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Unformatted text preview: i ! + n X i =1 q i q i + p i p i ! . Using Hamiltons equations we have q i q i = + q i H p i and p i p i = p i H q i . Interchanging the derivative these terms cancel one another ( ~v = 0 in phase space) and we are left with Liouvilles theorem: 0 = t + n X i =1 q i q i + p i p i ! = d dt . This is the motion of an incompressible uid, but in phase space instead of coordinate space....
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This note was uploaded on 12/11/2011 for the course PHY 4936 taught by Professor Berg during the Fall '11 term at FSU.
 Fall '11
 berg
 mechanics

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