Timeline for Modeling friction with Non-Lipschitz ODEs - Pendulum example
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| Jun 17, 2022 at 19:20 | history | edited | Joako | CC BY-SA 4.0 |
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| Jun 3, 2022 at 21:14 | history | edited | Joako | CC BY-SA 4.0 |
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| May 23, 2022 at 23:13 | history | edited | Joako | CC BY-SA 4.0 |
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| May 2, 2022 at 1:53 | history | edited | Joako |
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| Apr 21, 2022 at 3:32 | history | edited | Joako | CC BY-SA 4.0 |
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| Apr 20, 2022 at 1:51 | comment | added | Joako | @Andrew By the way, I am not meaning the proposed example is right, is just a toy model to figure out if this kind of non-Lipschitz component make the solution of finite duration, since is the kind of component used on the paper where I found about this solutions with finite ending times. | |
| Apr 20, 2022 at 1:48 | comment | added | Joako | @Andrew Think for this specific question that is an assumption, but my personal opinion is that the movement due their dynamics have an end, here I am asking it to figure it out. Also, it is not going against Newton's Laws, the proportionality of the friction coefficient to the derivative is an assumption/approximation of a more nonlinear law - it depends on the problem conditions but is accurate enough for common purposes, but as you said, it will never lead to a finite duration, that is why I am trying to look for an alternative. | |
| Apr 20, 2022 at 1:43 | comment | added | Andrew | "is more simple to think it indeed have stop moving" -- You say it is more simple, but on the other hand, as you have seen this hypothesis leads to the conclusion that Newton's laws must be wrong for describing the motion of a macroscopic, non-relativistic system, since Newton's laws don't have the solutions you are looking for. I would venture that in fact a simpler hypothesis is that Newton's laws are right, and that what you perceive as a pendulum being still, is actually a pendulum moving with a very small amplitude. | |
| Apr 20, 2022 at 1:41 | comment | added | Joako | @Andrew Thanks for getting interested. Indeed I can't prove it doesn't stop moving, but since otherwise its movement will disappear immersed in thermal noise, since thermal noise is modeled as Additive White Gaussian Noise (at least in telecom), and Normal distrib. is the maximum entropy distrib. for finite average and power, it means that all information related to the movement is already lost... so there is no data to support is still moving due the pendulum dynamics, so is more simple to think it indeed have stop moving (not meaning is right, but is more accurate from data). | |
| Apr 20, 2022 at 1:35 | comment | added | Andrew | "the fact that the experimental pendulum does indeed stop moving in reality" -- what makes you think this is a fact? (a) Do you think you could distinguish a pendulum oscillating with an amplitude less than 1 micron from a pendulum not moving? (b) Don't forget that a real pendulum is connected to other things (such as the Earth) which are moving, and that it has a finite temperature, so there is always some motion in a real pendulum. In fact it is an unrealistic idealization that you can write the motion of a pendulum in isolation from anything else, at the level of precision you want. | |
| Mar 29, 2022 at 18:08 | history | edited | Joako | CC BY-SA 4.0 |
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| S Mar 18, 2022 at 22:03 | history | bounty ended | CommunityBot | ||
| S Mar 18, 2022 at 22:03 | history | notice removed | CommunityBot | ||
| Mar 17, 2022 at 13:54 | history | edited | Joako | CC BY-SA 4.0 |
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| Mar 16, 2022 at 20:56 | history | edited | Urb | CC BY-SA 4.0 |
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| Mar 16, 2022 at 19:04 | history | edited | Joako |
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| Mar 15, 2022 at 18:00 | history | tweeted | twitter.com/StackPhysics/status/1503793178704502788 | ||
| Mar 15, 2022 at 12:13 | history | edited | Joako | CC BY-SA 4.0 |
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| S Mar 11, 2022 at 12:31 | history | suggested | gmz | CC BY-SA 4.0 |
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| Mar 11, 2022 at 12:07 | answer | added | Eli | timeline score: 0 | |
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| S Mar 10, 2022 at 20:31 | history | bounty started | Joako | ||
| S Mar 10, 2022 at 20:31 | history | notice added | Joako | Draw attention | |
| Mar 10, 2022 at 20:30 | history | edited | Joako | CC BY-SA 4.0 |
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| Mar 9, 2022 at 2:54 | history | edited | Kyle Kanos | CC BY-SA 4.0 |
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| Mar 8, 2022 at 23:24 | history | edited | Joako |
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| Mar 8, 2022 at 4:26 | history | edited | Joako | CC BY-SA 4.0 |
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| Mar 8, 2022 at 4:21 | history | asked | Joako | CC BY-SA 4.0 |