N-body simulation not working

Question

I am trying to write a code to solve the n-body problem and i run into trouble when using an array with all the bodies instead of using the different bodies seperately. I currently have no idea what's going wrong in my code but when i plot x in function of y for any body i get a straight line which obviously isn't right.

This is my current code:

#include <cstdlib>
#include <iostream>
#include <cmath>
#include <fstream>
#define h  10000.0
#define N  3
#define G  6.67384*pow(10.0,-11)

using namespace std;



class particle{
      public:
      double kx1,kx2,kx3,kx4, kv1, kv2, kv3, kv4;
      double ky1, ky2, ky3, ky4, kvy1, kvy2, kvy3, kvy4;
      double x,y,vx,vy,m;


      double dist(particle aap){
             double dx = x - aap.x;
             double dy = y - aap.y;
             return sqrt(pow(dx,2.0)+pow(dy,2.0));
             }

      double g(double x1, double y1,particle aap){
             return G*aap.m*(aap.x-x1)/pow(dist(aap),3.0);
             }

      double p(double x1, double y1, particle aap){
             return G*aap.m*(aap.y-y1)/pow(dist(aap),3.0);
       }


      void update(){                                      //object advances 1 step
           x = x + (1/6.0)*(kx1+2*kx2+2*kx3+kx4);
           vx = vx + (1/6.0)*(kv1+2*kv2+2*kv3+kv4);
           y = y + (1/6.0)*(ky1+2*ky2+2*ky3+ky4);
           vy = vy + (1/6.0)*(kvy1+2*kvy2+2*kvy3+kvy4);
           }

     void create(double x1, double y1, double vx1, double vy1, double m1){
                      x = x1;
                      y = y1;
                      vx = vx1;
                      vy = vy1;
                      m =m1;
                      }

     bool operator ==(particle &other){
          if(x == other.x && y == other.y && vx == other.vx && vy == other.vy){
               return true;
               }
               }

      };




particle bodies[N];



void set(particle (&bodies)[N]){
     bodies[0].create(1, 1, -2, 1, 2*pow(10.0,30));
     bodies[1].create(2870671*pow(10.0,6), 0, 0, 6800, 8.6810*pow(10.0,25));
     bodies[2].create(4498542*pow(10.0,6),0 ,0, 5430, 1.0243*pow(10.0,26));
     }


double xforce(double x1, double y1, particle aap, particle bodies[N]){    //force in the x- direction

       double fx = 0;
       for (int i = 0; i <= N; i++){
           if (bodies[i] == aap ){;}

           else{
                fx += aap.g(x1,y1,bodies[i]);
                }
                }
       return fx;
       }

double yforce(double x1, double y1, particle aap, particle bodies[N]){ //force in the y- direction 

       double fy = 0;
       for (int i = 0; i <= N; i++){
           if (bodies[i] == aap) {;}

           else{
                fy += aap.p(x1,y1,bodies[i]);
                }
                }
       return fy;
       }


void corr(double t, particle bodies[N]){                            //runge kutta 4
     for(int i =0; i <= N; i++){

            bodies[i].kx1 = t*bodies[i].vx;
            bodies[i].kv1 = t*xforce(bodies[i].x, bodies[i].y, bodies[i], bodies);
            bodies[i].ky1 = t*bodies[i].vy;
            bodies[i].kvy1 = t*yforce(bodies[i].x, bodies[i].y, bodies[i], bodies);

            bodies[i].kx2 = t*(bodies[i].vx + 0.5*bodies[i].kv1);
            bodies[i].kv2 = t*xforce(bodies[i].x + 0.5*bodies[i].kx1, bodies[i].y + 0.5*bodies[i].ky1, bodies[i], bodies);
            bodies[i].ky2 = t*(bodies[i].vy + 0.5*bodies[i].kvy1);
            bodies[i].kvy2 = t*yforce(bodies[i].x + 0.5*bodies[i].kx1, bodies[i].y + 0.5*bodies[i].ky1, bodies[i], bodies);

            bodies[i].kx3 = t*(bodies[i].vx+ 0.5*bodies[i].kv2);
            bodies[i].kv3 = t*xforce(bodies[i].x + 0.5*bodies[i].kx2, bodies[i].y + 0.5*bodies[i].ky2, bodies[i], bodies);
            bodies[i].ky3 = t*(bodies[i].vy+ 0.5*bodies[i].kvy2);
            bodies[i].kvy3 = t*yforce(bodies[i].x + 0.5*bodies[i].kx2, bodies[i].y + 0.5*bodies[i].ky2,bodies[i], bodies);

            bodies[i].kx4 = t*(bodies[i].vx + bodies[i].kv3);
            bodies[i].kv4 = t*xforce(bodies[i].x+ bodies[i].kx3, bodies[i].y + bodies[i].ky3, bodies[i], bodies);
            bodies[i].ky4 = t*(bodies[i].vy + bodies[i].kvy3);
            bodies[i].kvy4 = t*yforce(bodies[i].x + bodies[i].kx3, bodies[i].y + bodies[i].ky3, bodies[i], bodies);
            }
     }


void calculate(particle (&bodies)[N]){
     set(bodies);
     ofstream file;
     file.open("tester.txt");
     for(int i =0; i <=50000; i++){

             corr(h, bodies);                          
             for(int j = 0; j <= N; j++){
                     bodies[j].update();
                     }                   
             if( i%1000 == 0){

                 file << i*h;
                 for(int j = 0; j <=N ; j++){
                          file <<"  "<<bodies[j].x << "  "<< bodies[j].y;
                          }
                 file <<"  "<<"\n";
                 }
             else{;}
             }
     file.close();
     }


int main()
{   
    calculate(bodies);
    system("pause");
    return 0;
}

The problem probably lies outside of the class particle since the program worked before i started using the array bodies. Any suggestions for non essential improvements are ofcourse welcome. Another thing i'm trying to do is use std::vector instead of an array but i don't know how i could define a vector outside my functions like i defined the array bodies.

Answer 1

You are likely experiencing energy drift, as RK4 is not symplectic, and the n-body problem is a Hamiltonian system. I had this same problem trying to use RK4 for a solar system n-body as well. So did this person. You should try another symplectic numerical method like Euler, Verlet, Ruth's 3rd, or Ruth's 4th order symplectic integrator.

Answer 2

For a start, all of your i <= N are wrong, because your loop will execute 4 times (0, 1, 2, 3) instead of 3 for i < N.