Modelling the non-linear dynamics of the looping pendulum

TL;DR

This paper models the complex non-linear dynamics of the looping pendulum, deriving differential equations, and validating the model through experiments and simulations that closely match observed trajectories.

Contribution

It introduces a detailed theoretical model dividing forces into rotating and non-rotating components, validated by experimental data and MATLAB simulations.

Findings

Experimental data fits a logarithmic curve

Simulation results closely match experimental trajectories

Derived equations accurately predict the pendulum's motion

Abstract

The Looping pendulum phenomenon was first introduced in 2019 at the 32nd edition of the IYPT, wherein a lighter bob sweeps around a cylindrical rod to support the weight of a heavier bob. In this paper, the phenomenon was divided based on rotating and non-rotating forces, and differential equations were derived for each. To verify the theoretical derivation, an experimental analysis was done, varying the mass ratio with the vertical distance travelled by the heavier bob. (Tracked using tracker) Experimental findings fit a logarithmic curve fit -- falling succinctly with a similar trend with the simulation run with MATLAB solving the derived differential equations. Furthermore, to verify the simulation, the trajectory of both the lighter and heavier mass was also compared for the simulation and experimental findings. The experimental findings fit very closely to the simulation findings, accrediting the validity and accuracy of the derived theory.