Simulation Study on Methods for Modeling Elastic Collisions

Abstract

This paper is focused on investigating and describing collision processes and comparing the numerical results of different ODE solvers. The collisions are modeled on a system of two points of mass moving along circular paths. The equations of motion are derived using the Euler-Lagrange method. All the simulations are done in MATLAB, and the derivations of the equations are done in Maple. Explicit Euler and Heun methods are implemented, and the results of both solvers were compared to the ode45 solver of MATLAB, which is used as reference due to complexity of the equations of movement of this coupled system. The main question that this work aims to answer is how the different algorithms for solving differential equations behave when altered in a way that the collisions can be modeled.