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MECHANICS AND CALCULS OF VARIATIONS The Poisson brackets (115) satisfies several identities (F, G) = - (G, F) , (4.116) (F1 + F2, G) =

MECHANICS AND CALCULS OF VARIATIONS

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The Poisson brackets (115) satisfies several identities (F, G) = - (G, F) , (4.116) (F1 + F2, G) = (F1, G) + (F2, G) , (4.117) (F1, (F2, F3) ) + (F2, (F3, F1)) + (F3, ( F1, F2) ) = 0, (4.118) which are fairly easy to prove. The last identity is known as Jacobi's identity.\f

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