The Double Pendulum of Variable Mass: Numerical Study for different cases.

Abstract

The purpose of this project is to theoretically and numerically analyze the double pendulum with variable mass system, where different cases are presented: The first one corresponds to the classical analysis of the double pendulum, the second case corresponds to the double pendulum with variable mass, considering the upper mass as the variable one. The third case concerns the double pendulum with variable mass, where the lower mass varies. Finally, the fourth case corresponds to the double pendulum with variable mass, considering both of the masses as variable. For every case it is verified that m s ≫ m i which guarantees the general double pendulum behavior. We obtain the coupled equations of motion for every case by using the Lagrange formulation. The system equations are developed by means of simulations in order to solve the equations of motion, applying the fourth order Runge Kutta (RK4) numerical method. The outcomes for the numerical solution and the observed effects due to the variable mass are presented for every case.