Unformatted text preview: r = 1. What is its period T ? (b) (10 pts) Find that exact Poincar´ e map r n +1 = P ( r n ) using the Poincar´ e section Σ at θ = 0. (c) (5 pts) By evaluating the derivative of P at the periodic orbit, determine, in terms of μ , when the periodic orbit is stable and unstable. (d) (5 pts) Linearize (3) about r = 1 by setting r = 1 + y . Solve the resulting equation for y ( t ). How is y ( T ) related to y (0)? How is this related to the results of (c)? 1...
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- Fall '08
- pts, Conic section, θ, Applied Dynamical Systems