ME 680: INTRODUCTION TO BIFURCATION AND CHAOS SPRING 2010 HOME Work # 2 Due: February 18, 2010 Q1. Consider the one-dimensional ordinary differential equation ,,),,(uuFdtduwith ,0),0(allforuFthat 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 w0, that is, the springs are unstressed when w = w
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