Timeline for Invariance of dynamical system under a transformation
Current License: CC BY-SA 3.0
26 events
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| Jan 17 at 8:13 | history | protected | CommunityBot | ||
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| May 27, 2015 at 10:19 | answer | added | John B | timeline score: 2 | |
| Feb 13, 2015 at 0:52 | comment | added | Pietro Majer | Given $F$ and $\Psi$, the transformation $M$ that makes (2) true may be found solving the last condition you wrote for $M(y)$, at least if $F(y)$ is injective. | |
| Feb 13, 2015 at 0:37 | comment | added | Pietro Majer | I understand that (2) is a particular phenomenon arising in a special case Jorge is dealing with. | |
| Sep 21, 2013 at 1:18 | comment | added | Shuchang | How do you obtain (2) from (1)? I don't see why there's (2) | |
| Mar 28, 2013 at 13:56 | answer | added | Issa | timeline score: 0 | |
| Dec 19, 2011 at 16:36 | history | edited | Jorge | CC BY-SA 3.0 |
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| Dec 19, 2011 at 16:04 | comment | added | Jorge | Ok let me just be a little more formal on the math. The vectors x,y∈Rn (column vectors), thus differentiating gives $\dot x=DΨ \dot y$ ($D\Psi \in \mathbb{R}^{n\times n}$- a square matrix). It is indeed the change of variables formula for the derivative. | |
| Dec 19, 2011 at 13:49 | comment | added | Jacques Carette | Ok, I forgot that notation, I guess. Chain rule gives me $\dot{x} = \dot{y} \cdot D\Psi y$ for $x=\Psi y$. So there is a $y$ embedded in your $D\Psi$ which you elide (and some explicit computation confirm) that threw me off. Then the formula reads just like the change of variables formula on manifolds, no? | |
| Dec 19, 2011 at 12:43 | history | edited | Jorge | CC BY-SA 3.0 |
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| Dec 18, 2011 at 18:12 | history | edited | Jorge | CC BY-SA 3.0 |
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| Dec 18, 2011 at 17:32 | comment | added | Jorge | Jacque, if you're referring to $\dot x=D\Psi \dot y$, then this is correct. You can calculate it using basic analysis. | |
| Dec 18, 2011 at 14:15 | comment | added | Jacques Carette | Are you sure your elaboration is correct? In particular, it seems to me that in your very first line of your elaboration, you have not applied the chain rule properly. If you 'fix' that, you'll get a condition which is much more reasonable. | |
| Dec 18, 2011 at 2:56 | history | edited | Jorge | CC BY-SA 3.0 |
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| Dec 18, 2011 at 2:44 | history | asked | Jorge | CC BY-SA 3.0 |