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Unformatted text preview: sin( ) + T + af ( t ) . (a) Let a = 0. Find the energy of the system. Plot the energy level sets. Find the xed points. Linearize the system around the xed points. Find eigenvectors and eigenvalues (possibly numerically) of the xed points. Draw the skeleton of the phase space, localized around the xed points. (b) Let T = 0 ,g/l = 1 ,f ( t ) = cos ( t ) ,a = { , . 5 , 1 . } , where = 2 . Set up a grid of initial conditions on the square [, ] [1 , 1]. Set = t . Plot the trajectories of the Poincar e map for = 0 (dont forget to take the angle mod 2 . Describe the results. (c) Is it possible to execute an arbitrary motion ( t ) between time 0 and T by choosing appropriately f ( t )? If so, describe how. 1...
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 Fall '08
 Mezic,I

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