Numerical Analysis of the Spring Pendulum System using MATLAB

Date of Award

2008

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Colladay, Donald

Keywords

Classical Mechanics, Numerical Analysis, Chaos

Area of Concentration

Physics

Abstract

The spring pendulum is a physical system which exhibits chaotic behavior; the motion is sensitive to initial conditions. The ordinary differential equations of this system can be derived using Lagrangian formalism, but cannot be solved analytically. Using computer software such as MATLAB allows for the numerical simulation of the spring pendulum system for any set of initial conditions. The Lyapunov Exponent is a measure of the chaotic nature of a system, and can be computed numerically. Primarily, the relationship between the Lyapunov exponent of the spring pendulum system as a function of the spring constant and the motion of the spring pendulum system was studied. Particular attention was paid to the local minima and maxima and resulting motion. No consistent correlation was found between the Lyapunov exponent as a function of the spring constant and the resulting motion. Further analysis of other relationships between the Lyapunov exponent and the motion is necessary, preferably in an automated fashion.

This document is currently not available here.

Share

COinS