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Runge-Kutta on Elliptical Orbits

  1. Dec 18, 2017 #1
    1. The problem statement, all variables and given/known data
    Run a numerical analysis on elliptical orbits using the standard Runka-Kutta method. I already have the equations from Euler-Lagrange method in cartesian x,y-coordinates.

    d2x/dt2 = -K x (x2 + y2 )-3/2
    d2y/dt2 = -K y (x2 + y2 )-3/2

    2. Relevant equations
    I find it a little to get started. Most examples online are first order differential equations and/or single variable. So I'm not sure how to define my f(x,y,t) funktion. It's supposed to be the velocity dx/dt, right? But I "only" have the acceleration, so do I just multiply dt to get the velocity or what?

    3. The attempt at a solution
     
  2. jcsd
  3. Dec 18, 2017 #2

    gneill

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    Staff: Mentor

    Do a web search on "2D Runge-Kutta"
     
  4. Dec 18, 2017 #3

    DrClaude

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    Staff: Mentor

    You need to convert your system of second order equations into a system of coupled first order equations. That means introducing two new dependent variables, representing the first derivatives of x and y.
     
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