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Homework3 - ME 680: INTRODUCTION TO BIFURCATION AND CHAOS...

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ME 680: INTRODUCTION TO BIFURCATION AND CHAOS SPRING 2010 HOME Work # 3 Due: March 09, 2010 This homework is related to bifurcations at single and multiple multiple critical eigenvalues, the latter being based on the paper distributed in class: Dimitris S. Sophianopoulos, 2007, Bifurcations and catastrophes of a two-degrees-of-freedom nonlinear model simulating the buckling and postbuckling of rectangular plates, Journal of the Franklin Institute 344 (2007) 463–488. Q1. Consider the double pendulum model of a column, as shown in the figure. Show that the potential energy of the system (ignoring gravity or mass of the rods), is given by Then, follow the steps outlined (presented) in class notes to derive the bifurcation equations near the first critical point along the fundamental equilibrium path of the system. Please provide all steps involved in the derivation/analysis. You must finally have an approximate expression for the solution branches that emanate from the trivial solution.
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This note was uploaded on 12/29/2011 for the course ME 680 taught by Professor Na during the Fall '10 term at Purdue.

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Homework3 - ME 680: INTRODUCTION TO BIFURCATION AND CHAOS...

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