2.教科书(1.6) 在下边习题求解中会用到以下公式,请参阅有关资料。 柱坐标与直角坐标 =rose y=rsin 6 6= arc tg COS u= cos ou+sin e y ar r ae a cos0 a ue =-sin e u+ cos81 =sin e-+ r a0 ⅩA(r,O,z) u =w p=p(r,O,=)=p(x,y,=) r=r(x,y),b=0(x,y),z= ui +v+wk=u, e, +upeo+ue ao ao ar a0 00 cos e ao sin 0 ag ly=ui·n+y·en+wk:e,= cos0 u+ sino v ax ar ax a0 ax A ao ao ar a0 a0 ao cose ag ue=ui.ea+vj.eg+wk.ee=-sin 0 u+cos 0 v =sin0-+ ay a o0 ay ar r a0 u=ui.e+ve+wk.e=w     = = = sin cos z z y r x r          = = = + arc tg 2 2 z z x y r x y       = = − + = + sin cos cos sin u w u u v u u v z r                 =     +   =     −   =   cos sin sin cos z z y r r x r r       2. 教科书(1.6) 在下边习题求解中会用到以下公式，请参阅有关资料。 柱坐标与直角坐标 X A(r, , z) Z r  Y ( , , ) ( , , ) ( , ), ( , ), sin cos cos sin r z x y z r r x y x y z z r x r x x r r r y r y y r r z z                             = = = = =        = + = −               = + = +          =   cos sin sin cos r r z z r r r r z z z z ui vj wk u e u e u e u ui e vj e wk e u v u ui e vj e wk e u v u ui e vj e wk e w           + + = + + =  +  +  = + =  +  +  = − + =  +  +  =