Runge-Kutta on Elliptical Orbits

  • #1
DrDress
3
0

Homework Statement


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

Homework 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?

The Attempt at a Solution

 
Physics news on Phys.org
  • #2
Do a web search on "2D Runge-Kutta"
 
  • #3
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.
 

Similar threads

Replies
1
Views
4K
Replies
8
Views
1K
Replies
3
Views
2K
Replies
15
Views
2K
Replies
3
Views
4K
Replies
2
Views
5K
Replies
7
Views
2K
Back
Top