A Comparative Study of Numerical Modelling and Analysis for Large Articulated Pendulums

In this article, we present a large system of multiple pendulums, also articulated pendulums, with twenty pendulums as a multibody model. The main objective of the study is to compare the computational time efficiency of two multibody formulations: the augmented Lagrangian and the recursive method for each articulated system. The equations of motion were derived for each formulation and the fourth- and fifth-order Runge-Kutta methods were utilised to solve for the equations by representing the kinematics and dynamics of the systems numerically. The computational times that corresponded to the manipulated step size and tolerance were compared for both formulations. The results showed that the augmented Lagrangian formulation had a significant divergence towards the negative y-axis at tolerance 0.1s for all modified step sizes. The animations also demonstrated elongation for specific pendulums based on the step size selection at a tolerance 0.1s. The recursive method, on the other hand, produced the best-fit plots and stable results for all xy-position and velocity-time plots for each adjusted step size and tolerance. Therefore, the recursive method is concluded to be more efficient than the augmented Lagrangian formulation in solving large open-loop multibody systems.