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3、1 50 50112 l f 1- 710 4 cos 4 ) 4 sin ( 00 111 1 z y efy y efx z f z y f y x f xf xx p(xyz) = p(220) 2 01 ef x f 2 5050 5 5 6 6 yxzy 2 z z 0 50 545 2 2 545 54 4545 sin cos0sin cos sin 1 1 000 222 2 rfff r f r f rr f rf p(xyz) = p(220) 22)( 2 1 222 zyxr 242 2 arctan p(r) = p(22 24 ) 02 f f zrcoszfrff
4、 002 cos 0 222 2 f z z f z y f y x f xf 2 fp 0 f z 2 f f2 1.2sin cosrz 1- 8r = 1r = 2S1S2VVS S= S1+ S2 V21r020ddrdrdVsin 2 S1r = 1020VS S1ddr rSdsin 2 S1r = 2020S2ddr rSdsin 2 1 21 SSS S SdDSdDSdDI 2 00 2 2 2 00 1 2 sinsin rr dr rDddr rDd 0 2 0 2 0 2 0 2 sin)cos 2 1 (sin)cos(dddd r = 2r = 2 0 cos co
5、srzrz 0 0 0 2 2 1 2 2sinsin sin 1 2 2 rDDrDr rr D r 4 22 2 2 2 cos ) cos ( 1 )( 1 rrrr Dr rr r 1 2 1 2sincos 0 2 1 2 2 0 2 r dr dddVDI V V SV IIVS 1- 10Sl 321 llll 1 l3x = 0z = 0dyy l d ; 2 l3y = 0z = 0dxx l d 3 l:9 22 yx0x0y0zdyydxx l d S9 22 yx0x0y0zdxdyzSd )2 ( xzA ) 2 1 (9)9( 3 2 2 1 4 18)9(9 2
6、1 cos332 992)2( 2 3 3 0 22 2 0 2 3 0 2 9 0 3 0 2 3 0 2 xdxudu dxxxdxxdyxdxSdAI x S S 3333312 2)2( llllllll l xdyxydxxdyxydx l d A l d A l d AI 2 9yx 3 0 2 3 0 2 1 ) 2 1 (9 4 18992)(dyydyyI lS II S30 2 00zddzSd S y y ) dxx l d dx dxxdxxdxxdx 0 0zSd d 9 93 0 0 9 9 0 0 0 3 dxdx 321 llll 3 l3 2 00zd l d
7、 )cos2 ( )2 ( zxzA ) 2 1 (9)cos1 (9)cos2( 2 0 3 0 2 0 dddSdAI S S l d A l d AI llll l 312 1 l 2 l0 l d A 3 l cos2sincos2 2 yxxyxyxA cos2)cossin(sincos)sincos( 2 ) 2 1 (9 4 189)cos18cossin27( 3 2 0 22 d l d A l d AI ll l lS II 1- 121 32 1 zyA )23 ( )23 ( )2 ( 3222232 1 xyzzxzxyzxyyxyxxA 2cos3 2 A sin
8、sin2cos 2 zA 3 2 3 cos2 sin3 r A cos cos sin 2cos 33 3 rr r A 1- 221, , rabc A 2 cossinsincossinzyxr 2 1 222 2 1 222 2 1 222 zyx z z zyx y y zyx x x 2 2 i in in n 1891818 8 3(3 ( ) 2 zy3(3 ( )z 3(3) sin n 2 2 cos2 os r r cos sinsincoscoscos zyx 2 1 222 2 1 22 2 1 22 2 1 222 2 1 22 2 1 222 zyx yx z y
9、x y zyx z y yx x zyx z x 2 1 22 2 1 22 cossin yx x y yx y xyx 2 1 22 2 1 22 2 1 222 2 1 222 yx cy yxzyx bzx zyx ax xcbarA 2 1 22 2 1 22 2 1 222 2 1 222 yx cx yxzyx bzy zyx ay y 2 1 222 2 1 22 2 1 222 zyx yxb zyx az z 2 1 222 2 1 22 2 1 22 2 1 222 2 1 222 2 1 22 2 1 22 2 1 222 2 1 222 2 1 22 zyx yxba
10、z z yxzyx zyxcxbzyyxay y yxzyx zyxcybzxyxax x 3 2 1 22 2 1 22 cossin z z z z zr 2 1 22 2 1 22 sincos z z z z z 2 1 22 2 1 22 2 1 22 2 1 22 2 1 22 2 1 22 z baz zc z bza z b z az zc z bz z a cbarA 2 2 cos ayay y y 4 A r A r Ar rr A r sin 1 sin sin 11 2 2 cot 2 sin 1 sin sin 11 2 2 r b r ac r b r ar rr 5 r b r c r c r a rb rr rc r a r b c r r a rb rr rc r a r b c r r A rA rr rA r A r A A r r A rr cot sin sin sin sin sin sin sin sin sin sin sin sin
