michaelslab

In order to figure out the calculation error of the integration algorithm i it to a well known system as for example the elastic collision of hard particles. The conservation law for impuls and enery will be a measure for the accuracy of the simulation.

In order to simulate elastic collisions the force between two particles i assumed that the force behaves like the function below:

$$ F(r)=-F_{o}e^{-\frac{r^{2}}{2D}} $$(1)

The computations are done for two particles where one particle (M2) is at rest at the position (0,0,0) and the second particle (M1) moves with a constant velocity along the x axis towards this particle. The interacting force between them is described by the above formular.

The computation result is shown below. During the collision process the mass M1 transfers its complete impulse to the mass M2.

Fig. 1 - X-Traectory vs. time for two particles with identical masses

 

This below shows the central collision between a particle moving along the x-coordinate and a much bigger mass which is at rest. As expected the smaller mass is deflected during this process.

Fig. 2 - X-Traectory vs. time where one particle has a mutch larger mass then the other  (M2>>M1)

 

The last picture show a non central collision; where the color indicates the impuls of the particle.