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Schutz, page 224

  1. Oct 13, 2005 #1
    This question is just for those who have a copy of Schutz, A First Course in GR. I have tried to plug equations 9.43 and 9.44 into equation 9.42 in order to verify equations 9.45 and 9.46. So far, I have not been successful. However, I have come to the conclusion that probably 9.45 is incorrect. The book has:
    [tex]
    R = \frac{1}{2}l_{0}\Omega^{2}A/[(\omega_{0} - \Omega)^2 + 4\Omega^{2}\gamma^{2}]^{1/2}
    [/tex]
    But I believe it should be the following:
    [tex]
    R = \frac{1}{2}l_{0}\Omega^{2}A/[(\omega_{0}{}^{2} - \Omega^{2})^2 + 4\Omega^{2}\gamma^{2}]^{1/2}
    [/tex]
    Unfortunately, I haven't been able to successfully justify either equation. The reason I think that my version may be the correct one is by looking at equation 9.46
    [tex]
    tan \phi = 2\gamma \Omega / (\omega_{0}{}^{2} - \Omega^{2})
    [/tex]
    which implies:
    [tex]
    cos \phi = (\omega_{0}{}^{2} - \Omega^{2}) / [(\omega_{0}{}^{2} - \Omega^{2})^2 + 4\Omega^{2}\gamma^{2}]^{1/2}
    [/tex]
     
  2. jcsd
  3. Oct 16, 2005 #2
    Yes I get it to work out with your correction
    [tex]
    R = \frac{1}{2}l_{0}\Omega^{2}A/[(\omega_{0}{}^{2} - \Omega^{2})^2 + 4\Omega^{2}\gamma^{2}]^{1/2}
    [/tex]
    and the additional correction that
    [tex]
    tan \phi = -2\gamma \Omega / (\omega_{0}{}^{2} - \Omega^{2})
    [/tex]
     
  4. Oct 16, 2005 #3
    Thank you, thank you, thank you, thank you. I have spent hours on this one equation trying many different tricks, but somehow this one escaped me.
     
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