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Unformatted text preview: at velocity ∞ to zero, because otherwise the number and fow velocity wouldn’t be Fnite. The third integral then is ±or each vector component I 3 j = Z d 3 v v j ~ F · ∂f ∂~v = 3 X i Z d 3 v v j F i ∂f ∂v i =3 X i Z d 3 v f ∂v j F i ∂v i Because ±or all ±undamental interactions ∂F i ∂v i = 0 , we have ∂ ∂v i ( v j F i ) = δ ij F j ⇒ I 3 j = Z d 3 v f F j = ~ F j Pulling all three integrals together we Fnd ±or each component ∂ ∂t ( ρ V j ) + 3 X i ∂ ∂x i ( π ij + V i V j ρ ) F i = 0 Using the continuity equation ∂ρ ∂t + ~ ∇ · ± ~ V , ρ ² = 0 this reduces to the desired ρ ∂V j ∂t + V i ∂V j ∂x i ! + ∂ ∂x i π ij F j = 0...
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This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.
 Fall '08
 RABE
 Physics, Work

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