+ ul cos a sine a +vl sin e 06 a cos0 a+wa (cosO u+sine v)=+=(sin 0 u+ coSe v)aa 06 +u ar r ae a sin 6 a cos e r06 u= coSu+sin bv a cos0 a sn6-+ l =-sin Ou+cos0 v ar r a0
( ) ( ) sin cos cos sin 1 cos sin sin cos r z u u v w x y z u v w r r r r z u v u v w r r z u u u r r z = + + = − + + + = + + − + + = + + = = − + = + 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
(V川]=cosb(Vsin(nV cosolu +u +sin|u ra0 cos 6-+sin e e-+sin e 06 6 +u. cos0-+sin 0 u,(cos u+sin v)+er a (cos0 u+sin 0 v)-(sin 8 u+cos 0 v)] +u-(cos0 u+sin 0 v) lo tu ar r- r a sin 6 a ar cos0 u=cosO u+sin 6 v ar sIn 8+ cose sin eu+cos0 v r
( ) cos ( ) sin( ) cos sin cos sin cos sin cos sin cos s r r z r z r z r u u u u u v u u u v v v u u u u u u r r z r r z u v u v u u r r r u v u z z u u r = + = + + + + + = + + + + + = + ( ) 2 in [ (cos sin ) ( sin cos )] (cos sin ) z r r r r z r r r r z u v u v u v r u u v z u u u u u u u r r z u u u u u u u r r z r + + − − + + + = + − + = + + − = = − + = + 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
球坐标与直角坐标 x=rsin 0 cos o y=rsin sin g 6= arc tg z=rose o=arc tg 2 u, = sin 0 cos u+sin sin v+ cos 0 w uo =cos 6 cos p u+ cos sin v+(sin 0)w u,=-sin o u+ cos ov a. cos 6 cosφa SIn sin b cos ax a8 rsin 0 ao a cos 0 sinφa.cosφo esinφ ar a0 rsn 0 ao =cos0-+ 06
= = = cos sin sin sin cos z r y r x r = + = = + + arc tg z arc tg 2 2 2 2 2 x y x y r x y z = − + = + + − = + + sin cos cos cos cos sin ( sin ) sin cos sin sin cos u u v u u v w ur u v w − + + = sin cos cos sin sin cos x r r r + + = sin cos sin cos sin sin y r r r + − = z r r sin cos 球坐标与直角坐标