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ME 680: INTRODUCTION TO BIFURCATION AND CHAOS SPRING 2010 HOME Work # 2 Due: February 18, 2010 Q1. Consider the one-dimensional ordinary differential equation , , ), , ( u u F dt du with , 0 ) , 0 ( all for u F that is, u=0 is always a equilibrium solution for the system. Following the general discussion in class lectures, study the following: (a) Singular points – regular points, double points, singular turning points and cusp points. Derive the conditions on the function F and its derivatives for the existence of the various cases, and the explicit expressions for the local branches possibly arising. (b) Stability of equilibrium branches – for branches arising at double points and at singular turning points. Q2. Consider a one degree-of-freedom model of an elastic arch with initial deflection w 0 , that is, the springs are unstressed when w = w
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