The bead on a rotating hoop is a typical problem solved in Classical Mechanics. It is a simple yet dynamic system. In this project we take into consideration a bead with fixed mass that is free to move on a vertical hoop rotating with some angular velocity. The Lagrangian for this system is obtained using the kinetic and potential energy terms. These values are put in the Lagrange’s equation and the ODE is solved numerically using Python. We also analyze the trajectory of the bead for different values of angular velocity and the initial angle that it forms with the vertical. Points of stable and unstable equilibrium have also been examined. The study is further extended for the case where the hoop is tilted at some angle with respect to the vertical. For all the cases friction has been neglected.
Project completed as part of the 'Classical Mechanics' course in my bachelors
Link to report for further reading.