A case study of multi-arm pendulum system using Hamiltonian dynamics

Abstract

This work aims to analyze the behavior of multi-arm pendulum system using Hamiltonian dynamics. Multi-arm pendulum systems are mechanical systems consisting of multiple pendulums connected at a common point, exhibiting complex interactions and motion patterns.In this project, we apply Hamiltonian dynamics, to derive the equations of motion for multi-arm pendulum system. By formulating the Hamiltonian function and applying Hamiltonian equations, we obtain a set of coupled differential equations that describe the system’s behavior over time.Using analytical and numerical methods such as RK4, we solve these differential equations to simulate the motion of multi-arm pendulum systems. Through computational analysis and visualization, we investigate the system’s dynamics, including oscillation frequencies and phase relationships between pendulums. This project therefore contributes to the deeper understanding of the complex dynamics exhibited by multi-arm pendulum system and demonstrates the application of Hamiltonian dynamics in analyzing mechanical systems with multiple degrees of freedom.