Timeline for Noninvariance for a specific nonlinear oscillator
Current License: CC BY-SA 3.0
31 events
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| Oct 29, 2015 at 15:38 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
EDIT #1 changed: wrong statement found, proof not conclusive
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| Oct 29, 2015 at 15:31 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 28, 2015 at 13:05 | comment | added | Dr. Wolfgang Hintze | @ seno44: (28.10.15 14:04) unfortunately, I have just discovered a flaw in the "proof" of the recent comment. I try to mend it and return. | |
| Oct 27, 2015 at 20:22 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 27, 2015 at 20:17 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 27, 2015 at 20:09 | comment | added | Dr. Wolfgang Hintze | @ seno44: If the generalization I proposed in my last comment is correct, the Taylor method is easily generalized. As far as I can see it leads to an infinite set of equations of the form $(vx^k, vv) = 0 (k=0,1,2,...)$ where $vv = (v_{10}, ..., v_{N0})$ , $x^k = (x_{10}^k, ..., x_{N0}^k)$, and $(a,b)$ is the scalar product of the vectors $a$ and $b$. As the equations must hold for all k, the only solution for $vv$ is the trivial one. QED. | |
| Oct 27, 2015 at 19:37 | comment | added | Dr. Wolfgang Hintze | @ seno44: Ok. Please be more specific.Do you wish to generalize 0 = y_{10} + y_{20} to 0 = y_{10} + y_{20} + ... + y_{n0} ? | |
| Oct 27, 2015 at 15:07 | comment | added | user45183 | The problem is that I want to generalize this consideration to $N$ particles rather than $N=2$. In that respect the Taylor expansion approach does not generalize nicely in my opinion. | |
| Oct 27, 2015 at 13:35 | comment | added | Dr. Wolfgang Hintze | @ seno44: I agree, if you consider the Taylor Expansion "very dificult" which, honestly, I wouldn't. But, you are right, there should be some simple symmetry argument to give the proof (even simpler than in the answer of Fritz Veeman) because the contrary holds for a symmetric potential, i.e. you can have $d=0$ iff $x_{10}+x_{20}=0$ and $y_{10}+y_{20}=0$ | |
| Oct 27, 2015 at 13:30 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 27, 2015 at 12:32 | comment | added | user45183 | I think you have chosen the route that I was explicitly not interested in as I mentioned in the question. | |
| Oct 27, 2015 at 9:53 | comment | added | Dr. Wolfgang Hintze | @seno 44: Thanks for the hint to my trivial error. I have given a complete solution of the OP in the meantime. | |
| Oct 26, 2015 at 15:08 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
Beautifying of subscripts, oberservation added
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| Oct 26, 2015 at 14:57 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 26, 2015 at 14:52 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 26, 2015 at 14:43 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 26, 2015 at 11:46 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 26, 2015 at 11:31 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 26, 2015 at 11:05 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 26, 2015 at 10:56 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 26, 2015 at 10:27 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 26, 2015 at 10:16 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 26, 2015 at 10:09 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 26, 2015 at 10:07 | history | undeleted | Dr. Wolfgang Hintze | ||
| Oct 24, 2015 at 20:36 | history | deleted | Dr. Wolfgang Hintze | via Vote | |
| Oct 24, 2015 at 20:28 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 24, 2015 at 20:25 | comment | added | user45183 | the starting point is not correct. It should be $x^2(t)$ in the $\dot{y}$ equation! | |
| Oct 24, 2015 at 20:18 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 24, 2015 at 20:11 | history | edited | Dr. Wolfgang Hintze | CC BY-SA 3.0 |
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| Oct 24, 2015 at 20:03 | review | First posts | |||
| Oct 24, 2015 at 20:10 | |||||
| Oct 24, 2015 at 20:03 | history | answered | Dr. Wolfgang Hintze | CC BY-SA 3.0 |