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Unformatted text preview: Nonlinear Dynamic Systems Homework 1 1. A particle of mass m is constrained to travel along the path shown in Figure 1, which is described by the following function y ( x ) = 5 x 2 + 10 x 4 , (1) where x is defined as the horizontal location of the particle. Develop the equation of motion for the system, find the fixed points for the system, classify the stability of each fixed point, and sketch the neighboring trajectories. Explain how the stable and unstable fixed point(s) match or do not match your intuition?10.80.60.40.2 0.2 0.4 0.6 0.8 11 1 2 3 4 5 x [m] y(x) [m] Track Shape For Multiple Potential Wells Figure 1: Graph of the curved path y ( x ) in a vertical gravitational field. 1 2. Figure 2 is a schematic of a double pendulum undergoing parametric excitation (i.e. time periodic movement of the pivot point). The first pendulum is subjected to a harmonic displacement, of amplitude A and frequency Ω, oriented along an angle ( α ) which is at an incline with the horizontal.) which is at an incline with the horizontal....
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 Spring '08
 CHEN
 Equations, Strain, Double pendulum, pivot point, ﬁrst pendulum, double pendulum subject

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