The constrained motion of a particle along a circular curve: Newtonian and Relativistic model

Kostas Papamichalis, Dr of Theoretical Physics

Download the theoretical analysis of the models and the included activities, by clicking here: Constrained Motions

The objective of the simulation is to study the constrained motion of a paticle (bead) along a circular curve. The study is accomplished within two different theoretical context: a) the Einstein General Theory of Relativity and b) the Newtonian Mechanics. The mass of the bead and the initial condition of the mechanical system are identical in the two models. The motion of the bead is considered with respect to a Cartesian coordinate system, with space origin O. The center of the circular orbit coincides with O; its radius is L. The system is deterrmined by one degree of freedom: the deviation angle "theta" of the bead radius-position from the negative vertical axis Ox². The initial value of theta is controlled by the user. The initial angular velocity is zero. The bead is moving in a homogeneous vertical gravitational field, whose strength g is also controlled by the user.

The left window depicts the motion of the bead according to the relativistic model and the right one, according to the Newtonian model. The graph-windows show in real-time the change of the deviation angle and the angular velocity with time, for each model.

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