Constrained Motion of a Particle on an Elliptical Path

Khaled I. Nawafleh and Raed S. Hijjawi

Abstract

In this work we investigate the constrained motion of a particle on an ellipse in the framework of two approaches: The standard approach and Dirac’s approach. The Poisson brackets and Dirac brackets of the generalized variables are calculated by using Scardicchio’s technique, and it is observed that there exist nonconserved quantities in the system. On the quantum level, the nonvanishing commutators between the generalized variables leads to the principle of uncertainty. However, in the limit case of motion on a circle the generalized momentum is found to be a constant of motion.