1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Implicit differentiation; need help reproducing textbook derivation

  1. Sep 19, 2014 #1
    1. The problem statement, all variables and given/known data

    (The fourth equation is the central one)

    first, we have [itex]\frac{1}{r}=\frac{a}{b^2}(1+ecosθ)[/itex] and [itex]b^2=a^2(1-e^2)[/itex]

    now using these two, we transform

    [itex]acosψ=ae+rcosθ[/itex] into [itex](1-ecosψ)(1+ecosθ)=\frac{b^2}{a^2}[/itex]

    we want to find [itex]dθ/dψ[/itex], and the author performs an inplicit differentiation, and the result in the book is (treating θ as a function of ψ)
    [tex]dθ/dψ=\frac{b}{a(1-ecosψ)}[/tex]

    2. Relevant equations
    stated above

    3. The attempt at a solution

    I performed the implicit differentiation and got:
    [tex]esinψ(1+ecosθ)-esinθ\frac{dθ}{dψ}(1-ecosψ)=0[/tex]

    Is my implicit differentiation wrong or are some transformations needed? I tried to match the result in the book using the first two equations together with my result without success..
     
  2. jcsd
  3. Sep 20, 2014 #2
    Never mind, I found it. I just needed to use a relation between sinψ and sinθ (which I have not posted here).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Implicit differentiation; need help reproducing textbook derivation
Loading...