1. Not finding help here? Sign up for a free 30min 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!

Integration/Proving help! And check my work please!

  1. Oct 4, 2004 #1

    I am given the following equation.

    This is the total energy of a prticle moving in a central conservative field. m = mass, E = energy, L = angular momentum. The force the particle experiences is F = -Hmu^-3, where H is some constant, m is the mass of the particle, and u the distance. V(u), the potential, is just the negative integral of the force, and it is


    How can I show that the energy, E, if E < 0, then

    [tex]\alpha(t-t_{0})=\int_{R_{0}}^{R(\Theta)}\frac{du}{u\sqrt{a^2-u^2}} [/tex]

    , for real numbers alpha and a.

    And similarly, for E > 0, how can I show it's

    [tex]\beta(t-t_{0})=\int_{R_{0}}^{R(\Theta)}\frac{du}{u\sqrt{u^2+b}} [/tex]

    , for some real numbers beta and b?

    I really need help on this! :confused:

    I did show, for the E = 0 case, how it should be done. Please take the time check my work for this part.

    Since E = 0, the total energy equation simplifies to:


    then, plugging in V(u),


    [tex] Let s = m^2L^{-2}H[/tex]




    Since s is only a bunch of constants, we can factor it out.


    [tex] \ln {R_{\Theta}/R_{0}} = \sqrt{s-1)[/tex]

    then solve for [tex] R (\Theta) [/tex]
    [tex] R (\Theta) = R_{0}e^{(\Theta-\Theta_{0})\sqrt{s-1}}[/tex]
    Last edited: Oct 4, 2004
  2. jcsd
  3. Oct 4, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper

    I don't know whether you did your integrations correctly but the problems as you stated them only involve factoring numbers out from the radicals and rearranging terms.
  4. Oct 4, 2004 #3
    Yes...I was asked to get the equation...carry out the integral and arrange the terms so that it resembles the ones above with the alpha and beta.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integration/Proving help! And check my work please!
  1. Please Check My Work (Replies: 2)