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Math Help - Equilibrium stable or unstable - differential euqation

  1. #16
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    The OP already stated that these quantities are positive so the point is moot.
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  2. #17
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    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.
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  3. #18
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    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?
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  4. #19
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    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.
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  5. #20
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    Ok now I really understand what you meant Ackbeet with the exponentials! Thanks once again.
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  6. #21
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    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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