Столкновение частиц

Я пытаюсь написать код, который с учетом масс, скорости, смещения и радиусов N частиц в одномерной коробке будет возвращать свои позиции с небольшими приращениями 0,03 с.
Программа соответствует. Однако не выдает правильных значений.

#include <iostream>
#include <cmath>
#include <fstream>
#include <vector>using namespace std;struct particle {
double x;   //position of particle
double im;  //inverse mass
double v;   //velocity of particle
double r;   //radius of particle
};

void bonkers(vector<particle> &array, int NN, double t, double ddt, int T);
double time(vector<particle> &a, int NN, int &whichn);
void collision(particle &a, particle &b);
void position(particle &a, double ddt);

void position(particle &a, double ddt)//position of particles
{
a.x += ddt * a.v; //position = t * velocity
}

void collision(particle &a, particle &b)//velocities after collision
{
double realativeV = a.v - b.v;
double af = a.im / (a.im + b.im);
double bf = b.im / (a.im + b.im);
a.v -= 2.0 * af * realativeV;
b.v += 2.0 * bf * realativeV;
}

double time(vector<particle> &a, int NN, int &whichn)//Finds time of first collision.
{
double dt = 1e100; //really large number
for (int n = 0; n < NN - 1 ; n++)
{
double RelativeV = a[n].v - a[n + 1].v;
if (RelativeV > 0)//this means dt won't be 0, no negative times
{
double Collisiont = ((a[n + 1].x - a[n + 1].r) - (a[n].x + a[n].r))/ RelativeV;//gives time of collision
//time of collision worked out as time when the distance between the two balls centre is equal to their combined radi
if (Collisiont < dt)//finds smallest possible time of collision
{
dt = Collisiont; //returns time of first collision
whichn = n; //gives which particles collide. Therefore which particles velocities need to change
}
}
}
return dt;
}

void bonkers(vector<particle> &array, int NN, double t, double ddt, int T)
{

ofstream myfile;
myfile.open("example.txt");//sends all information to file called example.txt
int whichn = 0;
double k;
double l = 0;
for (int i = 0; i <= T; i++)//set arbitrary number of collision i.e. T
{
k = t;//after every collision k reset to 0 as time function works from 0
while( k <= time(array, NN, whichn) )
{
myfile << l; //prints the time
k += ddt; //incriments time
l += ddt; //increments time, but doesn't reset time so gives total time

for (int n = 1; n < NN -1 ; n++)
{
position(array[n], ddt);//calculates new position
myfile << "\t" << array[n].x;//prints the positions of all the particles at said time
}
myfile << endl;
}
collision(array[whichn], array[whichn + 1]);//asings new velocities to the two particles which collided
}
myfile.close();

}

int main()
{
int N; //number of balls
double m; //mass of balls
int T = 50; //number of collisions
double t = 0.0; //starts from 0 time
double ddt = 0.03; //invrements by 0.03 seconds each time

cout << "Input number of balls" << endl;
cin >> N;

vector<particle> a(N + 2); //extra two for the two walls, wall1 at 0 and wall2 at 20

for (int k = 1; k <= N; k++)
{
cout << "Input mass of ball " << k << endl;
cin >> m;
a[k].im = 1.0 / m;  //finds inverse mass
cout << "Input position of ball " << k << " between 0 and 20" << endl;
cin >> a[k].x;
cout << "Input speed of ball " << k << endl;
cin >> a[k].v;
cout << "Input radius of ball " << k << endl;
cin >> a[k].r;
}

//asign wall variables
a[0].im = 0;    //infinte mass, so walls don't move
a[0].r = 0;
a[0].x = 0; //wall1 at 0
a[0].v = 0;
a[N + 1].im = 0;
a[N + 1].r = 0;
a[N + 1].x = 20;    //wall2 at 20
a[N + 1].v = 0;

bonkers(a, N + 2, t, ddt, T);
return 0;
}

Существует очень очевидная проблема, когда у вас есть только один мяч. Радиусы, масса и скорость всего 1.
Скорость шариков изменяется в позиции 10.03 по какой-то причине, а не отскакивает от стены в 20.

Я полагаю, что проблема в «временной» функциональной части кода.
Эта проблема становится более очевидной, если вывести «k» в example.txt в функции bonkers вместо «l».

Большое спасибо 🙂