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Unformatted text preview: After substituting Eq.(6) into Eq.(2), we f nd dG = X j h q j d p j p j d q j i L t dt . (7) Now express the total di f erential of G in terms of its natural variables as dG = X j " G p j d p j + G q j d q j # + G t dt , (8) 1 and compare the coe cients of the independent di f erentials in Eqs.(7) and (8) to f nd q j = G p j , (9) p j = G q j , (10) and G t = L t . (11) These are the new equations of motion. 2...
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- Fall '10