole, so the section could simply be removed
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| S May 14, 2023 at 12:55 | history | suggested | Duke William | CC BY-SA 4.0 |
grammar correction
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| May 14, 2023 at 10:21 | review | Suggested edits | |||
| S May 14, 2023 at 12:55 | |||||
| Sep 2, 2022 at 12:16 | history | edited | Cleonis | CC BY-SA 4.0 |
Corrected misspelled 'criterium' to 'criterion', replaced two paragraphs, hopefully improving clarity
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| Sep 1, 2022 at 3:50 | history | edited | Cleonis | CC BY-SA 4.0 |
Various changes, attempting to improve the flow of the narrative, and the clarity of the narrative
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| Mar 27, 2022 at 6:59 | history | edited | Cleonis | CC BY-SA 4.0 |
Clarification; added some headers, removed some repetition
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| Feb 28, 2022 at 18:51 | comment | added | mohamed | ... Least action path. If you could give a detailed example showing calculations from scratch it would be very helpful | |
| Feb 28, 2022 at 18:51 | comment | added | mohamed | Your answer deserves more votes, very good at explaining the topic from scratch. However, the problem I am having is: what does the potential express? Is it the force by shortest distance between the two points or the force multiply the distance of the path under observation. What I mean is: energy is conserved so what would defer between other non least action paths i,e, the potential energy is slightly changing to kinetic (change is conserved). What I speculate is that you mean potential energy in this case is the energy which will be done when the force acts on the lease | |
| Feb 23, 2022 at 21:40 | history | edited | Cleonis | CC BY-SA 4.0 |
Removed unnecessary labels from units in equation 2.7, 2.8, 2.9
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| Oct 22, 2021 at 23:16 | comment | added | Cleonis | @AaronDaniel I rewrote multiple sections, capitalizing on the extended version of diagram 4. (I also felt the rewrite allowed removal of several sections, so I did that.) If you feel the rewrite is an improvement then please let me know. | |
| Oct 22, 2021 at 22:18 | history | edited | Cleonis | CC BY-SA 4.0 |
Significant rewrite in an effort to improve the clarity of the exposition. Multiple sections have been replaced. The replacements made some sections redundant; those were removed
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| Oct 17, 2021 at 19:39 | comment | added | Cleonis | @AaronDaniel I have replaced diagram 4 with an extended version. The diagram now includes display that as variation is swept out the potential energy and kinetic energy change together. The rate of change of the energies as a function of variation sweep has the same magnitude as the rate of change of energies (with respect to the position coordinate) as a particle is moving along the true trajectory. | |
| Oct 17, 2021 at 19:32 | history | edited | Cleonis | CC BY-SA 4.0 |
Replaced one of the diagrams. The newer version has 4 subpanels, the replaced version had 2 subpanels
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| Oct 15, 2021 at 17:41 | history | edited | Cleonis | CC BY-SA 4.0 |
added 308 characters in body
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| Oct 15, 2021 at 17:23 | comment | added | Cleonis | @AaronDaniel I added a section 'variation space and physical space'. (Presumably the same could have been said in more concise way. I'm not good at brevity.) My intention is to rework diagram 4 from a 2 subpanel diagram to a 4 subpanel diagram, and then the value of 'area ($E_k-E_p$)' can be demonstrated in a subpanel of its own. | |
| Oct 15, 2021 at 17:13 | history | edited | Cleonis | CC BY-SA 4.0 |
added 457 characters in body
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| Oct 15, 2021 at 17:02 | history | edited | Cleonis | CC BY-SA 4.0 |
Addes section with discussion of the previously introduced expressions 'physical space' and 'variation space'
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| Oct 15, 2021 at 13:08 | comment | added | Aaron Daniel | Thank you very much for this extensive answer! The point I am still unclear about is the sign flip between variation space and physical space, why exactly does that exist? | |
| Oct 14, 2021 at 18:03 | history | edited | Cleonis | CC BY-SA 4.0 |
Added introductory paragraph pointing out that the development of Lagrangian mechanics *predates* the introduction of Hamilton's stationary action.
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| Oct 13, 2021 at 20:25 | history | edited | Cleonis | CC BY-SA 4.0 |
Corrected an inconsistency in the derivations. The inconsistency caused wrong signs. The main reasoning was not involved, but the inconsistency had to be corrected, of course.
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| Oct 10, 2021 at 19:41 | history | edited | Cleonis | CC BY-SA 4.0 |
Fixed some yptos
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| Oct 10, 2021 at 19:09 | history | edited | Cleonis | CC BY-SA 4.0 |
Added multiple sections, expanding the answer in multiple ways
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| Oct 9, 2021 at 15:05 | vote | accept | Aaron Daniel | ||
| Nov 6, 2023 at 13:35 | |||||
| Oct 9, 2021 at 5:41 | history | answered | Cleonis | CC BY-SA 4.0 |