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Unformatted text preview: i + p i p 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 o i p i =- p i H q i . Interchanging the derivative these terms cancel one another and we are left with Liouvilles theorem: = 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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- Fall '11