Numerical Analysis Project

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Presentation transcript:

Numerical Analysis Project MA3232 LCDR Aaron Hay LCDR Heather Mattern LT Mike Holihan

Outline Background Equation Development MATLAB Code Chaos Theory

Background The double pendulum is an example of a simple dynamical system that exhibits complex behavior, including chaos. It consists of two point masses at the end of light rods. Each mass plus rod is a regular simple pendulum, and the two pendula are joined together and the system is free to oscillate in a plane. The double pendulum is an example of a simple dynamical system that exhibits complex behavior, including chaos. It consists of two point masses at the end of light rods. Each mass plus rod is a regular simple pendulum, and the two pendula are joined together and the system is free to oscillate in a plane.

Double Pendulum

Kinematics of the Double Pendulum

Kinematics of the Double Pendulum

Forces in the Double Pendulum

Equations of Motion

Numerical Solution

MATLAB Single Pendulum

Chaos Theory Two Pendula

References Kawski, Matthias. MATLAB resources. June 2, 2010 http://stat.asu.edu/~kawski/MATLAB/matlab.html Weisstein, Eric. World of Physics. June 2, 2010 http://scienceworld.wolfram.com/physics/DoublePendulum.html

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