Timeline for Inertial coordinate systems being invariant under time translation in Newton's Principle of Detrimancy
Current License: CC BY-SA 4.0
11 events
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| Jul 12, 2023 at 17:28 | comment | added | jd27 | @Chordx Yes that is correct, if $F$ depends on time we can see from what you wrote that $\tilde{\phi}$ will not be a solution in general by comparing it to the equation i wrote below equation 1. | |
| Jul 12, 2023 at 16:23 | comment | added | Chordx | Just to clarify, why is it true that $\tilde{\phi}$ is not always a solution to Newton's equation? Because $\ddot{\phi}(t)=F(\phi(t),\dot{\phi}(t),t) \implies \ddot{\phi}(t+s)=F(\phi(t+s),\dot{\phi}(t+s),t+s),$ correct? The example I gave seems to demonstrate that as well. | |
| Jul 12, 2023 at 16:20 | vote | accept | Chordx | ||
| Jul 12, 2023 at 15:38 | comment | added | Valter Moretti | To conclude you should also assume that $F$ is continuous, in order to have your last assumption: there is at least a solution for generic initial conditions. Uniqueness is not necessary here. | |
| Jul 12, 2023 at 14:54 | history | edited | jd27 | CC BY-SA 4.0 |
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| Jul 12, 2023 at 14:38 | history | edited | jd27 | CC BY-SA 4.0 |
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| Jul 12, 2023 at 14:28 | history | undeleted | jd27 | ||
| Jul 12, 2023 at 14:26 | history | deleted | jd27 | via Vote | |
| Jul 12, 2023 at 14:25 | history | undeleted | jd27 | ||
| Jul 12, 2023 at 14:25 | history | deleted | jd27 | via Vote | |
| Jul 12, 2023 at 14:24 | history | answered | jd27 | CC BY-SA 4.0 |