2008级(�)第22次课

2008级(�)第22次课 - P + l/ s ------...

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Unformatted text preview: P + l/ s ------ (stokes) s * t s * t --- s t * * + l s / P + l s / P * R( x , y , z ) * (stokes) , , , P ( x , y , z ), Q( x , y , z ), , R Q P R Q P ( - )dydz + - )dzdx + - )dxdy ( ( y z z x x y = Pdx + + Qdy Rdz * n h 6 v * s z n z= : 4 ~h* , h ~4 yh .~ 4 zy , C f ( x, y) o xoy y D xy . x y Dxy C 1 2 y P P P P z dzdx - y dxdy = ( z cos - y cos )ds cos = - f y cos , P P P P z dzdx - y dxdy = - ( y + z f y ) cos ds P P P P z dzdx - y dxdy = - ( y + z f y )dxdy P P P[ x , y , f ( x , y )] = + fy y y z P P z dzdx - y dxdy 1 = - P[ x , y , f ( x , y )]dxdy , D xy y ^* - P[ x , y , f ( x , y )]dxdy = P[ x , y , f ( x , y )]dx c y D xy , P P z dzdx - y dxdy = c P[ x , y, f ( x , y )]dx ^* 2 P P z dzdx - y dxdy = P ( x , y , z )dx , * Q Q x dxdy - z dydz = Q( x , y, z )dy , R R y dydz - x dzdx = R( x , y , z )dz , R Q P R Q P ( ( (y - z )dydz + - x )dzdx + - y )dxdy z x = Pdx + + Qdy Rdz .. * . s v* s v dydz dzdx dxdy x y z = Pdx + Qdy + Rdz P Q R cos cos cos x y z ds = Pdx + Qdy + Rdz P Q R n = {cos , cos , cos } Stokes~ + l ] x * Ȫ ~ * s : . ) (~ xoy 8* * ~ s v* 1 v * s sn * v @D x + y + z = 1A , @D zdx + xdy + ydz , . z 1 n , s o v* , zdx + xdy + ydz x 1 0 = dydz + dzdx + dxdy D xy 1 y H s y = 3 d D xy s y* dydz + dzdx + dxdy Dxy y 1 3 zdx + xdy + ydz = 2 D xy o 1 x 2 * ( 2 顿* ( 3y x+ y+ z= 2 0 y 1, 0 z 1(* ,( 顿* . ( y - z )dx + ( z - x )dy + ( x - y )dz 2 2 2 2 2 : 0 x 1, , z ox n 3 ( ( ( ( x+ += y z 2 y 顿* 8 . 1 n= {1,1,1} 3 o y x 1 cos = cos = cos = , 3 1 1 1 3 3 3 ds x y z 2 2 2 2 2 2 y -z z -x x - y Dxy x+ y= 1 2 x+ y= 3 2 I = 4 =- ( x + y + z )ds 3 3 (y y y x + y + z = ) 2 4 3 9 =- ds = -2 3 3dxdy = - . 3 2 2 D xy --- ^s * x 1. x * ^ s , : A( x , y , z ) = P ( x , y , z )i + Q ( x , y , z ) j + R( x , y , z )k , Ap C^x * s = A ds = Pdx + Qdy + Rdz C C s ^x A, Cp . stokes , = A ds = C i j k x y z ds P Q R 2. | s : i j x y P Q k s* | z R ( rotA) . i j k rotA = x y z P Q R R Q P R Q P =( - )i + ( - ) j + ( - )k . y z z x x y R Q P R Q P [( y - z ) cos + ( z - x ) cos + ( x - y ) cos ]dS = ( P cos + Q cos + R cos )ds 翪* 翪* n = cos i + cos t = cos i + cos j + cos k , j + cos k rot A ndS = A t ds (rotA)n dS = At ds ( rotA)n = rotA n R Q P R Q P =( - ) cos + ( - ) cos + ( - ) cos y z z x x y At = A n = P cos + Q cos + R cos Stokes ~ * * * = rot A ds = At ds : , A ~ * A ~ H ) . ( y 3 ^ * , + l s / P , P/sl+ =(, , ) , 1 2 3 r =OM M ^ M i j o O L ={x , y , z} M v k x꿪* v = r = 1 2 3 x꿪* . x y z { rot v = 2 1 , 2 2 , 2 3 } = 2 . dydz dzdx dxdy x y z = Pdx + Qdy + Rdz P Q R cos cos cos x y z ds = P Q R = rotA ndS = A t ds P210 , 9-6 7 , 8. P219 , 9-7 3 , 4 , 5. , 18 , 19 [end] ...
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This note was uploaded on 03/01/2010 for the course ENGINEER 261 taught by Professor Liu during the Spring '10 term at South University Online.

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