Question

I want to achieve that two points are rotating around each other. I therefore use a rotation matrix. However I now get the problem that the distance between the points is growing (see atached video 1). The distance however should stay constant over my whole simulation.

Here is my code I use for calculating the speed:

Where p1 and p2 are the two points.

double xPos = p0.x+p1.x;
double yPos = p0.y+p1.y;
//The center between p1 and p2
xPos /=2;
yPos /=2;
//the rotating angle
double omega = 0.1;
//calculate the new positions
double x0new = xPos + (p0.x-xPos)*std::cos(omega) - (p0.y-yPos)*std::sin(omega);
double y0new = yPos + (p0.x-xPos)*std::sin(omega) + (p0.y-yPos)*std::cos(omega);
double x1new = xPos + (p1.x-xPos)*std::cos(omega) - (p1.y-yPos)*std::sin(omega);
double y1new = yPos + (p1.x-xPos)*std::sin(omega) + (p1.y-yPos)*std::cos(omega);
//the speed is exatly the difference as I integrate one timestep
p0.setSpeed(p0.x-x0new, p0.y-y0new);
p1.setSpeed(p1.x-x1new, p1.y-y1new);

I then integrate the speed exactly one timestep. What is wrong in my calculation?

Update
It seems that my integration is wrong. If I set the positions direct it works perfect. However I do not now what is wrong with this integration:

setSpeed(ux,uy){
     ux_=ux;
     uy_=uy;
}
// integrate one timestep t = 1
move(){
     x = x + ux_;
     y = y + uy_;
}

Video of my behaviour

Answer 1

There’s nothing clearly wrong in this code, but the “speed” integration that isn’t shown, suggests that you might be integrating linearly between old and new position, which would make the orbits expand when speed > nominal speed and to contract when speed < nominal_speed.

As I suspected. The integration is actually extrapolation at the line segment between point p0 and p1 which are supposed to be at a fixed distance from origin (a physical simulation would probably make the trajectory elliptical…)

Thus if the extrapolation factor would be 0, the new position would be on the calculated perimeter. If it was < 0 (and > -1), you’d be interpolating inside the expected trajectory.

         O     This beautiful ascii art is trying to illustrate the integration
        /      x is the original position, o is the new one and O is the 
       / ___-----   "integrated" value and the arc is a perfect circle :)
      o--      Only at the calculated position o, there is no expansion.
   --/
  / /
 / /
| /
x