Ascending Disk: Theoretical and Numerical Study

Abstract

Abstract In this work we analyzed a classical mechanical problem: a disc with a circular hole rotating and ascending on a inclined plane. The principal idea is to show the basic equations in both Lagrangian and Newtonian formalisms and to present numerical solutions. The equations are not solvable analytically, then we proceed to integrate numerically using the standardized Runge-Kutta method of order 4. We present several phase space showing the time evolution of the system. Additionally we presented an extension of the system considering a damping factor that decays exponentially in time.