Timeline for mechanics: convergence to an equilibrium point
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 30, 2011 at 9:01 | vote | accept | Damien S. | ||
| Dec 30, 2011 at 9:01 | vote | accept | Damien S. | ||
| Dec 30, 2011 at 9:01 | |||||
| Dec 30, 2011 at 7:09 | answer | added | user12400 | timeline score: 4 | |
| Dec 29, 2011 at 20:02 | comment | added | fedja | OK, I posted the 2D example as an answer. When $d=1$, such effect is impossible, so the statement is true. | |
| Dec 29, 2011 at 19:59 | answer | added | fedja | timeline score: 6 | |
| Dec 29, 2011 at 14:05 | comment | added | Damien S. | Thanks for the saddle point ! in general, we require only $\nabla V=0$. I was making my drawings in 1D and thus I skipped it... For your 3), I am very interested in your example that I still do not understand. What happened if we restrict to $d=1$ ? | |
| Dec 29, 2011 at 13:39 | comment | added | fedja | 2) A saddle is perfectly possible as well. The right word in English is "a critical point". 3) a) You never reach the valley: the road makes infinitely many loops on the slope. b) OK, I'll post something a bit later. | |
| Dec 29, 2011 at 13:23 | history | edited | Damien S. | CC BY-SA 3.0 |
added 259 characters in body
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| Dec 29, 2011 at 13:18 | comment | added | Damien S. | I agree with point 1, in order to avoid to a trajectory to escape to infinity: I edit my post. For point 2), that's why I wrote "extremum" and not "minimum". My problem is with your point 3. Once you are in the flat valley, the friction is still operating and your velocity decreases exponentially and you should stop somewhere ! Can you exhibit a concrete example of the behaviour you mention. | |
| Dec 29, 2011 at 12:30 | comment | added | fedja | 1) "Bounded from below" isn't enough. You rather need "is greater than the initial value of $E$ near $\infty$. 2) The limit point doesn't need to be a minimum in general. 3) Contrary to your belief, you can oscillate forever. Imagine an infinite road carved into a gentle mountain slope like a trough that spirals into a flat disk-shaped valley. | |
| Dec 29, 2011 at 11:50 | history | edited | Damien S. | CC BY-SA 3.0 |
added 191 characters in body
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| Dec 29, 2011 at 11:07 | history | asked | Damien S. | CC BY-SA 3.0 |