## HomeNewton MechanisOverview

Calculating the movement of a system of $$N$$ particles requires that you know the interaction law $$F(x_{i},x_{j})$$ between pairs of these particles $$i /= j$$ and the initial conditions as the velocity and location for every mass $$m_{i}$$ in the system at the begin of the calculation.

$$\frac{dx_{i}}{dt}=v_{i}$$
$$x_{i}(0)=x_i$$

If this is known the prediction of the movement for a given point is done by providing a solution for the equation below:

$$m_{i}\frac{dv_{i}}{dt}\mid_{x(t)}=\sum_{j=1}^{N}F(x_{i}(t),x_{j}(t))$$

## Contents

In this section you will find various numerical experiments the newtonian movement of particles:

• Integration

In this chapter the basic concept of my computation algorithm is described.

• Elastic Collisions

This chapter presents a first verification of the algorithm accuracy.

• Keppler System

In this chapter the trajectory of a mass in the gravitational field of a much larger mass is calculated.

• Large Systems

In this section you find an example for larger systems

## Gallery

The gallery shows a few of the results of the projects above.