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B Recast a differential equation with a change of variable

  1. Mar 22, 2016 #1
    I obtained an extra factor of ##\frac{1}{l^2}## in the first term on the LHS of (3.34).

    From (3.33),

    LHS ##=u^2\frac{d}{d\theta}(\frac{u^2}{m}\frac{du}{d\theta}\frac{dr}{du})-\frac{l^2u^3}{m}##
    ##=u^2\frac{d}{d\theta}(-\frac{1}{m}\frac{du}{d\theta})-\frac{l^2u^3}{m}##
    ##=-\frac{u^2}{m}\frac{d^2u}{d\theta^2}-\frac{l^2u^3}{m}##

    Multiplying throughout by ##-\frac{m}{l^2u^2}##, we have
    LHS ##=\frac{1}{l^2}\frac{d^2u}{d\theta^2}+u##
    which differs from (3.34).

    What's wrong?

    Screen Shot 2016-03-22 at 12.56.41 pm.png

    EDIT: I found the mistake. The text has a typo. The "1"s in (3.33) are actually "##l##"s.
     
    Last edited: Mar 22, 2016
  2. jcsd
  3. Mar 22, 2016 #2

    BvU

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    Well done !
     
  4. Mar 22, 2016 #3

    Ssnow

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    yes, this was the error ... :wink:
     
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