c++ - N 体模拟不起作用

Question

我正在尝试编写代码来解决 n 体问题，但在使用包含所有物体的数组而不是分别使用不同的物体时遇到了麻烦。我目前不知道我的代码出了什么问题，但是当我为任何物体绘制 x 的 y 函数时，我得到一条直线，这显然是不正确的。

这是我当前的代码:

#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;
}

问题可能出在类粒子之外，因为程序在我开始使用数组体之前就已经运行了。当然欢迎任何非必要改进的建议。我想做的另一件事是使用 std::vector 而不是数组，但我不知道如何在我的函数之外定义一个 vector ，就像我定义数组主体一样。

Answer 1

首先，您所有的 i <= N是错误的，因为对于 i < N，您的循环将执行 4 次(0、1、2、3)而不是 3 次.