Point constrained to move on a frictionless ellipse under gravity

Modeling and simulating a particle constrained to move on a frictionless ellipse under gravity, initially considered a good project topic for an undergraduate course in Mechanical Engineering, since it is an extension of the classic problem of the nonlinear pendulum, presented difficulties that were not foreseeing beforhand. This outcome motivated their proponents to write this article, which can be considered as a guide for the safe exploration of the referred subject by undergraduate Mechanical Engineering students. It is only emphasized that they are expected to have previously taken courses in Theoretical Mechanics and Numerical Analysis and to carry out the project under the guidance of a tutor.