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Unformatted text preview: Numerical Integration Project Background Project Tasks Final Project T. Mercker Aerospace Engineering and Engineering Mechanics The University of Texas at Austin ASE 201: Introduction to Computer Programming April 27 / May 1, 2009 T. Mercker Final Project Numerical Integration Project Background Project Tasks Outline Numerical Integration Project Background Free Fall Bungee Extension Project Tasks T. Mercker Final Project Numerical Integration Project Background Project Tasks Numerical Integration I In cases where we cannot analytically integrate, we make use of numerical integration techniques I Assume you know the acceleration, a ( t ) , and you want to calculate the velocity, v ( t ) , and distance, h ( t ) I You know that a is the second derivative of h and the first derivative of v I Recall the definition of a derivative a ( t ) = lim t v ( t + t ) v ( t ) t I Instead of t 0 make t small then a ( t ) v ( t + t ) v ( t ) t I This leads to a simple iteration method for numerical integration T. Mercker Final Project Numerical Integration Project Background Project Tasks I Define t old t and t new t + t then t = t new t old and a ( t old ) v ( t new ) v ( t old ) t I Solve for the new velocity v ( t new ) = v ( t old ) + t a ( t old ) I Similarly for distance v ( t new ) h ( t new ) h ( t old ) t I Solve for the new distance h ( t new ) = h ( t old ) + t v ( t new ) I Note that calculating the new distance is dependent on the NEW velocity T. Mercker Final Project Numerical Integration Project Background Project Tasks Free Fall Bungee Extension Project Background I Your final project is investigate a bungee jump by using numeric integration techniques I Our bungee jump will consist of two parts: 1. Free fall 2. Bungee extension I You will create two functions (one for each part of the jump) that work within a script that calculates the entire jump I At the end you will create plots of the jump and investigate several questions I The final project is due at the beginning of class on the final day of class (May 8th) without exception T. Mercker Final Project Numerical Integration...
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 Spring '07
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