弹性力学吴家龙课后答案.pdf

6. 2225 2225 225 1120 10Pa 222265 10Pa 1090 10Pa vxxlxymxzn vyxyyyzn vzzxzyzn vvxvyvz vxyzyzxzxy vvv f flm flm ffff lmnmnlnlm f 10. 222222 222 22222 , 1 3 1 3 2 9 vxxvyyvzz vvxvyvzxyz vxyzxyz vvvxyzxyxzyz flfmfn ffff lmn f 12. 0 0 yy xy qABq 0 ,0 0 ,0 vvx vvy f f v(lmn) cos(90)sin,cos(180)0 0 0 tan vxxxy vyxyy lmn flm flm y x , xyxy tan tan q ABC 2- 13 011 0 00 xx xyx gyBg A 0 0 vx vy f f vvvxyzxyxzyzvvvxyzxyxzyzvvvxyzxyxzyz 0 0 qABqqABqqABqqABqqABq 0 ,0 vyxyy flmflm vyxyyvyxyy vvvxyzxyxzyzvvvxyzxyxzyzvvvxyzxyxzyzvvvxyzxyxzyz (lm mn n) ) cos(90)sin,cos(180)0cos(90)sin,cos(180)0 0 0 vxxxyvxxxy cos(90)sin,cos(180)0cos(90)sin,cos(180)0 flmflm vxxxy flmflm cos(90)sin,cos(180)0cos(90)sin,cos(180)0cos(90)sin,cos(180)0 vxxxy cos(90)sin,cos(180)0cos(90)sin,cos(180)0cos(90)sin,cos(180)0cos(90)sin,cos(180)0 flmflmflm flmflmflmflmflm v( lmn ) cossin0tan vxxxy vyxyy x Imn y fIm flm 2 1 2 1 2CCtgggtg Dgctgg r( lmn ) 3- 5 2222 133 444 133 444 rxyyzyzxzxym xa bxyxy cxyxy IImnmnr Inr I 3 22 221 333 2 3 2212 3333 ax ybca xybc vabcabc Imlm 3- 9 (1) 123 v 222 123v lmn 222222 3311 () r lmnlmn 1 3 01, 01, v v mnl lmn (2) 123 z 33 xy 221221 ybca 333 ybcaybca vabcabcvabcabcvabcabc 22 xybc 22 22122212 2222222222 vabcabc 2222222222222222222222 vabcabcvabcabcvabcabc 222222 333333333333 vabcabcvabcabcvabcabcvabcabcvabcabc 333333333 vabcabcvabcabcvabcabcvabcabc 31v vz 3 vxy 1 123123 (3) 1231v 3- 10 112233 23321331 1221 3223 1331 2112 xyz yzxz xy x y z Uvw CCC xyz vwuw CCCC zyzx uv CC yx wv wCC yz uw wCC zy vu wCC zy 3- 11 22 2 222 22 2 22 22,0 yxy x yxy x AyAx xyx y xyx y 3- 12 1 2 2 3 12 11122212 ( , ) ( , ) ( , ) 2 0 ( ) , x y z xy ugz uvxfy z xE vgz vvyfx z yE wgz wfx y zE ffuv yxyx fc yg zfc xg zcc 21122112 wCCwCC 21122112 wCCwCCwCC xyx yxyx y 2 2 22 yxyxyyxyx 22,022,022,022,0 2222 22,022,022,022,0 2222 yxyx 22,022,022,022,022,0 2 2 yxyxyxyxyx 2222222222 22,022,022,022,022,022,022,022,022,022,022,022,0AyAxAyAx22,022,0 yxyxyx 22 yxyxyx 2222 xyx yxyx yxyx y 31 333 11131 32 2 333 22223 111 122 22 0 0 ( ) 2 0 2 22 xz yz wu xz fgv gx Ezx v gx fD xgy E gD ZEDD ggvwv gy zyEzy v gy gC yE E gD ZEDC gz uvxC yD ZE E gz vvyC yD ZE E gzv gxv gy w EE 2 123 2 D xD yE E - 13 22 2 22 yxy x xyx y 2222 111112 1112 121212233 42 xByAx Cy CC C CABC 4- 1 13 max 0 1 0 1 1(1) (12 ) (1) , 12 222(1) xy xyz xxxzx xyzzxy xyz xz q v vq Ev vv vq EEv v q v 4- 2 gzv gxv gygzv gxv gy2 2 123123 2 2 D D1 23 xD yExD yE 123123123 E xD yE 123 xyxy yx yyx y 123123 xD yE 123123 xD yE 123 22222222 111112111112 1112 111112111112 22222222 111112111112111112 CABCCABC 1112 42 1112 121212233121212233121212233121212233 222222222222 111112111112111112111112 42 1112 0 1 1 2 1 2 1 2 xxyyzzyzyzxzxzxyxy IIIIJJIIJJIJJ IJIJ mJJm m v vCCk vk v k 4- 3 0 xyyzzx (4- 12)0 xyyzzx 4- 4 1 1 () 2(1) p v E v E v E Ev 2 , 11 Ev vv 2 2 (1)(12 ) 2 2(1) zz zz zz z G Ev G vv G E GG v G G ()()()()()()() v 11 EvEv 2G G2G G 2G G 2 2 (1)(12 ) 2 2(1) rr z rr rrr G Ev G vv G E GG v G G 5- 3 2 0 xyxy qq 1 2 0() 0() xyxaxxa yybyxyb q q 2( )0 xy 12 12 1 21 21 2 12 12 21 1 ( ) 1 ( ) 0 ( )( ) xxy yyx xy xy qvquvu rv yxxEE qvq uxfy E qvqv v yEE qvq vyfx E uv yxG fyCyDfxCxE qvq uxcyD E qvq vycxE E 5- 4 z f z o0 xyxy 0()0() yxybyxyb 0()0()0() 1 1 ( ) 1 xxy yyxyyx yxxEEyxxEE xxyxxyxxy uxfyuxfy 1( ) yEEyEE yyxyyxyyx rvrv uxfy 0 zxzy 1 1 xxyzxyz v v Ev 2H =0 22 22 00 2 ( )0 xyz zxyxzyz f zz f zAzB , 0 z zz FAg 0zz qBq 2 2 2 1 00 () 00 2 1 1 1 2 1 1 2 zxy x y zzxy v gzqgzq v u u x v v y v w v vgzq zEE v g v WzqzC E h 2 2 2 22 0 2 1 1 2 2 1 1 () 2 Zh W v g v Chqh E v g v whzq hz E 5- 5 0 zxyxyxzyz F A 00 ()00 () 00 vgzqvgzq 00 ()00 ()00 () Wz 2 00 () 2 2 1 1 1 v zEEzEE vgzqvgzqvgzqvgzqvgzqvgzqvgzqvgzq zEEzEEzEE vgzqvgzq zEEzEE vgzqvgzqvgzqvgzqvgzqvgzq 2 g Wz g WzWz2Wz g Wz2WzWzWz g WzWz2Wz g Wz 2 2 2 2 WzWzWzWz 00 () 0 1 2 3 12 111212 1 1 1 1 ( , ) ( , ) ( ,) 0 ( ) xxyz yyxz zzxy xy xz uvF v xEEA vvF v yEEA wvF v zEEA vF uxf y z EA vF vyfx z EA F wzfx y EA ffuv yxyx fc yg zfC xgz guw zx 3 111313 31 222323 0 ( ) 0 yz f zx gD zEfD xgy ggwv yzzy gD zEgD ZE E1=E2=E3=0 D1=D2=C1=0 , vFvFF ux vywz EAEAEA 5- 6 , , , 220 220 0 x xxy yxz z xy zy yyz z zx xzy yz z AvxAvx AvyAvy 2 2 2 1 22224 1 x AvAAvAA v x 5- 7FOF y MFe H 222323222323222323 111313111313 3 ( ) 0 0 D zEfD xgyD zEfD xgy 111313111313111313( ) ( ) g g yzzyyzzy gD zEgD ZEgD zEgD ZE D zEfD xgyD zEfD xgy 111313111313111313 g3g yzzyyzzyyzzy gD zEgD ZEgD zEgD ZEgD zEgD ZE 222323222323222323222323 gD zEgD ZEgD zEgD ZE 222323222323222323 gD zEgD ZE 222323 =0=0 vFvFFvFvFF ux vywzux vywz, EAEAEAEAEAEA ux vywzux vywz,ux vywzux vywzux vywzux vywz 3 12 0 zy y xyxyxzyz FFehb xI AI 22 22 22 22 bh bhz bh bhz dxdyF xdxdyFe 22 22 3 22 22 0 2 02 322 bh bhz bh bhz y F dxdybhF A Febh xdxdyFe I 6- 3 32 2 33 22 0 0 yx x xyy UvUV Fx xyx yxx yx UvVV Fy xyxyxyyy 22 2 2 22 2222223 2 22222222 2222 2222 2222 222 2 22 2 21 1 yxy x xy v xyx y UUUUU VVvV xxyyxyxy UU vUVV xyxy v Uv v 3232 2 2 FxFx xyx yxx yxxyx yxx yx 3232 UvUVUvUV 3232 2 Fx 2 2 xyx yxx yxxyx yxx yxxyx yxx yx 22 yxyx 2 yxyxyx 32 3333 2222 UvUVUvUV xyx yxx yxxyx yxx yx xyxyxyyyxyxyxyyy 32 UvUVUvUVUvUV 32 xyx yxx yxxyx yxx yxxyx yxx yx 333333 UvVVUvVVUvVV 333333 222222222222 xyxyxyyyxyxyxyyyxyxyxyyy 2222222222 2 2 2222 2 2 yxyxyxyxyx 22 22 yxyx 2 x x yxyxyxyxyx xyx y 22 2 2 22 2222223 2 22222222 2222 222 2222 222 2 1 22 1 2 1 1 yxy x xy v xyx yv UUUvUU VVV xxyyxyvxy UUv VUV xyxyv Uvv 6- 4 (1) 2 32 34 ,1,0 2 12 yxy xxyy z MF Fy hIhh , 32 , 1238 0 2 0 x xxy y xy yy y FyFy hhh 2( )0 xy L vy 0 2 2 0 22 0 0 0 xx yh y h dyF hxyxxyh y 23 222 0 22 222 3434 1 223 hhh hhxyxh FyFy dydyyF hhhh (2) 2 2 2 332 , 2 , 2 634 2 1,0 2 12 0 34 10 2 xxyy x xxy y xy xy y q x y qqxy x y hhhh qy hh L L vyvy 0 0 dyFdyF xyxxyx 0 0 dyFdyF xyx dyFdyFdyF y g (y) 2 2 3 2 0( ) 342 ( ) 10 22 34 0 23 y g y qyg y hhy qy g yyC hh 23 22 333 6224 0 xy qx yqy qy hhh x f (y) 2 3 6 ( ) x q x yf y h 2( )0 xy 2 32 3 3 24 0 4 ( ) f qy hy q f yyDyE h 2 2 2 2 0 0 yh y yh y xyh y q q C 42 22 0 3 22 53 22 3 0 22 32 23 3322 000 2 43 00 535 6433434 ,1 5232 hh hxxh hh hxh x xyxy qD dyyyEyEhE h q yyq ydyDD hh qqqqyqxy x yyyy hhhhhhh 6- 5g ()0()0 xyxy ()0()0()0()0()0()0()0()0()0()0()0()0 0 0 yyDyEyyDyEyyDyEyyDyE 2 q q 3223 22 2 2 2 2 , , 6226 0, x y xy gNx y ABCD Uxxxyy UU U CxDy x U AxBy y U gxBxCygx x y 0 0 2 2 000 00 0 sincos 0 tan ()sincos0 2tan0 sincos0 cot2cot cot2cot yy xyy xxyvx xyyvy x yxy AxA BxgxBg flm lm flm y x CxDyCy CD Cyg CgDg gxgy gxcotgy 6- 60( , ) x U x y 2 2 0( )( ) x U Uf x yg x y U 44 22 44 ( )( ) 0 f xg x Uy xx 44 44 3232 23456 3232 23456 ( )( ) 00 ( ),( ) f xg x xx f xC xC xC x g xC xC x UC xC xC x yC xC x gxgycot2cot ()sincos0()sincos0 2tan0 sincos0sincos0 cot2cotcot2cot sincos0 CgDgCgDgcot2cotcot2cot ()sincos0 sincos0sincos0Cygsincos0sincos0sincos0sincos0 CgDgCgDgCgDgcot2cotcot2cotcot2cot ()sincos0()sincos0()sincos0()sincos0 sincos0sincos0sincos0sincos0sincos0sincos0 cot2cotcot2cotcot2cotcot2cotcot2cotcot2cot cot2cotcot2cotcot2cot 2 2356 2 2 2 3234 6262 2 y xyy U C xyC yC xC x U F xC C xC xCgx x y 056 04 2 234 322 23 0 23 2 2 2 2 000 00 32 1 00 2 1 , 2 62 0 32 yy xyx x h h xy xy xy CC C qC hC hCghq dxC hC hgh qq CCg hh qq xyygy hh qq xx hh 6- 7( ) x yf xU (xy) 2 22 2 222 2223 222 4442 3 4442 4442 4442 32 1234 1 11 ( )( )( )( )( )( ) 26 1 ( ) 6 1 20 6 0020 ( ) ( ) x UU yf xf x yg xUf x yg x yx yy fg Uyyf x y xxx fg yyy xxxx fgf xxxx f xC xC xC xC xD x3 2 2 5432 1212 3 ( ) 10662 D x CCEE g xxxxxE x 323543232 122 1234312 1 610662 CCEE UC xC xC xCyxxxxE x yD xD x U U ( (U U x x ( ( UU 4442 44424442 1 1 Uyyf x y 26yyyy y) 1111UU ( )( )( )( )( )( )( )( )( )( )( )( ) 1111 ( )( )( )( )( )( ) fgfg yf xf x yg xUf x yg x yxyf xf x yg xUf x yg x yx( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( ) UU ( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( ) yyyyyy ( )( )( )( )( )( )( )( )( )( )( )( ) 22232223 222222222 22232223 fg 222222 2223 Uyyf x yUyyf x y 222222222 222322232223222322232223 fg 222322232223 fg 2223 Uyyf x yUyyf x yUyyf x y 22232223 222222222 fg 2223222322232223 fg 222322232223 fg 2223 Uyyf x yUyyf x yUyyf x y 222222222 6 6 6 Uyyf x yUyyf x y 6 222222 xxxxxxxxx 222222 Uyyf x yUyyf x yUyyf x y 222222 44424442 fgfg 44424442 4442 fgfg 4442 xxxx 22 32 1234 2 332 12121212 22432 11 123223 () 1 (62)2262 6 12 (32) 2232 xyxyxy y xy UU C xC xC xCyF yF x xx y C xCyC xC xE xEyD xD CE C xC xCyxC xxE xEgx , xyxy 0 2 1 2 2 2 2 0 0 0 0 yy xh x xh x xyh x h hxyy dx gh , xyxy 111 123121 3 11 234 233 000 25 802 ggg CCCDDE hhh ghg EgEC 3 1 3 3 31 1 33 242 2 11111 33 231 22 243 5 333 41080 x y xy xx gy hh gxx xygygh hhh gxggxgxgh y hhhh 6- 8 335333 UAx yBxyCx yDxyExFxy 222333 6620666 36361200 350 UAxyAx yBxyCxyDxExX AxyAxyBxy AB 234234 802 234 EgECEgEC 234234234 123121123121123121123121123121123121 hhhhhh 123121123121 ghg EgECEgEC 1111 233233 111111 000000 111111111111111111 11 ghg 11 EgECEgEC 1111111111 000000 EgECEgECEgECEgEC gy 3 231231 3 231 3 gygy 231231231 gygygygy 2 33 2 2 3 2 2 22422 6126 666 9333 x y xy U Ax yAxyDxy y U AxyCxyEx x U Ax yAyCxDyF x y 0 0 22 2 00 22 0 22 2 20000 333 000 00 0 0 63 3 354310 12480 L xxxx L yhyh yy xyh y hh hhxyxxyx L dxy x q L q Lq L dydy qqqqh ABCDl h Lh Llhh l qq lq h EF lhl 6- 9U=Ay3+Bxy+Cxy3 22 0U 2 2 2 2 2 2 66 0 (3) x y xy U AyCxy y U x U BCy x y 22 00 22 2 2 0 22 0 0 hh hhxxxxx yh y h hxyhxyxy y dyFydyM dyF , xyxy 333333 000000 ABCDlABCDl 333333333333 354310354310 333333 qq lq hqq lq h 000000000 qqqqqqqq 000000000000 ABCDlABCDl 000000000000000000000000 lhllhl124801248012480 ABCDlABCDlABCDlABCDl 000000000000000000 BxyBxy+ + 333333 354310 ABCDlABCDl 333333 h Lh Llhh l 333333 354310354310 333333 0000 qqqq 0000 ABCDl 000000002 ABCDlABCDlABCDl2ABCDl2ABCDlABCDl 354310354310 Cxy3 2 0 0 yCxyyCxy66 U 66 3 2 3 3 33 44 23 2 y yy Mh ABh CBhCF h FF CB hh 3 2 y M F L 33 2 3 1218 0 99 4 xy xy myM xy hh L MM y hlh L (7) 222 22 xyxyyx UUU F xF y yxx y (6- 13) 222 22 xxyyxyyx UUU F xF y yxx y (6- 14) (6- 13)(6- 14) (6- 13)(6- 14)(6- 14) U* 2*2*2* 22 2*22*22 2 2222 222 *2* 22 22 22 xxyyxy xy xy UUU F XF y yxx y UFxUyx xyFy yyxx Fxyx UxyU Fy yx 2 *2 22 22 222 y x xy F Fyx UUxy UU yy (a) 2 22 2 22 y xy xyxy F UFx Uxyyx x y U F yF x x y (b) (a)(b)(6- 13) (6- 13)(6- 14) 22 22 FxFx xyyx - 3 2 1112 2 11 vAv uCp Evv yyxxyyxx xy yxx yyxx y UFxUyxUFxUyxUFxUyxUFxUyxUFxUyxUFxUyx xxyyxxxyyx 2222 F XF yF XF y 2*2* F XF yF XF y 2222 xxyyxxxyyx 2222 F XF yF XF y 22 xy UFxUyx xyFy UFxUyx 2*2* UUUUUUUUU 2*2*2* UUUUUUUUU F XF yF XF yF XF yF XF y xxyyxxxyyxxxyyx 222222 xxyyxxxyyx 222222 yxx yyxx yyxx y xxyyxxxyyxxxyyxxxyyx UFxUyxUFxUyxUFxUyx 2 UFxUyxUFxUyxUFxUyxUFxUyx 2 UFxUyxUFxUyx xyFyxyFy UFxUyxUFxUyxUFxUyxUFxUyxUFxUyxUFxUyxUFxUyxUFxUyx 2 UFxUyxUFxUyx 2 yyxxyyxx2222 xyxy 2222 xyxy 2222 xyxy 2222 xyxy 2222 xyxy xyFyxyFy xyxy 2222 yxyx UxyU Fy 222222 UxyU Fy FxyxFxyx 2*222*22 2222 222222 yxx yyxx y UFxUyx xyFyxyFy 2222 2222 xy 22 UFxUyxUFxUyx yyxxyyxx222222 y (6- 14) 2* xxyyxy yxxyyx UUU 2* xxyyx xyFy xy UxyU FyUxyU FyUxyU Fy 22222222 UxyU FyUxyU Fy FxyxFxyx UUUUUUUUU xxyyxxxyyxy yxxyyx yxx yyxx y xxyyxxxyyxyxxyyx 2*222*22 UFxUyxUFxUyxUFxUyx 2*222*222*22 UFxUyxUFxUyxUFxUyx xyFyxyFyxyFyxyFy 222222 22 xyFyxyFyxyFy 2222 222222 2222 yyxx22222222 2222 FxyxFxyx 2222 FxyxFxyxFxyx UxyU FyUxyU FyUxyU FyUxyU FyUxyU FyUxyU FyUxyU Fy 222222 FxyxFxyx *2 UxyU FyUxyU Fy FxyxFxyxFxyxFxyxFxyx UxyU FyUxyU FyUxyU Fy 222222222222 yxyx22222222yxyxyx 222222222222222222222222222222 yxyx222222222222 222222222222 22222222 2 *2*2 2222 222222 y y F yx UUxyUUxy 222222 UUxy *2 UUxyUUxy 2222 UUUU 2222 22 2222 2112 2222 2222 12 2222 2222 12 2222 () 2() (1)2 1 (1)2 1 a b ba a bqqq aq b AC baba avbavb uqq Ebavba bvabav uqq Ebabav uuu - 4 22 220 AA CC 1a q 2 2 1112 20 11 A Cq a vAv uCpu Evv (1) 0 b u 2 1112 20 11 vAv Cb Evv (2) (1)(2) 4 2 1 1 22 (12 ) q a Aq a av b 2 1 22 2222 11 2222 2 1 22 1 2(12 ) 121121 121121 1212 1 121 q a C av b vv bb qq vv bb vv vb uq v E b 7- 5 22 220 1 (1)2(1) AA CC A uvv Cp E 2020 vAvvAv11121112 202020 11121112 Cb20 111211121112 2020202020202020202020202020 EvvEvv111111EvvEvvEvv1111111111EvvEvv1111111111Evv111111111111 4 (1) 2020 (2) (2) 2222 (12 )(12 )av bav b 222222 (12 )(12 )(12 ) 222222 (12 ) 2 2 1 1 2222 2(12 )2(12 ) 121121121121 q aq a 1 1 2(12 )2(12 ) 222222 121121 2(12 )2(12 )2(12 ) 222222 121121121121121121121121 2 2 a A qCq 2 2 2 1112 2 11 b b A C b vAv ucb Ev bv 2 2 (1)2(1)/ A C A uvv CE 2 222 00 22 b C q AAA CAC bb 2 2 2 11 (1)2 1112 2 11 bb A uvC bu Ebb vAv cb Ev bv 1 1 v E k v E 2 2 22 2 22 2 2 2 2 2 2 2 2 (1) 1 (1)( (12 )1) 1(1) 2 (1)( (12 )1) 1(12 )1 1(12 )1 1(12 )1 1(12 )1 k a Aaq k akvb k qa C k akvb b v kk q b v kk a b v kk q b v kk a 7- 6b CACCAC2222CACCAC2222CACCAC22222222222222 bb2 2 CACCAC 2 2222 bb CACCAC2222 1111 uvC buuvC bu 1111 (1)2(1)2 1111A A (1)2(1)2 A A (1)2(1)2 11 (1)2 11 (1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2(1)2 2 (1)2(1)2(1)2(1)2 2 (1)2(1)2 2 (1)2(1)2 2 2 EbbEbbEbbEbb bbbbbb (1)2(1)2 bbbb (1)2(1)2 bbbbbbbbbb EbbEbb bb EbbEbb bbbbbbbbbbbbbbbbbbbb (1)2(1)2(1)2(1)2(1)2 2 bb 2 (1)2 2 (1)2(1)2(1)2(1)2(1)2(1)2 bbbbbbbbbbbb (1)2(1)2(1)2(1)2(1)2(1)2 bb 2 bbbbbbbbbbbb 111211121112111211121112 uvC buuvC bu bbbb uvC buuvC bu bbbbbbbb 2 uvC bu 2 uvC buuvC buuvC buuvC buuvC buuvC buuvC buuvC buuvC bu 2 uvC bu 2 uvC buuvC buuvC buuvC buuvC bu 2 uvC buuvC buuvC buuvC buuvC buuvC buuvC buuvC buuvC bu bbbbbbbbbbbbbbbbbbbbbbbbbb 2 vAvvAv11121112 2 1112 cbcb 111211121112 2 2cb2cb Ev bvEv bv1111 2 2cb Ev bvEv bv1111Ev bvEv bvEv bv1111 sinsincos2 ( )sin2Uf 22 2222 24 2 2 242 2 2 24 2 42 1414 0 ( ) 1164 2sin2 6 212sin2 162 26sin2 ddd fdff dddd C fABD uUCD A UC AB uCD AB 2 4242 2 4242 00 sin2cos2 6462 20260 6462 2260 a bb CDCD AABa aaaa CDCD AABa aaaa 24224 22 2222 2244224422 223223 4 2 42 42 442 442 4 2()()2 2()() 0,0, 22 34 1sin2 332 1sin22 4 bba ba a b AB baba aba ba bbaa b CD baba aa ABCDa b aa aaa a max max ,4 4 7- 7q,qN( , , ) NL0 UL2 2 ( )Uf 4242424242424242 42424242 sin2cos2sin2cos2 64626462 20260 6462 64626462 bbbb 202602026020260 424242424242 6462646264626462 22602260 64626462 sin2cos2sin2cos2sin2cos2 bbbb sin2cos2sin2cos2 bb sin2cos2sin2cos2sin2cos2 20260202602026020260 424242424242 20260 4242424242424242 646264626462646264626462646264626462646264626462646264626462 226022602260 42424242 22602260226022602260 64626462646264626462 22602260 646264626462 226022602260 42424242 22602260 aa 424242424242424242424242424242424242 2()()2()() 4242424242424242 42424242 64626462 2 2026020260 2 42424242 64626462 2 64626462 22602260 646264626462 CDCD646264626462 2026020260 646264626462 20260 4242 6462 42424242 aaaa 2260 6462 22602260 64626462 20260202602026020260 2 42424242 20260 4242 20260 4242 226022602260 42424242 226022602260 4242424242424242 2260 4242 2422424224 22222222 22442244222244224422 223223223223 2()()22()()2 2()() 223223 bba ba 24224 4 24224 ABAB 22222222 2()()22()()22()()2 22222222 aba b 224422442222442244222244224422 CDCD 223223223223 2()() 223223223223 2222 AB 2222 AB bba ba 24224 ABABABAB 2()()22()()22()()2 2244224422 aba baba b 22442244222244224422 CDCDCD 2()() 222 2222222 24 224 1111 0 1 40 UUU d fd f dd 1234 ( )cos2sin2fCCCC 2 1234 2 1234 22 2 1234 2 234 cos2sin2 11 222cos22sin2 222cos22sin2 1 2sin22cos2 UCCCC UU CCCC U CCCC U CCC 2 22 0 qq 1324 cot0 22sin qq CCCC cotcos2 sin cotcos2 sin sin2 sin q q q q q 7- 9b 22 202 AA CC 0 a b q 222 2222 2() a bqa AqC baba 2 22 22 0,0 a Aa qC b aa qq 7- 10 222222 qqqqqqqqqq 22222222 qqqqqq 132132 2222 132132 s 132 qqqq CCCCCCCCC 132132132 qqqqqq CCCCCCCCC sinsin sinsin sin2sin2 132132 CCCCCC 132132132 C C C C cotcos2cotcos2 sinsin cotcos2 q cotcos2 q q cotcos2cotcos2 cotcos2cotcos2 sin cotcos2 sin2sin2 sinsin q q cotcos2cotcos2cotcos2 0 2 12 2 2 1122 22 12 2222 222222 1 1 3 1 0 11 00 1111 0 00 UU Uff UUU fCfC UCC UU C C 2 2 C 2 2b qCb q 2 2 2 2 0 1 0( ) b q U U vuf E 0 ( )00 11 0 ( ) a b uq u fu uu v E ug vuf0( )0( )vufvuf0( )0( )vuf0( )0( )0( )vuf0( )0( ) 0 0 uq ( )00 2 2 2 3 2 2 2 2 2 12(1)2(1) 2(1) 1 1 0 11 a uuu vv b q EE u b qv E v ub qC E v uCb q Ea v ub q Ea 9- 3()0 33 xx yyxa ( , )() 33 xx x yB yyxa 2 2 22222 3 Bxaax 2 2 4 4 5 22 5 22222 5 33 ( , ) 223 15 3 2 15 3 45 3 () 45 32 23 0 45 32 4()() 23 ,0, R xz yz xyzxy vxzyz x Bx yyxa aa aMM Ddxdy GDGa GMy xa ya GMxaxy ya Myxaxaxy a xay 3 max 15 3/(2)Ma 10- 1 zG w z u ZGZG u zp 2 2 2 1 , 11 , 1 ZGzZGzZGz w zz 111 , 1 2 2 2 2 2 2 )21)(/(, 1 , 2 2 vHvEvkkk 2 2222222222 2 2222222222 2 222222222222222222222222222222222222222222222 3 3 3 BxaaxBxaax2222222222 4 4 333333 223223 Bx yyxaBx yyxa 3333 ( , )( , )( , ) 33 223223 ( , )( , )( , ) 223223223 aMMaMM 4 4 aMMaMM 2 2 Bx yyxaBx yyxaBx yyxa( , )( , )( , )Bx yyxaBx yyxaBx yyxaBx yyxaBx yyxa 2 2 2 Bx yyxaBx yyxaBx yyxaBx yyxaBx yyxa 2 Bx yyxaBx yyxaBx yyxa 2 223223 Bx yyxaBx yyxa 223223223 5 45 3 ()() 45 3245 32 GMy xaGMy xa 5 45 3 ()()() yaya GMxaGMxa 45 32 GMxaGMxa yaya GMxaGMxaGMxa GMy xaGMy xa()()() GMxaGMxaGMxaGMxaGMxaGMxaGMxaGMxa 222222222222222222222222222222222222222222222Bxaax2222222222 Bx yyxa aMMaMM Bx yyxaBx yyxaBx yyxaBx yyxaBx yyxaBx yyxaBx yyxaBx yyxaBx yyxaBx yyxa 223223223 Bx yyxaBx yyxa 223 yayaya aMMaMMaMMaMMaMMaMM zz k z 2 2 2 , zz k z z 2 2 2 1 11 2 2 kk 0 1 21 1 2 2 2 2 zv v 0 1 1 1 2 2 2 2 2 322 zzZG k zzz k zz z z z 10- 4 10- 2 10- 130 22 22 2 r u r u rr u rrr 0 21 22122 2 2 2 2 3 3 22 2 dr d rdr d dr d ZG dr d rdr d rdr d ZGr u r u rr u rrr 10- 13 10- 3 0 22 2 2 r u r u rr u rrr C r u r u r u rr u rrrr 2 02 2 2 2 3r D r C ur 33 3 , 2 3r DC r DC tr C r 2 3 2 31)21)(1 ( DC v E C vv Ev 10- 410- 4 2 2 2 r r u ur 1 1 0 0 2 2u u r r u r rr r 2 2u u 1 1 2 3 3 dr d d ZGZG d d rdrdr d ZG 2 2 2 d d 2 2 1 q q b a 33 12 33 3 1 3 2 4 , 3 2baG qq D baGk aqbq C )1 (2 , )21 (1v E G vv Ev k 233 33 12 33 3 12 )(4 3 2 3 baG baqq baGk aqbq ur 333 33 12 33 3 1 3 2 )(2ba baqq ba aqbq 10- 5 =B A 2 B A ZG u2 1 2 B v vA B v vA t 21 1 2, 21 1 2 2 33 0)( ,)( ba uq v v a b q B v v a b zqb A 21 1 1 2 4 , 21 1 2 4 3 3 3 3 3 a uu v v a b q v v a b qb ZG u max 3 32 3 3 3 , 2