In this work, we study, simulate and compare the constrained motion of a particle within two theoretical models: a relativistic and a Newtonian. The main objective is to get the user acquainted with the differences emerging in the treatment of the same mechanical system within the frames of Newtonian and the relativistic point of view. In the virtual environment of the simulation, the user can change the initial state of the moving particle and the gravity field within which it moves; so he can notice the resulting variations in the motion of the system.  

To achieve the objectives we have set, the subsequent issues have been implemented:  a) In the context of Newtonian Mechanics, determine and study a mechanical system consisted of a particle moving along a fixed curve of the three-dimensional Euclidean space, in the presence of a homogeneous gravitational field. In particular, we have considered the motion of a bead along a vertical circular wire. The same mechanical system is considered and studied in the context of the General Relativity. Hence we are in the position to compare the predictions obtained by the Newtonian and the relativistic model for the evolution of a well-known mechanical system.  b) Simulate the motion of the particle according to the Newtonian and the relativistic model and compare their predictions in the virtual environment of the simulation.  The simulation has been compiled in JavaScript language on the Easy JavaScript Simulations platform.