Practical and theoretical methods for determining the trajectories for particles involved in elastic collisions

The present paper shows how to use the conservation of the energy-momentum in order to determine the trajectories of two particles after they are subjected to an elastic collision. While the problem is studied in existent literature, there are severe limitations in the solutions, like the fact that the solution only determines the angle between the particles after the collision and not their exact trajectories. This is not very satisfactory when it comes to setting up experiments aimed at verifying the theoretical predictions. In the following paper, we will show how to obtain a much more detailed fix of the trajectories of the particles post collision by determining their exact angles with respect to the trajectory of the particles before the collision. The new approach is extremely important in applications like particle accelerators where we can only work with directly measurable quantities, the kinetic energy KE and the momentum p. The paper is intended for particle physicists who work with particle accelerators as well as graduate students and teachers.