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Unformatted text preview: PHYS 3202 Classical Mechanics II - Homework #6 Due at 12:05pm, Friday March 11, 2011 in the class In homework, quiz, and final exam, please show intermediate steps of your calculations. Whenever appropriate, you may draw diagram(s). Problem 1 (10 points): Find the symplectic area A enclosed by a clockwise loop in the 2 dimensional phase plane: q ( ) = c 1 cos , p ( ) =- c 2 sin , where c 1 and c 2 are positive constants, and the parameter increases from 0 to 2 . If we parameterize the loop as q = c 1 cos( 2 ) , p =- c 2 sin( 2 ) , where the parameter increases from 0 to 2 , what is the symplectic area enclosed by the loop? If every point on the plane moves according to Hamiltons equations, governed by a particular Hamiltonian function H ( q,p,t ), the above loop will in general be transformed into different shapes at different locations in the phase plane at later times. If H t > 0 for all values of ( q,p,t ), how does the symplectic area of the...
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