ORIGIN OF POSITION DEPENDENT MASS IN A ROTATING PARABOLIC OR SEMI-PARABOLIC PATH: CLASSICAL AND SEMI-CLASSICAL - Rabab Jarrar; Tapas Roy; B. Rath; Prachi Prava Mohapatra; Dilip K Maiti; Jihad Asad (Journal of Mechanics of Continua and Mathematical Sciences, 2025)
For both classical and quantum elements of the system, parabolic and semiparabolic nature paths have been examined and analyzed. We use the most powerful semi-analytical techniques, namely the optimal and modified homotopy perturbation approach, to examine the dynamics of the particle motion with stability analysis. It is demonstrated that the particle's motion on a rotating parabolic path is precisely harmonic oscillator motion with mass depending on location. We find the exact analytical expression for the motion's frequency and amplitude. We then discuss the dependencies of amplitude and frequency on specific parameters and compare the accuracy of the analytical solutions to numerical simulations. We explore the effectiveness of analytical methodologies in solving the complex nature of particle motion and their significance to scientific and technical research.