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Differentiation of conic section equation

  1. Aug 31, 2014 #1
    1. The problem statement, all variables and given/known data

    I do not understand how the authors got the time derivative of equation 1.5-4 in the form given at 2.5-2.

    RimvVF6.jpg



    2. Relevant equations



    3. The attempt at a solution



    [tex]\frac{d}{dt}\frac{p}{1+e cos\sigma}=-\frac{p}{(1+ecos\sigma)^2}(-esin\sigma\dot\sigma)=\frac{pe\, sin\sigma\dot\sigma}{1+2e\,cos\sigma+e^2cos^2\sigma}[/tex]

    ?

    I tried various rewrites using trigonometric identities, but the equation just got so complicated that it'd take me a long time to typeset it in this post.
     
  2. jcsd
  3. Aug 31, 2014 #2
    Never mind. I got the derivation. I also found out I am blind/can't read.
     
  4. Sep 13, 2014 #3
    Hi tauon! I'm curious if you could share how you got the derivation, or which textbook your above excerpt is from. I'm trying to get to equation 2.5-2 from this excerpt, but seem to be getting stuck the same spot you were. Thanks!
     
  5. Nov 27, 2014 #4
    Hi. This might be very late now, but I didn't check this thread since I got the solution. :p
    In case someone runs into it in the future, this is the derivation I used
    xAij0s7.png
    Oh, and the excerpt is from "Fundamentals of Astrodynamics" (authors Roger Bate, Donald Mueller, and Jerry White) the 1971 edition.
     
    Last edited: Nov 27, 2014
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