c++ nbody simulation passing array as reference - c++

Question

I have a problem when trying to write a code to solve the nbody problem when using an array which contains all the bodies. My code doesn't do the right thing and i have no idea where it goes wrong though i suspect it has something to do with passing the array as a reference. To make it easier to spot my mistakes i will inculde a working version of the code which doesn't use the array containing all the bodies in the same way. The following is the code which doesn't work( when calculataing the orbit of a body you get a straight line instead of an ellipse with this code):
#include <cstdlib>
#include <iostream>
#include <cmath>
#include <fstream>
#define h 10000.0 // size of the timestep
#define N 3 // number of bodies
#define G 6.67384*pow(10.0,-11) // gravitational constant
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 body){
double dx = x - body.x;
double dy = y - body.y;
return sqrt(pow(dx,2.0)+pow(dy,2.0));
}
double g(double x1, double y1,particle body){
return G*body.m*(body.x-x1)/pow(dist(body),3.0);
}
double p(double x1, double y1, particle body){
return G*body.m*(body.y-y1)/pow(dist(body),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){ //choose the inital conditions for a new object
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 body, particle bodies[N]){ //force in the x- direction
double fx = 0;
for (int i = 0; i < N; i++){
if (bodies[i] == body ){;}
else{
fx += body.g(x1,y1,bodies[i]);
}
}
return fx;
}
double yforce(double x1, double y1, particle body, particle bodies[N]){ //force in the y- direction
double fy = 0;
for (int i = 0; i < N; i++){
if (bodies[i] == body) {;}
else{
fy += body.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;
}
Here is the working version of the code, both are supposed to solve the same problem:
#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 body){
double dx = x - body.x;
double dy = y - body.y;
return sqrt(pow(dx,2.0)+pow(dy,2.0));
}
double g(double x1, double y1,particle body){
return G*body.m*(body.x-x1)/pow(dist(body),3.0);
}
double p(double x1, double y1, particle body){
return G*body.m*(body.y-y1)/pow(dist(body),3.0);
}
void update(){
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;
}
}
bool operator !=(particle &other){
if(x != other.x || y != other.y || vx != other.vx || vy != other.vy){
return true;
}
}
};
particle zon, uranus, neptunus;
particle closest[] = {uranus, neptunus};
void set(){
zon.create(1, 1, -2, 1, 2*pow(10.0,30));
uranus.create(2870671*pow(10.0,6), 0, 0, 6800, 8.6810*pow(10.0,25));
neptunus.create(4498542*pow(10.0,6),0 ,0, 5430, 1.0243*pow(10.0,26));
}
double xforce(double x1, double y1, particle body){
particle bodies[] = {zon, uranus, neptunus};
double fx = 0;
for (int i = 0; i < 3; i++){
if (bodies[i] == body ){;}
else{
fx += body.g(x1,y1,bodies[i]);
}
}
return fx;
}
double yforce(double x1, double y1, particle body){
particle bodies[] = {zon, uranus, neptunus};
double fy = 0;
for (int i = 0; i <= 3; i++){
if (bodies[i] == body) {;}
else{
fy += body.p(x1,y1,bodies[i]);
}
}
return fy;
}
void corr(particle& body, double t){
body.kx1 = t*body.vx;
body.kv1 = t*xforce(body.x, body.y, body);
body.ky1 = t*body.vy;
body.kvy1 = t*yforce(body.x, body.y, body);
body.kx2 = t*(body.vx + 0.5*body.kv1);
body.kv2 = t*xforce(body.x + 0.5*body.kx1, body.y + 0.5*body.ky1, body);
body.ky2 = t*(body.vy + 0.5*body.kvy1);
body.kvy2 = t*yforce(body.x + 0.5*body.kx1, body.y + 0.5*body.ky1, body);
body.kx3 = t*(body.vx+ 0.5*body.kv2);
body.kv3 = t*xforce(body.x + 0.5*body.kx2, body.y + 0.5*body.ky2, body);
body.ky3 = t*(body.vy+ 0.5*body.kvy2);
body.kvy3 = t*yforce(body.x + 0.5*body.kx2, body.y + 0.5*body.ky2,body);
body.kx4 = t*(body.vx+body.kv3);
body.kv4 = t*xforce(body.x+ body.kx3, body.y + body.ky3, body);
body.ky4 = t*(body.vy + body.kvy3);
body.kvy4 = t*yforce(body.x + body.kx3, body.y + body.ky3, body);
}
void bereken(){
set();
ofstream file;
file.open("tester.txt");
for(int i =0; i <=50000; i++){
corr(zon, h);
corr(uranus, h);
corr(neptunus, h);
zon.update();
uranus.update();
neptunus.update();
if( i%1000 == 0){
file << i*h <<" "<<zon.x << " "<< zon.y <<" "<<uranus.x<<" " <<uranus.y <<" "<< neptunus.x<<" "<<neptunus.y<<" "<<"\n";
}
else{;}
}
file.close();
}
int main()
{
bereken();
system("pause");
return 0;
}

Answer 1

One problem is that you are overflowing your bodies[] array in 3 places:
#define N 3
particle bodies[N];
for (int i = 0; i <= N; i++) {
bodies[i].x = ... // Oops, access bodies[3] which doesn't exist
The correct loop, which you do use in two places, is:
for (int i = 0; i < N; i++) { // 0 to < N