Runge-Kutta on Elliptical Orbits

[DrDress]

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

 

[gneill]

Do a web search on "2D Runge-Kutta"

 

[DrClaude]

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.