Equations of Motion Formulation of a Pendulum Containing N-point Masses

This paper presents a general formulation of equations of motion of a pendulum with n point mass by use of two different methods. The first one is obtained by using Lagrange Mechanics and mathematical induction(inspection), and the second one is derived by defining a vector. Today, these equations can be obtained by employing numerous programs; however, this study gives a very compact form of these equations that is more efficient than solving Euler-Lagrange Equations for every pendulum with more complex structures than simple or double pendulum. Additionally, we investigate what will happen to our n-point mass system when we take limit as number of point masses goes infinity under well-defined assumptions. We find out that it converges to hanging rope system.