# Equilibrium stable or unstable - differential euqation

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• Jul 23rd 2010, 09:23 AM
lvleph
The OP already stated that these quantities are positive so the point is moot.
• Jul 23rd 2010, 09:25 AM
Ackbeet
Reply to lvleph at post # 16:

Take a closer look at post #3. Stability, in this context, is dealing with the boundedness of y. If y is bounded, you've got stability. Otherwise, you don't.
• Jul 23rd 2010, 09:26 AM
mathfilip
While we already are on the subject of physics. I could need some help understanding the derivatives of polar coordinates:

If I take the derivative with respect to time for theta(hat) - dont know how to type with math symbols

What will I get?

I know that if i do it for the radial unit vector i get - r(hat)' = theta'*theta(hat)

I can see it for the radial unit vector but not for the angular one. Any one dare to give an explanation?
• Jul 23rd 2010, 09:29 AM
lvleph
for the math symbols
\hat{\theta} = $\hat{\theta}$
\hat{r}' = $\hat{r}'$

As far as the polar coordinate question, I am actually not sure what you are asking.
• Jul 23rd 2010, 09:33 AM
mathfilip
Ok now I really understand what you meant Ackbeet with the exponentials! Thanks once again.
• Jul 23rd 2010, 09:34 AM
Ackbeet
To take the derivatives of $\hat{r}$ and $\hat{\theta},$ I would simply write them as functions of $\hat{i}$ and $\hat{j}$ and go from there.
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