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!

Derivation of Kepler's laws- differential equation question

  1. Sep 21, 2005 #1
    Hi group,

    Could someone 'remind me' why the equation u" + u = km/L^2 has the solution of the form u(theta) = km/L^2 + C cos(theta - theta(o)).
    Any references would be appreciated.
    Thanks

    Dave
     
  2. jcsd
  3. Sep 21, 2005 #2
    a linear differential equation with non zero additional term has a soulution which is a sum of a general solution of this equation with zero additional term and a particular solution of this equation. To be more clear (I assume that theta is independent variable) the equation

    [tex]u^{''}+u=0[/tex]
    has solution
    [tex]u_0=C\times cos(\theta-\theta_0)[/tex]

    on the other hand, your equation has a particular solution

    [tex]u_p=km/L^2=const[/tex]
    so the general solution is

    [tex]u=u_0+u_p[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derivation of Kepler's laws- differential equation question
  1. Keplers Laws (Replies: 13)

Loading...