Penalty formulation for the nonlinear dynamic analysis of a double pendulum

Abstract

A penalty fomulation for the nonlinear analysis of a double pendulum is presented which eliminates the use of Lagrange multipliers method. A numerical algorithm that employs the implicit Ru11ge-Kutta of order 2 along with Newton-Raphson method is developed to analyze the nonlinear dynamics of the system and to study the chaotic behaviour which the system portrays. A computer simulation of a numerical example is given to indicate the effectiveness of the penalty formulation and the algorithm developed.