张量的概念

《张量的概念》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

Ḅᭆ§1.1IὅᙠḄ⚪!"ὅ#ᨵḄ%&'()*+,⚪-
./0Ḅ▊23ὅ+,4Ḅᭆᨵ,/0Ḅᳮ6஺ᨵ89:;
,<=*᝞%<ஹ@A<BCᙠD.Eὃᙶ᪗IJᨵ8,ᑖ8,ᑖḄLᔠNOP,<஺Qᙶ᪗Rᓄᣚ.ᑖᢥ
OḄRᣚVᑣRᣚ஺ᙠ%JXᨵ
.YZᩖḄ஺*᝞\%ᱥ^ᑁ…aḄb%c᝱ᨵ9,b%ᑖ᝞efgᙶ᪗⊤iᵨk▣mnᑡᑣᨵo(5bb9,ᑖḄLᔠNOP
aḄb%c᝱pqb%஺Qᙶ᪗Rᣚ.b%Ḅᑖᢥ
OḄRᣚVᑣRᣚs᝞
aḄb%c᝱ᐹᨵub%vwḄឋypqbR஺z{2Ḅ%<ஹ@A<ஹb%ஹbRBḄឋy|}ᓄᥗᡠ⊤iḄḄᱥᳮឋy|ᐸᦪ{Ḅᐳឋ|}Ḅᭆ஺ᡠ
,ᱥᳮᡈᵫᙠDEὃᙶ᪗IJ
OᦪḄᑖḄLᔠᡠNOQᙶ᪗Rᣚ
.ᑖᢥ
OḄRᣚVᑣRᣚ஺ᨵḄ“▤”u“᪀”ᵫᡠ⍳ḄḄRᣚVᑣᩭᑖ஺<
▤b%ஹbR▤Xᨵ8▤ஹ▤.......B▤஺e<ᭆḄ஺ᐵ¡Ḅ¢£Ḅ6᪆O¥¦ᙠ§1.8J§¨஺ᵫḄᱯឋe
ª«¬¡ᱯOᙶ᪗IḄ⊤ᱥᳮO®Ḅ¯n஺°ᵨ±V⊤iḄ¯ᙠD
ᙶ᪗IJᡂ³ᑣᙠ´µRᣚḄᐸᙶ᪗IJ¶ᡂ³ᓽ¯ᐹᨵRឋ஺3ᱯ¸〉ᔠ¡⊤ᱥᳮO®ºqᱥᳮO®»¼qP½2ᡠ°ᵨḄᙶ᪗I¾ᐵ஺º¿ᑖ᪆q¼ÀPÁ¯Ḅᨵ%Ãᐹ஺¿᜜±VÅÆ
ªÇÈÉÊḄᦪË஺,ÌÍÎÏᱯ=Voigt✌ᐜḄᵨᩭ⊤iᨔ^Ḅb%=%Cc᝱Óᑖ᪆»Ôឋ%ᐵIḄ£ᑗ஺ᑖ᪆ᙠ%⚞×JᨵØḄbᵨ%Ã-ὅḄÙ⌕ᦪÃᐹ஺§1.2ÛÜ»ÝuÞOᙠᑖ᪆JØßᵨᢣ᪗஺,RḄLᔠx,,x,...,x„⊤iq2

1x,i=1,2,3,...,n஺,RḄLᔠy',y\y'...,y"⊤iqy,j=l,2,3,...,n஺ïðᢣy',yெ..,y"n,ò³RóRyḄ1ᑮnõö஺ᑏᙠøÛùúgḄᢣ᪗*᝞x,JḄipqú᪗஺ᑏᙠøÛù{gḄᢣ᪗*᝞ûJḄjpq{᪗஺ᙠeüḄ§¨J¦ýþ3ᵨ{᪗ᡈú᪗Ḅÿ
Ḅ஺ᵨ᪗᪗Ḅᡈ◀ᱯḄ1ᑮnḄᡠᨵ᦮ᦪᐸ&n'(ᢣ᪗Ḅ+஺,-.ᵨ/ᐵ1+Ḅ23ᩭ⊤6789:789Ḅ;Ḅ<=ᡠᨵᢣ᪗iஹjஹkஹ1ஹmஹ…Ḅ+
1ஹ2ஹ3Fᡠᨵᢣ᪗aஹ0ஹIஹ3…Ḅ+
1ஹ2஺J᝞ᙶ᪗ᢣ᪗i=1,2,3Ḅ6789Ḅᙶ᪗ᙶ᪗X”
a=1,2Ḅ:789Ḅᙶ᪗஺(R<᪗STᦪUV᝞(x)⊤ZXḄ:[\஺ஹ]ᙠ⚗&ᢣ᪗ᙠ᪗᪗&`abcᑣ⊤Z⌕fghᢣ᪗iᔊᐸ+1,2,3,...,nl஺g
m3'(lm3஺J᝞6789Ḅn☢\p(a,z'+a,z2+a,z}=p(1.2-1)w&a,,p
xᦪ஺g\pyᑏᡂ£a,z'=p(1.2-2)i=l}ᵨlm3ᑣgh\pyᑏᡂ᝞~wa.z'=p(1.2-3)iᔊᢣ᪗+lḄ`aᢣ᪗'(ᢣ᪗ᡈ᪗஺ᵫ1ᢣ᪗
⊤Zlᵨhᢣ᪗
᪵Ḅ஺J᝞a/yᑏᡂa/஺f1ᢣ᪗(lᢣ᪗)lḄᢣ᪗'ᵫᢣ᪗஺(Rᙠ⚗&hᢣ᪗Ḅᵨ[஺J᝞ᑏᡂa,x'a,x'}ᑏᡂ01=%*஺6ஹᑁ(Kronecker)¥¦3=ᑁ¥¦3=Ḅ3

2kJj=k(1.2-4)1-(0"k᪵3==3=1(1.2-5)5;=8=3=3=0ᑁᑏᡂ3ᡈ90!☢#$%&ᑁḄ(ᵨ஺$᝞,-./ᙶ᪗234ᑖ67dz',dz\dz'Ḅ=ᐗ?@ḄAB7ds2=(dz')2+(dz2)2+(dz')2(1.2-6)(ᵨᑁ4FGᑏᡂds?=3,jdz'dz'(1.2-7)(JKL4FG3ᨵNOPQ4RSTUᔊᢣ᪗iḄZ4[RSTUᔊᢣ᪗jḄZ஺ᑁᨵR\&]Ḅឋ_4᝞"A4==3a஺dx1cஹeᣚeᣚe,"9gh7’1Jj*T1,2,3ḄᏔe123,231,312)e,=e1,k=--1JᡭFT1,2,3Ḅ᜻e213,132,321)(1.2-8)jk0Jij,kḄḄpLNSᢣi,j,kḄ\᣸ᑡᑖstuvw᣸ஹ⌮vw᣸ᑡQyvw᣸ᑡ஺eᣚz7{᜻(Ricci)4~TRSᢣ᪗4ᵨᩭ▤ᑡG஺a%a=aaaaa+aaa+aaa-aaa-aaa-aaaaaa⊤ᑡG3ḄU⚗4|a|⊤ᑡG4ᑣFᑡGᑏᡂa=|a|=eMaa(1.2-9a)FG3ᔜ⚗Ḅ!᪗Reᣚ4$᝞eᣚ7,JᑡGḄ

3ᑡ¨©ᣚ«ᑡwᦋ¥¦1-a,®¯ᣚ[°ᦋ[¥¦,±ᑮ+a஺g²ឋ´y⊤Zᡂ᝞Ḅ~w=ae,=ea'a*a'(1.2-9b)ImnrMImn'/·(1.2-9a)S(1.2-9)w¸ᔠᑣla'.Ie.=eaFaa'(1.2-9c)jIImnrstIninஹ'ᳮy½ᑮ=e"'a=a=a=(1.2-9d)Àஹᑁ¥¦S¯ᣚ¥¦ḄᐵTᑁ¥¦S¯ᣚ¥¦Á9Âᙠ3ḄᐵT஺ÃÄ᝞:9h;3F(ᓫÇÈ▣ḄᐗËÌÍḄ«ᑡw11஺]ᵨÎÏiḄ~w⊤Z☢Ḅ«ᑡwᑣÐ可8rmA"8s83-mn可88ltmnw&]r,s,t=l,m,n=l,2,3,A=1஺ᵫ1gÔ᣸ᑡ&ḄÖ¯ᣚᦋ«ᑡwḄ¥¦ᡠ«ᑡwA(5—r8nrA-8se-crstn材5'n×Ø/«ᑡw½en,e,=8,'5sS'-5F55'+8r8F8'-S'S'S=+5r8'5F(1.2-10)lainImmInmn1mnmImnImInw&Ḅ᪗h᪗ÜᑭᵨᐵTw5"=3=,ywÞb☢ḄᐵTw'(e-3e”'e=3'33'—3à'z)+&(x&&-5s5')z+5'(5'5'-5'5')zrmnr'mnnmnrmmrm'nrrn(1.2-11)=8S5'-8S5'innnmeMe=35'_8s8'=25'x(1.2-12)zrsnnnsn

4=25==6(1.2-13)ᑭᵨgÔ¸åy·«ᑡwḄ×Øæw(1.2-9b)ᓄᡂèhéᨵᵨḄ~w஺e"””U(1.2-9b)wê½ae,e""n=6a=aFa'a'ee'™(1.2-14)linnImnrstஹ/íஹlm3yîïᑮðᑖæwòf(x',x'…,X")(nhôõ;x',x2,...,x"ḄöᦪᑣÌḄðᑖyᑏᡂdf=^-dx'(1.2-15)ᙠøðᖪÎ■&iûü(
᪗஺ᦋ§1.3ýþᙶ᪗ò/&=1,2,3)
ÿ2)Ḅᙶ᪗஺ᦪ=xlz',z2,z')(k=l,2,3)(1.3-1)ᙠRᨵ!"Ḅ⌮ᦪzk=zk(x',x2,x5)(k=l,2,3)(1.3-2)ᑣ&pᨵ()ᙶ᪗᱄"+ᩭ-./01ᐵ34ᑏ6(1.3-2)7஺/ᓫ:ஹ<=.ᨵ<=Ḅ"▤?@ᦪ஺ABCD(jacobi)Kᑡ7j=MᙠRᑁOPQ0,ᓽaz1o1az1ax'K26z2dz2j=H0(ᙠR)(1.3-3)3x,ax1-2Sx'3*ax'G-ax'ᑣ(1.3-2)7ᨵX"Ḅ⌮ᦪ(1.3-1)7஺YZQx'(z[z2,z')=\ᦪ]x2(z]z2,z?=\ᦪ]x.(z',z'z')=\ᦪ._`7(1.3-1)ᑖbc6(☢,efghQP&஺j(☢klᙶ᪗(☢஺mnoᙶ᪗(☢Ḅh)pq"ᙶ

5᪗()஺rsP&ᨵ3ᩩOuᔠḄᙶ᪗()஺efc6w&PḄ()ᙶ᪗(x,,x'x.).᝞y1-1ᡠ{y1-1ᙠ()ᙶ᪗3.P&Ḅ|}~r()ᙶ᪗(x',x?,x,)Ḅᦪ஺lᵫy1-1(1.3-2)7Cr(z',z2,z3)=r[z'(x',x2,x3),z2(xl,x2,x3),z3(x,,x2,x3)]=r(x],x2,x5)(1.3-4)ᜐᳮឋ⚪.ᵫQᱥḄ01.Yᨵ⚪ᵨᙶ᪗3O〉ᔠ.ᵨ()ᙶ᪗3஺ᨬ\ᵨḄ()ᙶ᪗3h()ᙶ᪗3.᝞ᙊᙶ᪗3ஹᳫᙶ᪗3ஹ☢᩽ᙶ᪗3P஺¡"ᙊᙶ᪗3(y1-2)y1-2ᙊᙶ᪗/ᵫef¢ᙶ᪗7Ḅᐵ3ᩭpq஺/01ᐵ3C£ᑏ6Z1=X1COSX3z2=x'sinx2(1.3-5)z5=x'BCDKᑡ7cosx:-x1sinx20j=sinx2x1cosx;0=x'001◀ᙠz,¥¦3=O)defᨵj=0᜜.(1.3-5)7ᙠᔜᜐ©ᨵX"Ḅ⌮ªᣚx1=7(z')2+(z2)27x2=arctan—(1.3-6)z,'='xzYQᙊᙶ᪗3.r\ᵨ¬☢Ḅᙶ᪗®.x'=rx2=0x'=z(1.3-7)

6j᪵.ᙊᙶ᪗3Ḅᙶ᪗☢1-=\ᦪḄᙊ☢°.0=\ᦪḄ±☢°.²z=\ᦪḄ☢°(y1-2)஺³ᑖ᪆Ḅµ⚪Ẇ·ᙶ᪗ªᣚ³ᑖḄªᣚ¸ᑣ஺¹³ᑖ᪆ᯠ»ᙶ᪗ªᣚ.¼ᐸᙠ¾¿ÀÁ³".ᯠ»()ᙶ᪗3ÂÃḄªᣚ஺ÄŪx',x2,x.ḄÆᔠC£ÇÈᙠÉᙶ᪗3Êp"&PḄᙶ᪗஺Ëx',x'xஹrs£¬Ḅ_`ªᣚᡂ"ͪx',xÎx’ḄÆᔠ஺x=x(x',x:,x')(k=l,2,3)(1.3-8)ᑣ¦7Êpw"ᙶªᣚ஺⌮ªᣚx*=xlx',xÎx)(k=l,2,3)(1.3-9)ᢥgÐḄ_ᔣÒK஺lwÓÔj᪵"ªᣚC⌮Ḅ.Aᙠª(x,,x'x')ḄÉRᑁ""YZḄ.ÕᓽᙠRḄÖᨵ×ᦪÆ((x1,x'x.)pq"X"Ḅᨵ×ᦪÆ((x',xÎx’).AÐᐸÕᯠ.ᐸᐙᑖᩩÙÎᦪx"(x',x'x')ᙠRᓫ:ஹ<=.ᨵ<=Ḅ"▤?@ᦪ.BCDKᑡ7_kaxj=®ᙠRᑁḄmn&ᙳOPQ0.ᐹᨵ¦ÜឋÝḄᙶ᪗ªᣚklÞߪᣚ஺àá£â¿Ḅᙶ᪗ªᣚ©Þߪᣚ஺BCDKᑡ7j=|ãᜐᜐl.ᑣ"äåᙶ᪗3ªᣚlæ"äåᙶ᪗3஺§1.4ç~ᙠ()ᙶ᪗3.èÃ"&PḄ|}~r()ᙶ᪗᱄Ḅᦪ
(1.3-4)7é஺()ᙶ᪗/ᨵêëìdx1ᑣ|}~rᨵìdr஺ᵫ(1.3-4)7.|}~rḄêᑖdrlQvdr=—dxk(1.4-1)ᦋèÃ"&PḄ|}~Cᵨᙶ᪗⊤{lr=z1(1.4-2)

77Llðᙶ᪗¥z._ᔣḄᓫ|~(y1-1),ñklᙶ᪗3Ḅç~஺Zᵨ(1.3-2)7(1.4-2)7.Códrdr5zjdi'.___—_______—____I(k=1,2,3)(1.4-3)3x'dz'5xk5xkj¦7⊤÷.஽ᓫ|~i,Ḅ)ឋùᔠ.¹Âñ~.ᵫ(1.4-1)7C3xkú5xk~⊤üýx-ªᓄ|}~rḄ
ᓄ0Ḅᔣᙶ᪗x'Ḅᑗr*3xkAr_ᔣ஺?ᙶ᪗Ḅg,⊤#(%1-1).*᪵,*g*Ḅ-.Arᑖ7j⁐=4(k=l,2,3)(1.4-4)ᵫ(1.4-1)9:;<Ḅ=ᑖdr?dr=gkdxk(1.4-5)BCDEFᙠᙶ᪗HIJKLḄMNOPᨵRS,g-,g,NTUᓫ;WXUYZ[,ᨵ\]NOḄRS,Ḅ\U^[,U_`aḄᜧcdᔣefJ`aᡠᙠOḄᙶ᪗஺,&ឋjᐵ`aUᐳ☢RS,n᪀ᡂqNSrsḄt᯿᪗v(rsḄwxyᙶ᪗)஺ᵨᙠNOḄ{E|Ḅᔣᢥ~ᑣᑖFv=u£(1.4-6)ᙶ᪗x
ᣚᡂNᙶ᪗x\xk=xk(x',x2,xJ)(k=l,2,3)(1.4-7)ᐸ⌮
ᣚ?xk=xk(x,x,x)(k=1,2,3)ᑣᙠᙶ᪗(H,n?-drdr3x'dx.1gk==^=ajc-k=gjy(1.4-8)SxSx'dx3xᵫᙶ᪗ᵫx'
ᓄ?•[(1.4-7)9],ᑣ,ᢥ
ᣚᑣ(1.4-8)

89
ᣚ஺,nX?
,*NOᙠ§1.6H¡¢஺§1.5IJ{£ᙶ᪗BC✌ᐜᙠ¦ᙶ᪗H᝞£¨©¨஺ªᙠᙶ᪗Hᨵᐗdr,ᵫ(1.4-5)9dr¬ᐸ®ḄO¯°ᐗ©¨Ḅ~஺ᓽds2=dr-dr=gdxk-gdxm=g-gdxkdxmfcmkmµ-.g”“=gg,"I)º|Jds2=gdxldxm(1.5-2)ki½ᦪ¿“(1.5-1)?ᙶ᪗HḄ,Á¨¨஺ᵫ9ᙠRÃKL,Á¨¨“ᨵ9Sᑖ஺(1.44)9Åᐭ(1.5-1)9:᪷È,Á¨¨Ḅ-.É(L5-1)9Ë,ᵫ᪗¯ḄZᣚឋgm=g.*(L54)ᓽ,Á¨ÂgmḄᢣ᪗kᔜmZᣚ஺ᙠ§1.4HÎᢣÏᙠᙶ᪗H,ÐUᓫ;஺ᵫ(1.5-1),Ḅᜧcᵫ,Á¨Â⊤#?|gÑ=(gÒgj%=Ô(L5-5)Õ9HKK⊤#IkU×d஺ØHÙÏÚ*ÛÜÝᙳ¬^஺ᙶ᪗X'
ᣚ?NSᙶ᪗f,
ᣚà?xk=xk(x,,x2,x3)(k=l,2,3)(1.5-6)ᐸ⌮
ᣚ?xk=xk(x',x',x")(k=l,2,3)ᑣ

9Axk—idxk=—dx(1.5-7)Sxᵫ(1.5-2)9:ds-gdxdx(1-5-8)trodxdx-.ᑣ1.5-8
9ᑏᡂds2=gdx'dx1.5-10
lnâ1.5-10
9¬1.5-2
9^᪵9É?ᙶ᪗MḄ¨Â஺ä=ᑖ9âL5-2
9d1.5-10
9᩽?æ⌕`-.qᙠNTᙶ᪗Hᐗ©¨Ḅ~஺ᙶ᪗
ᣚè.NSḄᑖḄ
ᣚᑣ¦Ḅæ⌕ឋé஺ᵫâ1.5-9
9ᙶ᪗᱄
ᣚ?NSᙶ᪗M1.5-6
9Ë,ᑣ¨ÂgMâxஹìᢥâ1.5-9
9ᡠ⊤#Ḅᱯ-Ḅ
ᣚᑣ
ᣚ஺g.”îᡠ?¨ÂN☢?`¨KLᐗ©¨Ḅ~âᡠ?“¨”ì[N☢?ïᙶ᪗
ᣚè`ᢥ᯿1.5-9
9*Nᱯ-Ḅ
ᣚᑣ
ᣚ*ÂḄ,Áᱯឋâᡠ`Âì“?¨Â஺*NSð_æ⌕Ḅ,ÁÂᡠñ?,Á¨Â஺ᐵJÂḄ,Áᱯឋᙠ§1.8òó஺ᵫâ1.5-1
9ôÏᙠyxᙶ᪗Hõ.=ஹ„,,ᓽᙠyxᙶ᪗H,Á¨Â_ᦪ஺,Á¨Â÷øKLḄឋé஺᝞ùᨵúûüᙶ᪗
ᣚýᐭNSᙶ᪗þ:ᙠ¦ᙶ᪗Hg”ÿ
ᦪᑣ“!"#$%Euclid
”஺᝞ᐭ᪵Ḅᙶ᪗ᑣ“(!"#$”஺ᙠ§3.8*+,-./⚪஺§1.6Ꮤஹ0123ஹᏔᏔ3ᵫ5☢Ḅ789:;

10gr-gs=8=(1.6-1)ᵫ>?:;>@A=ᙠBCDᙶ᪗*ᏔgḄ7ᔣFrwsḄGᡈᚖJKᙠLM*g',g\g'ᑖOᚖJ&ஹg,,g,>g,Qgrg?ᡠᙠḄS☢஺gḄᜧUVWgKg,=l(r=s)஺Ꮤg'XY>ZgஹḄ7ᔣᑖ[Yg'=g”g,(1.6-2)9*g”Ꮤᙠg,7ᔣḄᑖᐳᨵ9஺Y^g“+(1.6-2)9`abcg,$gJg'gYjg'gBng"ᓽg"=g'g'(1.6-3)?9XYg”Ḅ:;஺e9F(L5-1)9fghg”iY0123஺ᵫḄbj〉ᔠmᣚoᵫ(1.6-3)9pg”Ḅᢣ᪗r,s>mᣚᓽg"=g”(l-6-3a)F8,᪵Ꮤ3BᓫstḄᜧUᵫ59uv:|g'|=(g=g+=VF(r^x)(1.6-4)bḄLᏔg᪀ᡂ|}Ḅ~᯿᪗XᵨᙠebḄ>ZgḄ7ᔣᑖ[஺Ꮤ3iY⌮஺ஹ0123ᙠ./Ꮤ8*,0123g”(L6-3)9,tiYᐳ23஺☢ᐜ./0123F23Ḅᐵ஺+(1.6-2)9ᐭ(1.6-1)9ᑣg""gjg,=஺

11ᓽgmg=8d-6-5)msᑭᵨ?9Auvg”Ḅ9:Ḅrxs=1,2,3,?9A>5Lᑖ78=g„gr'+g,gr+gi,g"=3g—'+g"g"+g*ஹg"=3g"g"+g"g=+g*g'ஹ=3gpᑣr=1,2,3,>?☢78[Ag”1᪷¡(Cramer)¢111sᑣAuvg”Ḅ9᝞5(£ᣚᢣ᪗)Dcs,gR=—(1.6-6)g9*§11S12§13g=|gj=§21§22g1}(L6-7)§31S.U§33D=|gj*ᐗ¥g.Ḅᦪ¦§9ᙠ3ᑖ᪆*g"Ḅ©⌕ឋxgj᪵஺+(1.6-2)9¬`aᙳc>¯,ᓽgg.=gmg.g",ᑣgg,=3&=gஹ,£ᣚᢣ᪗$g,=g,ஹg,(L6-8)(1.6-2)9x(1.6-8)9AxᏔ°᩽Y©⌕Ḅᐵ=g'=g"g.(1-6-2)g,=g.g'(L6-8)⊤³g,xᏔg'°´23x0123>µᓣᡈ5·ᢣ᪗¸gxgs¹0ᣚ஺rLஹḄ⌮ᑖxºᑖ

12»☢¼ᢣA½¾(1.4-69)V>ᵨtZg,7ᔣḄᑖᩭ⊤³V=vrg,(1.6-9)ᑭᵨ(1.6-8)9ᑣ?9⊤³Y7=v'g,=vஹg'(1.6-10)9*v,=gy(1.6-11)1À᪵$Vr=g"v.(1.6-12)(1.6-10)9⊤ÁV>ᵨtZ⌮g7ᔣḄᑖ⊤³஺ViYVḄ⌮ᑖKvg,Vᙠº8,7ᔣḄᑖKv,iYVḄºᑖvஹg,Vᙠ⌮g,7ᔣḄᑖ஺+g,bc(1.6-9)9`a+g,bc(1.6-10)9Ḅ¬axÂÃÄḄaᑖO$ᑮ᝞5Ḅ`©⌕ᐵ9=vs=V-g'(1.6-13)v=V-g,(1.6-14)r⊤³Ḅ⌮ᑖxºᑖḄᜧUÃx0fḄḄbj஺ᑭᵨ`Ã9ᑣ(1.6-9)9x(1.6-10)ḄÂ9ᑏᡂV=(V£)g,(1.6-15)V=(V,gஹ)g'(1.6-16)ᙠCDᙶ᪗*g,xg
tÇÈÉbḄᙶ᪗஺ᡠ>ᙠCDᙶ᪗*ᵨᑖ⊤³½(1.6-10)9,ᑣÊË⌱ÍÎ:bᓽḄXᵨbÏÐÑb(Ò1-3)⊤³MCDᙶ᪗ḄஹᏔxVḄ⌮ᑖxºᑖ஺ᙠJÓᙶ᪗*g,xgḄ7ᔣ©ᔠghḄ⌮ᑖxºᑖḄÔOÕᜫ஺ᵫ>?Ḅ./>@AUxᓃÀVᑖ[YᑖḄ`ØÀḄ7

139ᡈὅÚÀVḄ`ØÀḄ3⊤Ü9஺CDᙶ᪗Ḅᱯb,ÊËÞßᙢᳮ[஺Ò1-378(1.6-12)x(1.6-11)9èéᑖḄᢣ᪗µᓣ(ᵫ5᪗µᓣY?᪗ᓽᵫºᑖᣚY⌮ᑖ)xᢣ᪗5·(ᵫ?᪗·Y5᪗ᓽᵫ⌮ᑖᣚYºᑖ)Ḅ7¢஺êஹᏔஹ0123Ḅᣚ¢ᑣëᙶ᪗/ᣚᑮíᙶ᪗N,ᣚ78Yxk=xk(x',x2,x')k=l,2,3)(1.6-17)ᑣdxl=yydx'(1.6-18)+(1.4-5)9`abcù,£ᣚúᢣ᪗$dr-gk=(g.-gk)dx'fᵨ(1.6-13)9?9ᡂYdxk=(g,-gk)dx'(1.6-19)+(1.6-18)9F?9þÿ
_3xkt8'-gFᵨ(1.6-16)
AM..-(1.6-20)r=(rg)gl=gl$%ᙶ᪗ᢥ(1.6-17)*ᣚ,⌮*.᱄Ḅ*ᣚ1ᑣ஺ᵨ(1.6-3)(1.6-20)
456789:ᙠᙶ᪗*ᣚ(1.6-17),Ḅ*ᣚ1ᑣ<(1.6-21)ax'*ax'dx?@A.g,Ḅ*ᣚ1ᑣC(148)EFGᏔ.IḄ*ᣚ1ᑣ

14C(1.6-20)EḄJK஺?ᙶ᪗Lx**ᣚᑮ”(1.6-17)E,.Ḅ*ᣚLᦪKL4-8)ERSTUV*ᣚLᦪWX.YZU[*.\]GᏔ.ox-kḄ*ᣚLᦪ^C(1.6-20)EᑣSTU⌮*ᣚLᦪWXGᏔ.YZUdx⌮*.஺_᪵?@A.a9:Ḅ*ᣚ1ᑣKL5-9)Ed789:*Ḅ*ᣚ1ᑣC(1.6-21)EḄJK஺§1.7Vefgᙶ᪗LᑡiஹVefgᙶ᪗Lkfgᙶ᪗LḄᙶ᪗fg7lVeᑣZUVefgᙶ᪗L஺ᙠVefgᙶ᪗Lm.7lVenoipᓫr_isḄᔜ.
uᨵo_Ḅw஺GᏔ.F.Ḅxᔣ7_nᜧ{o7|஺.a9:(H)(i=j)(1.7-D0(ij)LᦪH,ZU᫥(Lame)Lᦪᡈ9LᦪᡈW஺ᵫ(1.6-7)ᙠVefgᙶ᪗Lmg=g„gg„=(H,HH,)2(1.7-2)222789:ᵫuᐵL<11(iod)(1.7-3)g"=0(i#j)(1.7-4)GᏔ.Ugr=g"gk(kod)(1.7-5)ᙠVefgᙶ᪗Lmᵨᓫr.e,e,=/lg,l=g,/H,(iod)(1.7-6)gi$᪵ᙠVefgᙶ᪗Lmᵨᓫr.e/Ḅ[*ᑖd⌮*ᑖḄJKᜫ஺ᙠឋmᨬᵨḄVefgᙶ᪗Lᙊᙶ᪗Lஹᳫᙶ᪗Ld¡☢᩽ᙶ᪗L஺☢ᑖK¤R¥Ḅ.ஹ.a9:ஹ789:dGᏔ

15.ᑡ6஺¦ஹᙊᙶ᪗L(§-4)ᵫ§1.31Z1=x1cosx2z2=x1sinx2z3=x3X—+(Z?)22+Z2x'=arctan—z'x3=z3§14.<ᵫ(1.4-4)gi=(cosx2)i,+(sinx2)iIg.1=1g=(-x1sinx2)i+(x1cosx2)iIg1=x12122§3=lg"=l(1.7-7).a9:<ᵫ(1.5-3)az,3z2Sz3v2g“=(Q)-+(7T)-+(Q)dxdxdx=(cosx2)2+(sinx2)2=1dz2g822=(——2)24-(ߟ^2)2+(——2)2dxdxdx=(-xlsinx2)2+(x'cosx2)2=(x1)2g33=(^7)-+(=)+(3)-=1(1.7-8)dxdxdxg,2=g”=g,3=0

16100g=o(x')20=(x')2(1.7-9)001789:<ᵫ(1.6-6)g"=l,g"=l/(x),g"=l(1.7-10)g"=g"=g"=OGᏔ.<ᵫ(1.6-2)g'=g,|g'|=1g2=g/(x')2,|g2|=l/x'(1.7-H)2g=g,=i,|g'|=lIஹᳫᙶ᪗L(§1-5)z1=x1sinx2cosx3z2=x1sinx2sinx3(1.7-12)z3=x'cosx2X1=J(z)+(Z?C+(z3)2,z3x'=arccos.=(1.7-13)J(z)+(z)+(z)3Z2x=arctan—z1§1-5.<ᵫ¾1.4-4¿

17g,=(sinx2conx5)i+(sinx2sinx3)i+(cosx2)i,,t2lg.l=1g=(x'conx2cosx')i]+(x,cosx2sinx5)i4-(-x'sinx2)i,223(1.7-14)|gj=x,g,=(-x1sinx2sinx3)i,+(x'sinx2cosx5)i,2|gj=x'sinx2.a9:<ᵫ(L5-3)g=(sinx2cosXi?+(sinx2sinx')2+(cosx2)2n=1g”=(x1cosx2cosx5)2+(x'cosx2sinx1)2+(-x'sinx2)2=(x')2>(1.7-15)g=(-x1sinx:sinx3)2+(x1sinx:cosx')233=(x1sinx2)2g=g"g"12100g=0(x1)20=(x')4(sinx2)2(1.7-16)00(x'sinx2)2789:<ᵫ(1.6-6)g"=1,gÂ/(x')2,(1.7-17)g'2=g”=g"=0GᏔ.<ᵫ(1.6-2)g1=g,1§'1=1g2=g/(x')2,|g<|=l/x'(1.7-18)2g5=g,/(x'sinx2)2,[g[="(x'sinx?)§1.8:

18iஹ᪗ஹ⌮*ஹ[*ᙠᱥᳮᡈÇÈmᨵiÉFÊὃᙶ᪗Ìᐵ᝞ÎஹÏ9ஹÐ9|\ÑᨵiÉR¥ḄᑖᓾFÊὃᙶ᪗Ḅ⌱Ôᨵᐵ᝞rÕஹÖ9|஺×ὅZU᪗ÙὅZU஺ᙠᦪᢥ᯿ᙶ᪗ÛÜÝ*ᣚ,$ÉḄᑖᡠßàḄ*ᣚ1ᑣḄo_]ᑖKáupâ஺ãiḄᑖᙠfgᙶ᪗LXmpâR¥ᙶ᪗xlx'x'Ḅäᦪ஺kᙶ᪗LxiÛÜÝ*ᣚᡂÑiæᙶ᪗LmN=M(x',x'x'),ᑣ
upâèᙠæᙶ᪗LmḄᑖé᪷ëèḄᑖᙠᙶ᪗*ᣚ,ᡠ⍳íḄo_Ḅ*ᣚ1ᑣáîèuo_ḄïZ஺☢pâ(1)᪗iSZU᪗ᡈðG᪗kRᙠᙶ᪗LXmñᨵiᑖ°,ᙠæᙶ᪗LmYñᨵiᑖ3,éóᙠôᙶ᪗LmḄGs஺஺FḄᦪõ7|ᓽ0[x'(x),x2(x),x3(x)],=0(X,x,x)=^(x,,x2,x3)(1.8-1)᪗YSZUo▤:(2)⌮*(i▤⌮*:)iSZU⌮*ᡈi▤⌮*:kRᙠᙶ᪗LX1mᨵIᑖA1,ᙠᙶ᪗LMmᨵIᑖøR¥ùúuḄ*ᣚ1ᑣ

193஺_3஺Ox'(1.8-5)Sx'ᦋ°x'/_ᙠᙶ᪗ᣚ1ᢥ(1.8-4)34Ḅ5Ḅᣚᑣᣚ஺5x5Ḅᣚᑣ`(1.8-4)abcḄᣚᑣd.4-8)aefᣚᦪgUhᣚᦪᡠH9“5”஺⌮Ḅᣚᑣ`(1.8-2)abkᏔcḄᣚᑣ`(L6-20)aefᣚᦪgU⌮ᣚᦪᡠH9“⌮”஺ᵫO/q᪗r᪗ᔜᨵᐸᱯ3Ḅv4஺wxyvzUᙠᙶ᪗ᣚ1{|U}஺~UḄᑖB}U}ᙶ᪗ᣚ1Ḅᑖᢥᱯ3Ḅᣚᑣᣚ஺⌮A'r5A,B}U}fḄUkfAḄ}fḄ⌮UAUAḄ⌮ᑖ5A,UAḄ5ᑖ஺ஹ▤7?ᙶ᪗Ḅ7g“D᪵Ḅ<ᨵ9ᑖ஺ᙶ᪗Xᣚ`1;DEᑖᢥᱯ3Ḅᑣ`(1.5-9)aᣚ஺D᪵Ḅᢥ᯿ᙠᙶ᪗ᣚ1<ᡠ⍳Ḅᣚᑣ34B}fḄ9஺☢34I(1)▤⌮7A"Au(x)=Amn(x)——(1.8-6)axmax"(2)▤57A,¢—\A/x5xm"A”(x)=A*)(1.8-7)dxdx(3)▤¦ᔠ7A,A¨Ḅªᡈ(1.8-8)«ஹ…5xmdxAJ(x)=A———3xOx”?ஹ©▤7q☢ᐵ¯▤7Ḅ34H°±ᑮ©▤7஺AIII89Up▤⌮ஹq▤5Ḅ¨▤(r=p+q)7;ᙠᙶ᪗ᣚ1<Ḅᑖᢥ

20ᣚI¶…=£ᵯ1¹¹A""."'(1.8-9)'i……º»wxyvᢣ᪗Ḅ¼½¾¿}ÀÁvÂᣚᙠᢣ᪗ḄÃᜐÅᵨÆᙊÈ᪗É᝞ËË1.8-8ÌË1.8-9ÌÍᓺᑵÐᶍÒÍ᪗Éᢣ᪗¼½ÃÓḄÆᙊÈ஺Ôஹ7Ḅᱯឋ7Uᭆ×Ḅ°±᪷ÙHqᐵ¯7ḄÚ᪆34ÜÝ7ḄᱯឋªHÞᔠ஺7ᵫ<ḄᑖḄßᔠᡠà3஺7Ḅc{ឋáᵫᙶ᪗ᣚ17Ḅᑖᡠ⍳Ḅᣚᑣᩭã3ᣚᑣb7⊤Näåᱥᳮèᐵ஺7ḄᣚᑣË1.8-1ÌஹË1.8-2ÌஹË1.84ÌஹË1.8-6Ì~Ë1.8-9Ì⊤êᙶ᪗ëìíᣚ17ᙠᙶ᪗MḄïᑖUð7ᙠñᙶ᪗XᐰóᑖḄôឋõᔠᣚᦪUö÷Ḅ஺᪷Ù7ḄᣚᑣḄ}fᩭ347Ḅ“▤”b“ø”Ë“ù᪀”Ì஺7ᑖû▤ஹ▤ஹ▤.......7Ḅ▤ü¯ᣚᑣᣚᦪḄPü¯7Ḅᢣ᪗Ḅᦪýᙠ?,r▤7ḄᑖþᦪN=3'1.8-10᪗▤▤஺ᢥ᯿Ḅ᪀ᑖ⌮ஹ!"#ᔠ%ᵫᣚ(ᑣ*Ḅᣚ+ᦪ⌮ᣚ+ᦪ-ஹ.ᣚ+ᦪ-ᡈ0ᨵ2ὅᩭ56஺Ḅax1dx7ᵫḄᢣ᪗Ḅ9:;᪗ஹ<᪗ᡈ0ᨵ;᪗<᪗ᩭ56஺᝞>ᙠ@ᙶ᪗+*B@ḄᐰDᑖEFo,ᑣᙠIJᐕLᣚḄᐸNOPᙶ᪗+*QḄᐰDᑖ7EF0,%ḄR⌕ᱯឋ஺Ḅ%@ᱯឋVWXᐹᨵZឋ%ᙠ[☢]^_`a஺§1.9b@R⌕Ḅᱯcdef§1.2*Ḅijᑁilm":ᣚlmᑖ6noᙶ᪗+z1*Ḅ2▤"3▤q᪷stuḄᢣ᪗9:ᑖ6!ஹ⌮ᡈ#ᔠv’1xi=j"=V=3="=10xiwj(1.9-1)

211x|123ḄᏔ:x~123Ḅ᜻:(1.9-2)0xᳫḄ(2@ᢣᙠᙶ᪗+X'*tuḄᑖ%᪷sḄᣚ(ᑣᑏ஺ஹijᑁilmḄᣚdzmdz",ge=-a---'-5-xj-Omn(1.9-3)Xᦋ0X,gH,J=------5Ommn"(1.9-4)dzmdzn♦:v=☋=3UM(1.9-3)¡¢᧕ᳮ¥,¦t§(1.5-3)¨஺ᙠ(1.9-4)*5™=ii",ᓽnoᙶ᪗+Ḅ«Ꮤ¬Ḅ®,ᣚᑮᙶ᪗+[tu°g±g²,᪷s(1.6-3)%@®g”஺](1.9-4)§(1.6-21)~µᑣ(1.9-4)7¢᧕ᳮ¥஺¶᪵«F(1.9-5),3v=¸¹¦ºᣚ[°gvg,,ᓽgv஺ᵫº»xnoᙶ᪗+ᣚᙶ᪗+¼ijᑁilmᣚ½±#ᔠឤEF3±,tᙠᡠᨵḄᙶ᪗+*ÀÁᦪ஺2ஹ:ᣚdz'dz'dz'=e,7gG=------------------et(1.9-6)ex'dx'dx”n,axn,ஹ1=e',kÅ(1.9-7)dz"3zsOx'dz%Ç@ᣚḄ*ÈḄEmÉᵨËÌᑡḄÎÏÐ(1.2-9c)"1.2-9d)»ᨬ[ḄE◤⌕Ö×Ḅ஺ᵫ(1.6-5)ØggmJ=8±imᵫÌᑡḄÙ(»ij|g“.g[=|g,Hgu|=W|=ld-9-8)ᵫà"g”Ḅ⊤â(1.9-3)ஹ(1.9-4)q°ᵨÌᑡḄÙ(Ødz'dz1dz,(1.9-9)ax’ᦋ5xj

22Isxd_|Sx'ã(1.9-10)II⁰å᪶ᵫ(1.6-7)Øg=“ᵫ§L3»,«F¢Lᣚ蔫Féêᙶ᪗+,&1>0,¦ºᦋ(1.9-11)ì=(ᒓ)_=3(1.9-12)%᪵,(1.9-6)ஹ(1.9-7)ØᑮËÖ×஺ᵫº»vdnoᙶ᪗+ᣚᙶ᪗+ᑣ:ᣚlmeïஹnoᙶ᪗+*Ḅ)4ஹU*,ò:ᣚ஺ᵫ(1.2-8)ó(1.9-6)»xô=123ஹ231ஹ312xô=321ஹ213ஹ132(1.9-13)xᳫ*Oõ2@ᢣ§ºö÷ᵫ(1.2-8)ó(1.9-7)»Jö°Ḅøᑖ6+úஹ-/=ᡈJgJg0oüஹ:ᣚ§ijᑁilmḄᐵ+Jᐹᨵþÿ
Ḅឋ§1.2ᵨe.ஹᓽ⊤Ḅᣚᡂ,ஹU"⊤ᑭᵨ(1.9-6ஹ(1.9-7)",ᑣ$%⊤&'ᣚᡂᙠᔜ*ᙶ᪗-./〉ᵨḄ
12஺ᵫ(1.2-9b)67aa:a:a;(1.9-14)<=>aG-=Glmna:asa'(1.9-15)lmnᵫ(196)ஹ(1.9-7)67(1.9-16)ImnImn

23F=Gᐭ(1.2-10)~(1.2-13)67LMḄe-3ᐵ-:=3:3'3'P3:3'3'—333;+3'3'3:-3’3:3'(1.9-17)ers,e=5'8'(1.9-18)rmnmnnITe's,e=28'(1.9-19)rsnn_-rst_z-GG=O(1.9-20)(1.2-14)'ᣚᡂae.e'"'"=6a=a'a'a'ee(1.9-21)Imn1mnrstXஹYZ[\Ḅ]ᣚ
^ឋ_`abc⚪eYZḄ஺᝞g☢i_ஹg☢i'c⚪jkᵫg☢ᙶ᪗x',x2ᩭnoᙠↈqᳮs◤ᵨu☢=ḄYZᙶ᪗᱄,x?ᩭno஺xyzYZ[\6L{|eP}~Z[\Ḅ[\ᓽᙠYZᙶ᪗X,᜜=~ᙶ᪗X3,~ᙶ᪗Ḅ
g,ᓫ
L,ᐸ1ᔣᚖ
g.o$᪵gc=ga,=0g.»=1,

Ḅᑡgug012g”Sl2g3g”0(1.9-22)§21§22001ᙠ]ᣚ
ḄḄᑖ
¡¢M᪗P£¤3஺¥¦§¨]ᣚ©6Lᢣ᪗k=3,ei,jḄ¯°▲ᑴᙠ1.2$᪵6L³ᐭPYZ]ᣚ
4(1.9-23)ᵫ=7EII=£—22=—0JE2=ஹV/©?=—£(1.9-24)⌮'ᑖ
e(1.9-25)ᵫ=7e"=e"=0e=-e(1.9-26)

24¸¹☢ᵨ4,ᓽº»~▤ᑡP᪵6Lᵨ4V"º»Y▤ᑡ஺ᨵᐵ¾ᑡ¿᝞MÀὅ6ÂÃÄÅ஺xYᑡa:a:a=a;a;Mᑡᔜ¾ᡂÆa/=a"Ya?6eaBlt(1.9-27)ae,e=a"a?J(1.9-28)2a=:a"a'eU(1.9-29)]ᣚ
ḄÇ3:6-(1.9-30)e%,6=3:(1.9-31)e"&p=2(1.9-32)§1.10ÈᓱÊ
¹ÃḼÌᢣ¿ᙠuÍᙶ᪗-£¤aÎᙢᳮÐ⌮'
<Ñ'
ḄÒÓLÔjkḄ'ᣚÕᑣḄÖ×஺Øe᝞ÙᡠÛsḄc⚪ÜᵨÝᙶ᪗noᑣ
Ḅ⌮'<Ñ'ḄÖ×Þᜫ஺LàÅázlz-z¸âeãÝᙶ᪗-jk\Ḅ'ᣚ12ä=å+/(1.10-1)a,æᦪa:eèᙶ᪗éä<71ᔣḄᓫ
\ᜳÝḄ1ᔣëìᓽa\=cos(z',zj)(1.10-2)í᝞a;=cosফz').(1.10-1)Ḅ⌮'ᣚ12z'=.N+b'(1.10-3)P'.=cos(z1,2')(1.10-4)ᵫ(1.10-2)ஹ(1.104)6L{¿a:=P;.(1.10-5)

25$᪵(1.10-6)Û‘,kazkñò§1.8ó▤⌮'
¸Ñ'
Ḅ'ᣚÕᑣḄÖ×Þᜫ஺6ôõᡠÛsḄc⚪ö▲Ýᙶ᪗-ᑣ6Lᡠᨵ
Ḅᢣ᪗ᑏᡂM᪗஺ò
øÈᓱÊ(Cartesian)
ᡈÝᙶ᪗
஺ᙠüGýb^ឋ_`ஹþÿ
ḄᵨᓱᑏḄḄஹḄ᪗!"஺§1.11$%&Ḅ⊤()⁚+,ᵨ-⊤./0ᙶ᪗2$Ḅ%&ஹ$3Ḅ᪗&4ᵨ(1.6-10)<=$uஹvḄ᪗&@⊤Au-v=(u1g)(vg)=uYg/g=u'vᵪ=u'v,(1.11-1)J=-KLMᙶ᪗2$Ḅ᪗&Ḅ-(X•Y=x,y,+x,y,+xy)জTUVḄ஺Wᯠuஹv@Y⊤Au•v=uY=uyg"=u'vjg“(1.11-2)^ஹ$Ḅ$&ᐜ+,`$Ḅ$&ᙠLMᙶ᪗2ᓫc`$de<=Ḅ$&i,xi,=ej(i,j,k=l,2,3)(l.H-3)i,j,kT1,2,3Ḅlm᣸ᑡ஺ᙠLMᙶ᪗2g,ᡈg*rTᓫc`$i,ᡈi"஺stuḄ`$ᑏᡂg,ᡈg1ᑣu@ᑏᡂg,xg,=e,"g'ᙠLMᙶ᪗2e,=eoJ᪵u@ᑏᡂjkijkg,xgj=4g"(1.11*4)J=Tᵨ{|-⊤AḄ}(~ᙠLMᙶ᪗2ᡂᙠᐸ}ᙶ᪗2ᡂ஺(JTḄᨬ⌕Ḅឋ
)ᙠYY,஺)᝞`$ᢥg,,g°,gஹḄᡂ᯿᪗ᑣ(1.114)g,ஹggjgj,

26Jὅᡂ2஺(1.11-4)UVg'xg)=eijkg(l.H-5)kuT{|ᡂḄ஺+,de<=$AஹBḄ$&஺C=AxB=(Ag)x(Bg)=AB=gk=Cgk(1.11-6)tC=AB'Gijk(l.H-7)tᡈc=AxB=^A£xBg=A,BjᓽCkggk=k(1.11-8)ck=ABUjk(l.H-9)«J%&CḄᔣKABᚖL஺J@ᵫACḄ᪗&£¤0ᩭ¦C-A=CAk=A'B'e,Ak=A'BJAke7g(1.11-10)tjkijkuTᑖ¨Y$AஹBAḄᑖ©Ḅ©ᑡḄª«¬(1.2-9a)®஺ᵫ¤J=©ᑡᨵ<©U£°T$AḄᑖJ=©ᑡ£¤0.ᵫ¦CA±²஺³᪵@Y¦CB±²஺J᪵CḄᔣᚖL¤AஹBᡠᙠḄ☢$AஹBஹCᡂ2᝞¶1*6ᡠA஺$&C(=AxB)Ḅᜧ¸£¤Y$AB¹ºḄ»©¼º-Ḅ☢&஺Jᙠ$½ᦪᨵ¦J¿(À஺$&Ḅ=4ᵨT⊤A☢ᐗ஺Y$ᐗdrஹds¹ºḄ»©¼º-☢ᐗdA(¶1-7)dA=drxds=dr'ds'egk(1.11-11)iik¶1-6¶1-7

27ᡈdA=dridsie,(1.11-12)kjkJ᪵YdrஹdsḄ¹ºḄ»©¼º-☢ᐗḄᜧ¸ᔣᵫ$dA⊤A஺$&ḄÆ=4ᵨT⊤AÇ஺ᵨᙠPÉḄF¤ÆÉ஺ḄÇ£¤ḄᵨÉPḄ$Ër(=OP)K$FḄ$&஺$ËḄÍÉÇÎᔠ(¶1-8),ÇM=rxF=rF'egk(1.11-13)ijkLO¶1-8ᡈM=r'F1e(1.11-14)tijkஹ$ḄÔᔠ&$ḄÔᔠ&AxB-C@ᵨ×ØAxBC=ABjÙO-C'g,=ABC3=A'B'Ckj(1.11-15)OIijk\ijk$ḄÔᔠ&T=᪗஺ᵫÉ&ḄÛܶ1-9ᨵAxB.C=|AxB|-|C|cosp¶1-9uTY$AஹBஹCáḄ»©â☢ã(¶1-9)Ḅã&V,@YᑏᡂYḄ-V=ABC.AxBC(1.11-16)W²ᣚ%&AxB-CḄdæ<=3çè²ᣚ/U4Ḅ᪗é᝞AxCB=A'CkBje=-A'B'Cke=-Vik)ijk

28ᵫ@êlm²ᣚᔜᐸì(íîᔜḄ⌮lmðᣚᑣñòUóḄô!஺4ᵨ$ḄÔᔠ&@Y×ØY`$áḄ»©â☢ãḄã&஺ᵫ(1.114)(1.9-13)õg,xgg'=Tgg'2J᪵@õg,xg-g,=7gg5-g=7g(i.u-17)25u⊤¦᯿£¤Yøí`$áḄ»©â☢ãḄã&஺Kùúᵫ(1.11-5)(1.9-13)@õg'xg2.g'g,=5(l.H-18)4ᵨ$ḄÔᔠ&@Y⊤AãᐗY$ᐗdr,ds,dtáḄãᐗᢥ(1.11-16)@ᑏᡂsV=drxds-dt=ᵫ᝞@"e(1.11-19)ijküãᐗ᝞¶1-10ᡠA஺¶1-10é1ᵨ⊤A¦Ax(BxC)=(AC)B-(A-B)C.Ax(BxC)=Ax(BJxCg)g|k=AX(BVeg1)jtl=A,gix(BVg1)¦=ABC.g'Xg1=A.B'C1ee"mg(1.11-20)jUm=ABjCk(551-55)gikra=AkCkBmg-ABjCmgkOmjOm=(AC)B-(AB)Cᵨ(1.9-18)Ax(BxC)"#$%&Ḅ$(%&)஺

29+⚪1ஹ./ᑡᔜ:(a)3=3(b)e.ejki=6ஹijkte#AA=O(d)88=8'\/Jkk(e)e,Me=8s8'-5s8'''nnnmnnm2ஹ<=>☢᩽ᙶ᪗CḄD%&ஹDEF&G&ஹHᏔD%&JKF&G&>☢᩽ᙶ᪗Ḅᑖ
=r,=஺஺(⚪1.2M)3ஹ.ᳫᙶ᪗C(x'=r,x2=(p,x'=6»)(M1-5)ḄD%&ஹDEF&G&ஹHᏔD%&ஹJKF&G&Ḅ⊤P(1.7-14)3(1.7-18)஺4ஹ.Qᐗ(dx\O,O)ḄSFTJi7ldx'I,Qᐗ(O,dx-O)ḄSFTUIdxV஺5ஹQᐗ(dx',0,0)WQᐗ(O,dx',O)XᑢḄᜳ[\஺Jg”Jg?2`Pᐜ<=Qᐗᙠc[ᙶ᪗CḄᑖ&஺ᯠefᵨᙠc[ᙶ᪗C<=g%&Xhᜳ[Ḅ\஺6ஹij<=JKF&G&Ḅ\(1.6-6)„„D,g=ng஺'=ᙠoᑡgᐗpgḄqᦪst1sg=|gjvwxyD”Ḅᐹ{⊤P஺7ஹᙠ|}~Qᙶ᪗C(H,)2(i=j)()

30gn=1-=y^p(i)g.(H,)-g"=0(i*j)g'=g*kg,(k)8ஹ:vr=vgB(1.6-12)K=%d-6-11)9ஹ5zr5zs3zl|6zm|/—€ijk=dx'axjaxkCrs,=eijk|aF|=eijk^gᓽ=le▢|”|=—dz'dz'dz'|6z"I«g=|gj஺10ஹijᐵ▤oᑡḄ\(1.9-27)(1.9-29)11ஹ~Qᙶ᪗CT|}ᙶ᪗CḄ⌕ᐙᑖḄᩩ¡Tᙠ᦮£¤ᑁg“=0(iHj)஺12ஹg,.xg,=,g',grxg'g,§¨©%&g1WgzxgஹḄ᪗&)⊤Pt#Kg,ggஹ)]ᡈ(g,gxgjᑣᨵ2[ggg[=(gig3xgj=Ji[g'g2g3]=(g'g2xg')=%13ஹ¯%ᐗds2=gadx2ds&=gஹdxஹ#±²Ḅ>o³²´☢ᐗḄ☢)TdA,=|dsxds,|=|g,xgJdx2dx32dA=^/(gg")dxJdxk(iiwjwk)¶y஺14ஹ¸ὃº12⚪{ᐗḄ{)#dV=ds,-dsxds=[g.g,gJdx'dxMx3=^/gdx'dxMx3ds=g,dx,,23(

31ds,=g,dx\ds,=gஹdx'஺2006-5-11