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Unformatted text preview: Nonlinear Dynamic Systems Homework 2 1. Find the equilibrium solution(s) and bifurcation point(s) for the system system described by Eq. 1. Next, classify the fixed points, the bifurcation type, and construct a bifurcation diagram using β as a control parameter. Label stable and unstable solutions as well as the bifurcation point(s). ˙ x 1 ˙ x 2 = " x 2 2 x 2 sin( x 1 ) + β 2 4 sin 2( x 1 ) # . (1) 2. Find the equilibrium solution(s) and bifurcation point(s) for the system system described by Eq. 2. Next, classify the fixed points, the bifurcation type, and construct a bifurcation diagram using β as a control parameter. Label stable and unstable solutions as well as the bifurcation point(s). ˙ x 1 ˙ x 2 = x 2 2 x 2 + βx 1 x 2 1 . (2) 3. Aeroelastic galloping or flutter is a common problem that is encountered when specifying the flight envelope of an aerospace system (i.e. this constrains the flight speed of an aircraft). Find the equilibrium solution(s) and bifurcation point(s) for the aeroelastic system described by Eq. 3the equilibrium solution(s) and bifurcation point(s) for the aeroelastic system described by Eq....
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 Spring '08
 CHEN
 Chaos Theory, John Wiley, bifurcation point, E. N. Lorenz

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