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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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