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ME 680: INTRODUCTION TO BIFURCATION AND CHAOS
SPRING 2010
HOME Work # 2
Due: February 18, 2010
Q1.
Consider the onedimensional 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 degreeoffreedom model of an elastic arch with initial deflection w
0
, that is, the
springs are unstressed when w = w
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 Fall '10
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