kXkX JQK2Mib /ǶBM2`iB2

(1)

k

+BMĀiB[m2

2N Ua3LCěa3 NNā3 NRnc qRNc 0ā$njā Iȕājn03 03 I Lā,NC\n3 0n cRIC03 Ua I ,CNāLjC\n3 0n cRIC03 UnCc Ua I cjjC\n3 03c cRIC03cY

ġ H ,CNāLjC\n3 3cj Iȕājn03 3j I ,a,jāaCcjCRN 03c LRnq3L3Njc 0ȕnN cRIC03.

ġ I cjjC\n3 ,Raa3cURN0 © Iȕājn03 03 Iȕā\nCIC$a3 cjjC\n3 VcNc LRnq3L3NjW 0ȕnN cRIC03 cRnLCc © 03c ,jCRNc Lā,NC\n3c 3ujāaC3na3cY

ġ +3c 03nu ājn03c c3 cRNj UUnwā3c cna I LR0āICcjCRN 0n Lā,NCcL3 VICCcRNcWY

MRnc IIRNc ,RLUIāj3a ,3 ,Rnac Ua I 0wNLC\n3 0n cRIC03. ,ȕ3cj © 0Ca3 Iȕājn03 0n LRnq3L3Nj 03c cRIC03c q3, I3na Lcc3 3j CN3ajC3 cRnLCc 03c ,jCRNc Lā,NC\n3c 3ujāaC3na3c. 3N ,RLL3NÓNj Ua 0ā~NCa I3c NRjCRNc 03 Lcc3 3j 0ȕCN3ajC3 3j I ,CNājC\n3Y

kXRX Jbb2 2i BM2`iB2

kXRXRX LQiBQMb /ǶBM2`iB2

MRnc cqRNc. Ua 3uUāaC3N,3. \nȕCI 3cj UInc ŋ 0C|,CI3 Ō 0ȕ,,āIāa3a nN ,LCRN \nȕnN3 LRjR ,RLL3 CI 3cj UInc ŋ 0C|,CI3 Ō 03 I3 8a3CN3aY HȕCN3ajC3 ,a,jāaCc3 I aācCcjN,3 \nȕRUURc3 nN ,RaUc Ua c Njna3 UaRUa3 © nN3 qaCjCRN 03 LRnq3L3NjY

TRna nN LRnq3L3Nj 03 jaNcIjCRN. I Lcc3 cn|j URna 0ā~NCa ,3jj3 \nNjCjā. Ua ,RNja3 URna nN LRnA q3L3Nj 03 aRjjCRN. CI 3cj Nā,3ccCa3 03 Uaā,Cc3a I aāUajCjCRN 03 ,3jj3 Lcc3Y

H ,CNājC\n3 3cj Iȕājn03 03c ,a,jāaCcjC\n3c 0ȕCN3ajC3 0ȕnN cRIC03Y kXRXkX Jbb2 @ `TT2Hb

H Lcc3 ,a,jāaCc3 I \nNjCjā 03 LjCěa3. ,ȕ3cj nN3 <aN03na ,RLUIěj3L3Nj 00CjCq3Y bRCj.Σ1.Σ203nu cwcjěL3c LjāaC3Ic 0CcERCNjc IRac -

m(Σ1∪Σ2) =m(Σ1) +m(Σ2) q3,Σ1∩Σ2=φY

H Lcc3m_Σ03 Iȕ3Nc3L$I3Σ3cj 0ā~NC3 Ua -

m_Σ=

Σ0m=

Σρ(P)0v q3,ρ(P)Lcc3 qRInLC\n3 n URCNjP3j 0vnN āIāL3Nj 03 qRInL3Y

`3La\n3 -

S

(2)

ġ bC I3 cwcjěL3 LjāaC3I 3cj ccCLCI$I3 © nN qRInL3. RN UaI3 03 Lcc3 qRInLC\n3 ρ(P)^{n URCNj}P- 0m=ρ(P)dvd

ġ bC I3 cwcjěL3 LjāaC3I 3cj ccCLCI$I3 © nN3 cna8,3 RN UaI3 03 Lcc3 cna8,C\n3σ(P)n URCNj T - 0m=σ(P)dsd

ġ bC I3 cwcjěL3 LjāaC3I 3cj ccCLCI$I3 © nN3 IC<N3. RN UaI3 03 Lcc3 ICNāC\n3λ(P)n URCNj T - 0m= λ(P)dlY

VX *QMb2`piBQM /2 H Kbb2

QN 0L3j 3N Lā,NC\n3 ,IccC\n3 \n3 I Lcc3 3cj nN3 <aN03na CN0āU3N0Nj3 0n j3LUc. CNcC URna 03nu CNcjNjct13jt2\n3I,RN\n3 -

m(Σ,t1) =m(Σ,t2)^. QN 3N 0ā0nCj nN3 a3IjCRN CLURajNj3 -

⎡

⎣d dt

P∈Σ

# » f(P,t)0m

⎤

⎦

R

=

P∈Σ

d dt

# » f(P,t)

R

0m.

\nC U3aL3j 0ȕCNq3ac3a I 0āaCqjCRN Ua aUURaj n j3LUc 3j IȕCNjā<ajCRN Ua aUURaj © I Lcc3Y kXRXjX *2Mi`2 /ǶBM2`iB2

VX .û}MBiBQM

QN UU3II3 ,3Nja3 0ȕCN3ajC3 0n cwcjěL3 LjāaC3IΣ. I3 URCNj ; 0ā~NC Ua -

P∈Σ

# »

GP0m= ^#»^{0 .} 2N 8CcNj CNj3aq3NCa I3 URCNjO. I a3IjCRN 03qC3Nj

Σ

# » GO+OP^{# »}

0m=

Σ

# »

GO0m+

Σ

# »

OP 0m= ^#»⁰ q3,m_Σ·OG^{# »}=

Σ# »

OP0m3j ~NI3L3Nj

# » OG= ¹

m_Σ

P∈Σ

# » OP 0m

/Nc nN a3Uěa3 ,ajācC3N. RN NRj3(xG,yG,zG)I3c ,RRa0RNNā3c 03 # »

OG3j(^x,^y,z)I3c ,RRa0RNNā3c 03 # » OP . RN U3nj 0RN, ā,aCa3 -

xG= ¹ m_Σ

Σx· 0m. yG = ¹ m_Σ

Σy· 0m. zG= ¹ m_Σ

Σz· ^0m.

`3La\n3c -

ġ bC I3 cwcjěL3 LjāaC3I 3cj nN cRIC03 CN0ā8RaL$I3. I3 ,3Nja3 0ȕCN3ajC3 3cj nN URCNj ~u3 0n cRIC03 d ġ bC I3 cwcjěL3 LjāaC3I URccě03 nN āIāL3Nj 03 cwLājaC3 LjāaC3II3. UIN Rn u3 03 cwLājaC3. nccC $C3N

0n URCNj 03 qn3 <āRLājaC\n3 \n3 0n URCNj 03 qn3 03 I aāUajCjCRN 03c Lcc3c. I3 ,3Nja3 0ȕCN3ajC3 UUajC3Nj © ,3j āIāL3Nj 03 cwLājaC3 d

ġ H3 ,3Nja3 0ȕCN3ajC3 3cj ,RN8RN0n q3, ,3Nja3 03 <aqCjā 0Nc I3 ,c 0ȕnN ,@LU 03 U3cNj3na nNC8RaL3Y

Hw,ā3 +@aI3L<N3ATaCc l

(3)

# VX *2Mi`2 /ǶBM2`iB2 /ǶmM 2Mb2K#H2 /2 +Q`Tb mN 3Nc3L$I3 LjāaC3I Σ 3cj ,RLURcā 03 n cRncA 3Nc3L$I3c LjāaC3IcΣiY ¨ ,@\n3 cRncA3Nc3L$I3Σi

3cj ccR,Cā c Lcc3 mi 3j cRN ,3Nja3 0ȕCN3ajC3 Gi. IRac

# » OG_Σ = ¹

m_Σ

∑

n i=1

mi·OG^{# »}i.

H3 ,3Nja3 0ȕCN3ajC3 0ȕnN 3Nc3L$I3 03 ,RaUc 3cj I3

$aw,3Nja3 03c ,3Nja3c 0ȕCN3ajC3Y

bC I3c ,RaUc cRNj 03c cRIC03c CN0ā8RaL$I3c CLLRA

$CI3c I3c nNc Ua aUURaj nu nja3c. I3 ,3Nja3 0ȕCN3aA jC3 03 Iȕ3Nc3L$I3 3cj ~u3 0Nc nN a3Uěa3 ICā © ,3j 3NA c3L$I3Y

G×

Σ

×

G1

G2

Gi

Gn

Σ1

Σ2

Σi

Σn

7ϔόЛЁζ lYSY Ģ +3Nja3 0ȕCN3ajC3 0ȕnN 3Nc3L$I3 03 ,RaUc

+ VX h?ûQ`ĕK2b /2 :mH/BM

ĀNRN,ā V+3Nja3 0ȕCN3ajC3 0ȕnN3 ,Rna$3 UIN3W bRC3Nj(C)nN3 ,Rna$3 0n UIN(Π)3j(Δ)nN3 0aRCj3 0n UIN N3 ,RnUNj Uc(C)Y

HȕCa3 03 I cna8,3 3N<3N0aā3 Ua I aRjjCRN 03 I ,Rna$3 (C)njRna 03 I 0aRCj3 (Δ)3cj ā<I n UaR0nCj 03 I IRN<n3na 03 I ,Rna$3LUa I3 UāaCLěja3 0ā,aCj Ua cRN ,3Nja3 0ȕCN3ajC32π·rGY

S=2π·rG·L

QN ccR,C3 © I ,Rna$3(C)nN3 Lcc3 ICNāŧ\n3λ,RNcjNj3. 0m= λ·dl0ȕRɵ I Lcc3 jRjI3 03 I ,Rna$3 mc =λ·^LY

H URcCjCRN 0n ,3Nja3 0ȕCN3ajC3 03 I ,Rna$3 3cj ,I,nIā3 Ua I a3IjCRN <āNāaI3 - mc·OG^{# »}=

C

# » OP· 0m C,C ,3jj3 a3IjCRN 03qC3Nj -

λ·L·OG^{# »}=

C

# »

OP·λ· ^0l.

Uaěc cCLUIC~,jCRN UnCc 3N N3 Ua3NNj \n3 I UaRE3,jCRN cnCqNj #»r - L·OG^{# »} =

C

# »

OP0l⇒ L·rG=

Cr0l +I,nIRNc LCNj3NNj I cna8,3 3N<3N0aā3 Ua I aRjjCRN 03 I ,Rna$3

S=

S

r·dθ·0l= ^2π

0 dθ·

Cr· 0l=2π

Cr· 0l 2N cn$cjCjnNj

Cr· 0l= L·rG0Nc ,3jj3 ā<ICjā RN a3jaRnq3 $C3N I3 aācnIjj ,@3a,@āY

ĀNRN,ā V+3Nja3 0ȕCN3ajC3 0ȕnN3 cna8,3 UIN3 @RLR<ěN3W bRC3Nj (S) nN3 cna8,3 0n UIN (Π) 3j (Δ) nN3 0aRCj3 0n UIN N3 ,RnUNj Uc(S)Y

Hw,ā3 +@aI3L<N3ATaCc k

(4)

(Δ)

(C)

dl

(C)

dl Π

#»r Q

×^P ^r

r_G

×G

VW +3Nja3 0ȕCN3ajC3 0ȕnN3 ,Rna$3 UIN3

(Δ) (C)

((CC)) Π

#»r Q ds

r rG

×G

V$W ,3Nja3 0ȕCN3ajC3 0ȕnN3 cnaA 8,3 UIN3

7ϔόЛЁζ lYlY Ģ i@āRaěL3c 03 ;nI0CN

H3 qRInL3 3N<3N0aā Ua I aRjjCRN 03 I cna8,3 UIN3 jRnaNNj njRna 03 Iȕu3(Δ)3cj ā<I n UaR0nCj 03 IȕCa3 03 I cna8,3 Ua I IRN<n3na 0n UāaCLěja3 0ā,aCj Ua cRN ,3Nja3 0ȕCN3ajC3Y

V=2π·rG·S

QN 0āLRNja3 ,3jj3 ā<ICjā ,RLL3 I Uaā,ā03Nj3Y QN ccR,C3 © (S)nN3 Lcc3 cna8,C\n3 0m = σ·ds ,RNcjNj3 3jmS= σ·SY

Ta 0ā~NCjCRN -

mS·OG^{# »}=

S

# »

OP· 0m⇒S·OG^{# »}=

S

# » OP·ds cRCj 3N UaRE3,jCRN cnCqNj#»r

S·rG=

Sr·ds

H3 qRInL3 3N<3N0aā Ua I aRjjCRN 03 I cna8,3(S)cȕā,aCj - V =

v

r·dθ·ds= ^2π

0 dθ·

Sr·ds=2π

Sr·ds 0ȕRɵ I a3IjCRN ,@3a,@ā3 -

V=2π·rG·S.

`3La\n3 - IȕnjCICcjCRN 03c j@āRaěL3c 03 ;nI0CN U3aL3j 03 cCLUIC~3a I3 ,I,nI 03 URcCjCRN 0n ,3Nja3 0ȕCN3ajC3 0Nc I L3cna3 Rɵ IȕRN ,RNNţj I3c ,a,jāaCcjC\n3c 0n qRInL3 3j 03 I cna8,3 $Iwā3Y

Hw,ā3 +@aI3L<N3ATaCc :

(5)

kXkX JQK2Mib /ǶBM2`iB2

#»x

#»y

#»z

#»

#»yyy

(Δ)

×

#»δ P×

H A

7ϔόЛЁζ lYkY Ģ KRL3Nj 0ȕCN3ajC3 Ua aUURaj © nN3 0aRCj3 H Lcc3 N3 cn|j URna ,a,jāaCc3a IȕCN3ajC3 \n3 0Nc I3 ,c 0ȕnN

LRnq3L3Nj 03 jaNcIjCRNY TRna nN LRnq3L3Nj 03 aRjjCRN Rn nN LRnq3L3Nj UInc ,RLUI3u3. CI 8nj Ua3N0a3 3N ,RLUj3 I aāUajCjCRN 03 ,3jj3 Lcc3 cna I3 cRIC03Y H3c LRL3Njc 3j UaR0nCjc 0ȕCN3ajC3 ,a,A jāaCc3Nj ,3jj3 aāUajCjCRNY

kXkXRX JQK2Mi /ǶBM2`iB2 T` `TTQ`i ¨ mM TQBMi

QN UU3II3 LRL3Nj 0ȕCN3ajC3 0n cRIC03 b Ua aUURaj © nN URCNj I \nNjCjā URcCjCq3 -

IA(S) =

S

# »

AP²0m

kgm²

kXkXkX JQK2Mi /ǶBM2`iB2 T` `TTQ`i ¨ mM2 /`QBi2

QN UU3II3 LRL3Nj 0ȕCN3ajC3 0n cRIC03 b Ua aUURaj © nN3 0aRCj3 (Δ)I \nNjCjā URcCjCq3

I_Δ(S) =

S

#»δ ∧AP^{# »}₂

0m

kgm²

2N 8CcNj CNj3aq3NCa I3 URCNj ?. UaRE3,jCRN 03 T cna I 0aRCj3(Δ)RN 0ā0nCj - I_Δ(S) =

S

# »

HP²0m=

Sd²_P· 0m q3,dP 0CcjN,3 0n URCNj T © I 0aRCj3(Δ)Y

H3 LRL3Nj 0ȕCN3ajC3 Ua aUURaj © nN3 0aRCj3 3cj I3 LćL3 3N jRnj URCNj 03 I 0aRCj3Y kXkXjX _vQM /2 ;B`iBQM

H3 LRL3Nj 0ȕCN3ajC3 ājNj @RLR<ěN3 n UaR0nCj 0ȕnN3 Lcc3 Ua nN3 0CcjN,3 n ,aaā. CI 3cj jRnERnac URccC$I3 0ȕā,aCa3 I3 LRL3Nj 0ȕCN3ajC3 njRna 0ȕnN u3 0ȕnN cRIC03 \n3I,RN\n3 cRnc I 8RaL3 -

I = M·R²_g q3,MI Lcc3 0n cRIC03 3jRgI3 awRN 03 <CajCRNY

H3 awRN 03 <CajCRN Uaā,Cc3 I aāUajCjCRN 03c Lcc3c njRna 03 Iȕu3 ,RNcC0āaā CNcC I3c jaRCc cRIC03c 03 I ~<na3 lY: RNj I3 LćL3 LRL3Nj 0ȕCN3ajC3 Ua aUURaj © Iȕu3 03 aRjjCRN IRac \n3 I3c Lcc3c cRNj 0Nc nN aUURaj 0Nc nN aUURaj 03 S © eY

kXkX9X JQK2Mib /ǶBM2`iB2 /Mb mM `2Tĕ`2 +`iûbB2M

bRCj nN a3Uěa3R(O,#»x,#»y,#»z). nN URCNjP03 ,RRa0RNNā3cx.y.z0NcRY KRL3Nj 0ȕCN3ajC3 0n cRIC03SUa aUURaj n URCNjO

IO(S) =

S

# »

OP²0mcRCj

=

S

x²+y²+z² 0m 0Nc I3 a3Uěa3(^O,^#»x,#»y,#»z)^Y

KRL3Nj 0ȕCN3ajC3 0n cRIC03SUa aUURaj © Iȕu3(O,#»x)

Hw,ā3 +@aI3L<N3ATaCc 9

(6)

H₁ = 2·^R1. m₁

R2 = 2·R1. H2 = ¹₈ ·R1. m2 ≈ ^{0, 25}·m1

Rext = 2·R1. Rint ≈ 1.68·R1. H3 = ¹₄ ·R1. m3 ≈ ^{0, 15}·m1

7ϔόЛЁζ lY:Y Ģ `wRN 03 <CajCRN

I₍_O,^#»_x₎(S) =

S

#»x ∧OP^{# »}₂

0m=

S(^#»x ∧(x·^#»x +y·^#»y +z·^#»z))²· 0m I₍_O,^#»_x₎(S) =

S

y²+z²

· ^0m 7CNI3L3Nj RN U3nj ā,aCa3 -

I₍_O,^#»_x₎ =

S

y²+z²

· 0m. LRL3Nj 0ȕCN3ajC3 0n cRIC03 Ua aUURaj ©(^O,^#»x)d I₍_O,^#»_y₎ =

S

z²+x²

· 0m. LRL3Nj 0ȕCN3ajC3 0n cRIC03 Ua aUURaj ©(^O,^#»y)d I₍_O,^#»_z₎ =

S

x²+y²

· 0m. LRL3Nj 0ȕCN3ajC3 0n cRIC03 Ua aUURaj ©(^O,^#»z)Y Ta 3uj3NcCRN RN 0ā~NCj nccC -

I₍_O^#»_x^#»_y₎ =

Sz²· 0m. LRL3Nj 0ȕCN3ajC3 0n cRIC03 Ua aUURaj n UIN(O,#»x,#»y)d I₍_O^#»_y^#»_z₎ =

Sx²· 0m. LRL3Nj 0ȕCN3ajC3 0n cRIC03 Ua aUURaj n UIN(O,#»y,#»z)d I₍_O^#»_z^#»_x₎ =

Sy²· 0m. LRL3Nj 0ȕCN3ajC3 0n cRIC03 Ua aUURaj n UIN(O,#»z,#»z)Y kXkX8X _2HiBQMb 2Mi`2 H2b KQK2Mib /ǶBM2`iB2

ġ IO = I₍_O^#»_x^#»_y₎+I₍_O^#»_y^#»_z₎+I₍_O^#»_z^#»_x₎= ¹₂ I₍_O,^#»_x₎+I₍_O,^#»_y₎+I₍_O,^#»_z₎ ġ I₍_O,^#»_x₎= I₍_O^#»_x^#»_y₎+I₍_O^#»_z^#»_x₎

ġ I₍_O,^#»_y₎= I₍_O^#»_x^#»_y₎+I₍_O^#»_y^#»_z₎ ġ I₍_O,^#»_z₎= I₍_O^#»_z^#»_x₎+I₍_O^#»_y^#»_z₎ kXkXeX h?ûQ`ĕK2 /2 >mv;2Mb

bRCj nN cRIC03S03 ,3Nja3 0ȕCN3ajC3G3j 03 Lcc3 mV~<na3 lY9WY

ġ (Δ1). nN3 0aRCj3 UccNj Ua 03 q3,j3na nNCA jCa3#»δd

ġ (Δ2). nN3 0aRCj3 UaIIěI3 UccNj UaGd

ġ d. I 0CcjN,3 3Nja3 I3c 03nu 0aRCj3cY QN NRj3 -

ġ I(^A,^#»^δ) =

S

#»δ ∧AP^{# »} ₂

0m . I3 LRL3Nj 0ȕCN3ajC3 Ua aUURaj ©(Δ1)

Hw,ā3 +@aI3L<N3ATaCc f

(7)

ġ I(^G,^#»^δ) =

S

#»δ ∧GP^{# »} ₂

0m. I3 LRL3Nj 0ȕCN3ajC3 Ua aUURaj ©(Δ2)

ġ HI UaRE3,jCRN 0n URCNjP0n cRIC03Scna(Δ1)

ġ KI UaRE3,jCRN cna(Δ2)Y

#»x

#»y

#»z

#»

#»yy

(Δ1)

×

#»δ

(Δ2) × ^d

P

H K

A G

7ϔόЛЁζ lY9Y Ģ i@āRaěL3 03 ?nw<3Nc MRnc cqRNc \n3 I(^A,^#»^δ) =

S

#»δ ∧AP^{# »}₂

0m=

S

# »

HP²0m= I(^A,^#»^δ) =

S

# »

HK+KP^{# »}₂ 0m I(^A,^#»^δ) =

S

# »

HK²0m+

S2# »

HK·KP^{# »}0m+

S

# » KP²0m H3 Ua3LC3a j3aL3 cȕā,aCj -

S

# »

HK²0m=m·d² QN a3,RNNţj I3 jaRCcCěL3 -

S

# »

KP²0m= I(^G,^#»^δ) BI N3 a3cj3 UInc \nȕ© 0āj3aLCN3a I3 03aNC3a -

S2# »

HK·KP^{# »}0m=2# » HK·

S

# »

KP0m3N 8CcNj CNj3aq3NCa I3 ,3Nja3 0ȕCN3ajC3G

S2# »

HK·KP^{# »}0m=²·HK^{# »}·

S

# »

KG+GP^{# »}0m

=2·HK^{# »}·

S

# »

KG0m+2·HK^{# »}·

S

# » GP0m Ua ,RNcjan,jCRN -

# »

HK ⊥KG^{# »}⇒²·HK^{# »}·

S

# »

KG0m=⁰ Ua 0ā~NCjCRN 0n ,3Nja3 0ȕCN3ajC3 -

S

# »

GP0m=0 7CNI3L3Nj. RN 0ā0nCj I a3IjCRN - I(^A,^#»^δ) =^I(^G,^#»^δ) +^m·d²Y

ĀNRN,ā Vi@āRaěL3 03 ?nw<3NcW H3 LRL3Nj 0ȕCN3ajC3 0ȕnN cRIC03 Ua aUURaj © nN u3 A,#»δ

3cj ā<I n LRA L3Nj 0ȕCN3ajC3 Ua aUURaj © Iȕu3 G,#»δ

. UaIIěI3 3j UccNj Ua I3 ,3Nja3 0ȕCN3ajC3 0n cRIC03. n<L3Njā 0n UaR0nCj 03 I Lcc3 0n cRIC03 Ua I3 ,aaā 03 I 0CcjN,3 cāUaNj I3c 03nu u3cY

I(^A,^#»^δ) =^I(^G,^#»^δ) +^m·d²

ĀNRN,ā V+RaRIICa3W /3 jRnc I3c u3c UaIIěI3c © nN3 0Ca3,jCRN 0RNNā3. ,3InC Ua aUURaj n\n3I I3 LRL3Nj 0ȕCN3ajC3 3cj LCNCLnL 3cj Iȕu3 UccNj UaGY

VX _2HiBQM 2Mi`2 H2b KQK2Mib /ǶBM2`iB2 T` `TTQ`i ¨ /2mt /`QBi2b T`HHĕH2b

Hw,ā3 +@aI3L<N3ATaCc e

(8)

QN c3 UaRURc3 03 0āj3aLCN3a nN3 a3IjCRN 3Nja3 I3c LRL3Njc 0ȕCN3ajC3 Ua aUURaj © 03nu 0aRCj3c UA aIIěI3c \n3I,RN\n3cI(^A,^#»^δ)(^S)3jI(^B,^#»^δ)(^S)0ȕnN cRA IC03SV~<na3 lYfWY

I(^A,^#»^δ)(^S) = I(^G,^#»^δ)(^S) +m·d²_A I(^B,^#»^δ)(^S) = I(^G,^#»^δ)(^S) +m·d²_B /ȕRɵ I a3IjCRN 3Nja3 I3c LRL3Njc 0ȕCN3ajC3

I(^A,^#»^δ)(^S)−I(^B,^#»^δ)(^S) =m·d²_A−m·d²_B q3, dA 3j dB a3cU3,jCq3L3Nj 0CcjN,3 3Nja3 I3c

0aRCj3cΔA.ΔB3jΔGY

#»x

#»y

#»z

#»

#»yy

(ΔA)

×

#»δ

(ΔB) ×

(ΔG) ×

dA

dB

P

H K

L

A G B

7ϔόЛЁζ lYfY Ģ `3IjCRN 3Nja3 I3c LRL3Njc 0ȕCN3ajC3 kXkXdX S`Q/mBib /ǶBM2`iB2

H3c UaR0nCjc 0ȕCN3ajC3 ,a,jāaCc3Nj Iȕ$c3N,3 03 cwLājaC3 0Nc I aāUajCjCRN 03c Lcc3cY

H 0āj3aLCNjCRN 03c UaR0nCjc 0ȕCN3ajC3 c3a 0ā0nCj3 0n ,I,nI 03 IȕRUāaj3na 0ȕCN3ajC3 0Nc I3 ,@UCja3 cnCqNjY

kXjX PTû`i2m` /ǶBM2`iB2

kXjXRX PTû`i2m` /ǶBM2`iB2 2M mM TQBMi

HȕRUāaj3na 0ȕCN3ajC3 cwNj@ājCc3 Iȕ3Nc3L$I3 03c ,a,jāaCcjC\n3c 0ȕCN3ajC3 0n cRIC03Y +3j RUāaj3na 3cj nN3 8RN,jCRN ICNāCa3 3j U3nj ćja3 a3Uaāc3Njā Ua nN3 LjaC,3Y

VX .û}MBiBQM

QN UU3II3 RUāaj3na 0ȕCN3ajC3IO(S)n URCNjO0ȕnN cRIC03SIȕRUāaj3na \nC © jRnj q3,j3na#»u 03 Iȕ3cU,3 ccR,C3 I3 q3,j3na

IO(S)·^#»u =

P∈S

# »

OP∧ ^#»u ∧OP^{# »}

0m.

# VX Ji`B+2 /ǶBM2`iB2 cRCj

ġ (^O,^#»x,#»y,#»z). nN a3Uěa3. 3j(^#»x,#»y,#»z)^{nN3 $c3 d} ġ P. nN URCNj 0n cRIC03S. q3, # »

OP= x·^#»x +y·^#»y +z·^#»z d ġ #»u =α·^#»x +β·^#»y +γ·^#»z. nN q3,j3naY

/āj3aLCNRNc # »

OP∧ ^#»u ∧OP^{# »}

# »

OP∧ ^#»u∧OP^{# »} =

(x·^#»x +y·^#»y +z·^#»z)∧((α·^#»x +β·^#»y +γ·^#»z)∧(x·^#»x +y·^#»y +z·^#»z)) = +α·y²+z²

−β·x·y −γ·x·z

#»x + −α·x·y +β·z²+x²

−γ·y·z

#»y + −α·x·z −β·y·z +γ·x²+y² #»z

Hw,ā3 +@aI3L<N3ATaCc 4

(9)

2N CNjā<aNj cna I3 cRIC03S-

P∈S

# »

OP∧ ^#»u∧OP^{# »}

· 0m=

+α·

P∈S

y²+z²

· 0m −β·

P∈S

x·y· 0m −γ·

P∈S

x·z· 0m

#»x

+ −α·

P∈S

x·^y· ^0m +β·

P∈S

z²+^x²· ^0m −γ·

P∈S

y·^z· ^0m ^#»^y

+ −α·

P∈S

x·z· ^0m −β·

P∈S

y·z· ^0m +γ·

P∈S

x²+y²

· ^0m ^#»z

QN U3nj L3jja3 ,3 aācnIjj cRnc I 8RaL3 0n UaR0nCj 0ȕnN3 LjaC,3 3j 0n q3,j3na #»u

IO(S)·^#»u =

⎛

⎜⎜

⎜⎝ +

P∈S

y²+z²

· 0m −

P∈S

x·y· 0m −

P∈S

x·z· 0m

−

P∈S

x·^y· ^0m +

P∈S

z²+^x²· ^0m −

P∈S

y·^z· ^0m

−

P∈S

x·z· 0m −

P∈S

y·z· 0m +

P∈S

x²+y²

0m

⎞

⎟⎟

⎟⎠

·

⎛

⎜⎜

⎜⎝ α β γ

⎞

⎟⎟

⎟⎠

+3jj3 LjaC,3 3cj ,a,jāaCcjC\n3 03 I aāUajCjCRN 03 I LjCěa3 0ȕnN cRIC03 njRna 0ȕnN URCNj VC,COW 3j 0Nc nN3 $c3 0RNNā3(^#»x,#»y,#»z)Y

QN U3nj URna ,@\n3 cRIC03 0ā~NCa nN3 LjaC,3 0ȕCN3ajC3Y Ta ,RNq3NjCRN. RN URc3

IO(S) =

⎛

⎝ A −F −E

−F B −D

−E −D C

⎞

⎠

O(^#»x,#»y,#»z)

RnIO(S) =

⎛

⎝I₍_O,^#»_x₎ −Pxy −Pxz

−Pxy I₍_O,^#»_y₎ −Pyz

−Pxz −Pyz I₍_O,^#»z)

⎞

⎠

O(^#»x,#»y,#»z)

QN a3,RNNţj cna I 0C<RNI3 03 I LjaC,3 A= I₍_O,^#»_x₎=

P∈S

y²+z²

· 0m. I3 LRL3Nj 0ȕCN3ajC3 0n cRIC03SnjRna 03 Iȕu3(O,#»x)d

B= I₍_O,^#»_y₎=

P∈S

z²+x²

· 0m. I3 LRL3Nj 0ȕCN3ajC3 0n cRIC03SnjRna 03 Iȕu3(^O,^#»y)d C= I₍_O,^#»_z₎ =

P∈S

x²+y²

· 0m. I3 LRL3Nj 0ȕCN3ajC3 0n cRIC03SnjRna 03 Iȕu3(O,#»z)Y Ta ,RNq3NjCRN RN URc3

F=Pxy =

P∈S

x·y· 0m. I3 UaR0nCj 0ȕCN3ajC3 Ua aUURaj UIN(O,#»x,#»y)d E=Pxz=

P∈S

x·z· 0m. I3 UaR0nCj 0ȕCN3ajC3 Ua aUURaj UIN(O,#»x,#»z)d D= Pyz=

P∈S

y·z· 0m. I3 UaR0nCj 0ȕCN3ajC3 Ua aUURaj UIN(^O,^#»y,#»z)^Y

`3La\n3c -

ġ mN3 LjaC,3 0ȕCN3ajC3 0āU3N0 03 I $c3 3j 0n URCNj 03 ,I,nI. CI 3cj 0RN, CLURajNj 03 Uaā,Cc3a ,3c 0RNNā3c d

ġ H LjaC,3 0ȕCN3ajC3 3cj nN3 LjaC,3 cwLājaC\n3 d ġ QN NRLL3 nccC ,3jj3 LjaC,3 j3Nc3na 0ȕCN3ajC3Y

Hw,ā3 +@aI3L<N3ATaCc O

(10)

+ VX .ûi2`KBMiBQM /m KQK2Mi /ǶBM2`iB2 T` `TTQ`i ¨ mM t2 [m2H+QM[m2 Ta 0ā~NCjCRN I3 LRL3Nj 0ȕCN3ajC3 njRna 03 Iȕu3Δ= O,#»

δ cȕā,aCj I_Δ(S) =

P∈S

#»δ ∧OP^{# »} ₂

0m.

/ā,RLURcRNc I3 ,I,nI 0n LRL3Nj 0ȕCN3ajC3 I_Δ(S) =

P∈S

#»δ ∧OP^{# »} ₂

0m=

P∈S

#»δ ∧OP^{# »}

· ^#»δ ∧OP^{# »} 0m.

H3 j3aL3 cRnc IȕCNjā<aI3 U3nj ćja3 ,RNcC0āaā ,RLL3 I3 UaR0nCj LCuj3 03c q3,j3nac #»u. #»v 3jw#»

#»u·(^#»v ∧w^#») = (^#»u,#»v,w#») q3, #»u = ^#»δ . #»v =OP^{# »}3jw#»= ^#»δ ∧OP^{# »}

Y

2N U3aLnjNj I3c j3aL3c 0n UaR0nCj LCuj3 RN N3 ,@N<3 Uc I3 aācnIjj - (u^#»,#»v,#»w) = (^#»v,w,#» #»u) = (w,^#» #»u,#»v) cRCj C,C #»δ ∧OP^{# »}· ^#»δ ∧OP^{# »}

=OP^{# »}∧ ^#»δ ∧OP^{# »} ·^#»δ

H3 LRL3Nj 0ȕCN3ajC3 cȕā,aCj 0RN, -

I_Δ(S) = ^#»δ ·

P∈S

# »

OP∧ _δ∧OP^{# »}

0m QN a3,RNNţj. cRnc IȕCNjā<aI3. IȕRUāaj3na 0ȕCN3ajC3 n URCNjO0n cRIC03SY

TRna 0āj3aLCN3a I3 LRL3Nj 0ȕCN3ajC3 0n cRIC03 b njRna 03 Iȕu3Δ. CI cn|j 0ȕ3{3,jn3a I3 UaR0nCj c,ICa3 0n q3,j3na nNCjCa3 #»δ q3,IO(δ)·^#»δY

I_Δ(S) = ^#»δ · IO(δ)·^#»δ

bC RN URc3IO(S) =

⎛

⎝ A −F −E

−F B −D

−E −D C

⎞

⎠

OB

3j #»δ = (α,β,γ)0Nc I $c3BIRac

I_Δ(S) = (α,β,γ)·

⎛

⎝ A −F −E

−F B −D

−E −D C

⎞

⎠

OB

·

⎛

⎜⎝ α β γ

⎞

⎟⎠

/ VX *?M;2K2Mi /2 TQBMi- i?ûQ`ĕK2 /2 >mv;2Mb ;ûMû`HBbû

bRCj # I $c3(^#»x,#»y,#»z)Y QN a3,@3a,@3 I a3IjCRN 3Nja3 I LjaC,3 0ȕCN3ajC3 3NA0n cRIC03S3j I LjaC,3 0ȕCN3ajC3 3NGI3 ,3Nja3 0ȕCN3ajC3 0n cRIC03Y

Ta 0ā~NCjCRN. IȕRUāaj3na 0ȕCN3ajC3 0n cRIC03Sn URCNjA0Nc I $c3Bcȕā,aCj - IA(S)·^#»u =

P∈S

# »

AP∧ ^#»u ∧AP^{# »} 0m /3 LćL3 IȕRUāaj3na 0ȕCN3ajC3 0n cRIC03Sn URCNjG0Nc I $c3Bcȕā,aCj -

IG(S)·^#»u =

P∈S

# »

GP∧ ^#»u ∧GP^{# »} 0m

Hw,ā3 +@aI3L<N3ATaCc Sz

(11)

2N 0ā,RLURcNj I3 Ua3LC3a - IA(S)·^#»u =

P∈S

# » AG+GP^{# »}

∧ ^#»u∧ AG^{# »}+GP^{# »}

0m

UnCc 3N 0āq3IRUUNj

IA(S)·^#»u =

P∈S

# »

AG∧ ^#»u ∧^{# »}AG

0m+

P∈S

# »

AG∧ ^#»u ∧GP^{# »}

0m +

P∈S

# »

GP∧ ^#»u ∧AG^{# »}

0m+

P∈S

# »

GP∧ ^#»u∧GP^{# »}

0m

H3c 03nuCěL3c 3j jaRCcCěL3c j3aL3c 03 ,3jj3 cRLL3 cRNj NnIc VUa 0ā~NCjCRN 0n ,3Nja3 0ȕCN3ajC3

P∈S

# » GP0m=

#»0W -

P∈S

# »

AG∧ ^#»u∧GP^{# »}

0m= AG^{# »}∧

#»u∧

P∈S

# » GP0m

= ^#»⁰

P∈S

# »

GP∧ ^#»u ∧AG^{# »}

0m=

P∈S

# » GP0m

∧ ^#»u ∧AG^{# »}

= ^#»^{0 .}

Hȕā<ICjā 03qC3Nj -

IA(S)·^#»u =

P∈S

# »

AG∧ ^#»u ∧^{# »}AG

0m+

P∈S

# »

GP∧ ^#»u∧GP^{# »} 0m QN a3,RNNţj 0Nc I3 c3,RN0 j3aL3 IȕRUāaj3na 0ȕCN3ajC3 3NG-

IG(S)·u=

P∈S

# »

GM∧ ^#»u ∧GM^{# »} 0m.

BI a3cj3 © 0āj3aLCN3a I3 Ua3LC3a j3aL3 -

H3c j3aL3c cRnc IȕCNjā<aI3 N3 0āU3N03Nj Uc 03 I Lcc3 VqaC$I3 0ȕCNjā<ajCRNW

P∈S

# »

AG∧ ^#»u ∧AG^{# »}

0m=m # »

AG∧ ^#»u ∧AG^{# »}

/ȕRɵ I3 j@āRaěL3 03 ?nw<3Nc <āNāaICcā

IA(S)·^#»u =IG(S)·^#»u +m # »

AG∧ ^#»u ∧AG^{# »}

/āj3aLCNRNc # »

AG∧ ^#»u ∧AG^{# »}

3N 8RN,jCRN 03c ,RRa0RNNā3c 03c 03nu q3,j3nac

#»u = (α,β,γ) 3j # »

AG = (^a,^b,c)^.

$c3(^#»x,#»y,#»z)-

# »

AG∧ ^#»u∧AG^{# »}

=

⎛

⎝b²+c² −a·b −a·c

−a·b a²+c² −b·c

−a·c −b·c a²+b²

⎞

⎠·

⎛

⎝ α βγ

⎞

⎠

IA(S)·^#»u =IG(S)·^#»u+m·

⎛

⎝b²+c² −a·b −a·c

−a·b a²+c² −b·c

−a·c −b·c a²+b²

⎞

⎠·

⎛

⎝ α β γ

⎞

⎠ QN URc3 URna I3c LjaC,3c 0ȕCN3ajC3 3N 3j ; -

Hw,ā3 +@aI3L<N3ATaCc SS

(12)

IA(S) =

⎛

⎝ AA −FA −EA

−FA BA −DA

−EA −DA CA

⎞

⎠

A(^#»x,#»y,#»z)

3j IG(S) =

⎛

⎝ AG −FG −EG

−FG BG −DG

−EG −DG CG

⎞

⎠

G(^#»x,#»y,#»z)

QN 0ā0nCj. 0Nc I $c3(^#»x,#»y,#»z). I a3IjCRN 3Nja3 ,3c LjaC,3c -

⎛

⎝ A_A −F_A −E_A

−F_A B_A −D_A

−E_A −D_A C_A

⎞

⎠

A

=

⎛

⎝A_G −F_G −E_G

−F_G B_G −D_G

−E_G −D_G C_G

⎞

⎠

G

+m·

⎛

⎝b²+c² −a·b −a·c

−a·b a²+c² −b·c

−a·c −b·c a²+b²

⎞

⎠

q3,

AA= AG+m·b²+c² BA= BG+m·a²+c² CA=CG+m·a²+b²

DA=DG+m·b·c E_A=E_G+m·a·c

FA= FG+m·a·b

VlYSW

QN a3jaRnq3 cna I 0C<RNI3 I3 j@āRaěL3 03 ?nw<3Nc URna ,@,nN 03c u3c 0n a3Uěa3Y 2 VX *?M;2K2Mi /2 #b2

+RNNCccNj I LjaC,3 0ȕCN3ajC3 0n cRIC03S3N nN URCNjA0Nc I $c3B₁. RN c3 UaRURc3 03 0āj3aLCN3a ,3jj3 LjaC,3 3N ,3 LćL3 URCNj 0Nc I $c3B2Y

Ji`B+2 /2 Sbb;2 , QN UU3II3PB1,B2. I LjaC,3 03 Ucc<3 03 I $c3B1© I $c3B2,3jj3 LjaC,3 3cj ,RNcjCjnā3 3N ,RIRNN3c 03c ,RRa0RNNā3c 03c q3,j3nac 03 I NRnq3II3 $c3B2ā,aCjc 0Nc I $c3 0ȕRaCA

<CN3B₁Y QN IȕUU3II3 nccC LjaC,3 03 ,@N<3L3Nj 03 $c3. ,3jj3 LjaC,3 3cj nN3 LjaC,3 CNq3acC$I3Y

*?M;2K2Mib /2 #b2 , bRCjIA(S)_B₁ 3jIA(S)_B₂ I3c LjaC,3c 0ȕCN3ajC3 0ȕnN cRIC03Sa3cU3,jCq3L3Nj 0Nc I $c3B₁3j I $c3B2. 3jPB₁,B2 I LjaC,3 03 Ucc<3 03 I $c3B₁© I $c3B2. RN IRac -

IA(S)_B₂ = P_B⁻₁¹_,B₂· IA(S)_B₁·PB₁,B2

q3,P_B⁻₁¹_,B₂ I LjaC,3 CNq3ac3 03PB1,B2Y

kXjXkX S`QT`Bûiûb 2i /B`2+iBQMb T`BM+BTH2b /2 H Ki`B+2 /ǶBM2`iB2

H LjaC,3 0ȕCN3ajC3 3cj nN3 LjaC,3 cwLājaC\n3. nN3 cCLUI3 ājn03 Lj@āLjC\n3 03 I LjaC,3 0ȕCN3ajC3 NRnc U3aL3j 03 0Ca3 \n3 -

ġ H3c qI3nac UaRUa3c 03 I LjaC,3 cRNj aā3II3c d

ġ BI 3uCcj3 nN3 $c3 Raj@RNRaLā3 0Nc I\n3II3 I LjaC,3 3cj 0C<RNI3Y VX t2b T`BM+BTmt /ǶBM2`iB2- #b2 T`BM+BTH2 /ǶBM2`iB2

BI 3uCcj3 URna jRnj URCNj nN3 $c3 Raj@R<RNI3 03 q3,j3nac UaRUa3cB = x^#»,#»

y,#»

z

Y /Nc ,3jj3 $c3 I LjaC,3 0ȕCN3ajC3 0n cRIC03Sn URCNj A3cj nN3 LjaC,3 0C<RNI3 -

IA(S) =

⎛

⎝A 0 0

0 B 0

0 0 C

⎞

⎠

A,B

.

+3jj3 $c3 3cj UU3Iā3 $c3 UaCN,CUI3 0ȕCN3ajC3 n URCNj Y H3c u3c A,#»

x

. A,#»

y

3j A,#»

z

cRNj I3c u3c UaCN,CUnu 0ȕCN3ajC3 3jA.B3jC I3c LRL3Njc UaCN,CUnu 0ȕCN3ajC3Y

Hw,ā3 +@aI3L<N3ATaCc Sl

(13)

`3La\n3c -

ġ TRna jRnc I3c cRIC03c Uaāc3NjNj 03c cwLājaC3c 0Nc I aāUajCjCRN 03c Lcc3c. CI 3cj 8,CI3 03 0āj3aLCA N3a I3c u3c UaCN,CUnu 3N cȕUUnwNj cna ,3c cwLājaC3cY

ġ bC I3 URCNj 0ȕā,aCjna3 3cj I3 ,3Nja3 0ȕCN3ajC3. RN UaI3 IRac 03 $c3 ,3NjaI3 3j 03 LRL3Njc ,3Njanu 0ȕCN3ajC3 d

ġ H3c LRL3Njc ,3Njanu 0ȕCN3ajC3 cRNj LCNCLY

MRnc IIRNc qāaC~3a \n3 I3c UajC,nIaCjāc <āRLājaC\n3c 0Nc I aāUajCjCRN 03c Lcc3c VcwLājaC3. u3 03 aāqRInjCRNW c3 a3jaRnq3Nj 0Nc I 8RaL3 03 I LjaC,3 0ȕCN3ajC3Y

aQHB/2 p2+ mM THM /2 bvKûi`B2 HRac\n3 I3 cRIC03 URccě03 nN UIN 03 cwLājaC3. I3c UaR0nCjc 0ȕCN3aA jC3 ,RLURajNj I NRaLI3 n UIN 03 cwLājaC3 cRNj NnIcY

H3 cRIC03S03 I ~<na3 lYe URccě03 nN UIN 03 cwA LājaC3(O,#»x,#»y). Iȕu3(O,#»z)3cj NRaLI © ,3 UINY BI c3L$I3 En0C,C3nu C,C 03 0āj3aLCN3a I LjaC,3 0ȕCN3aA jC3 03 ,3 cRIC03 3N nN URCNj 0n UIN 03 cwLājaC3Y

IO(S) =

⎛

⎝IOx Pxy 0 Pxy IOy 0

0 0 IOz

⎞

⎠

O,B

pāaC~RNc \n3 I3c UaR0nCjc 0ȕCN3ajC3.Pxz3jPyz0Nc I3 a3Uěa3(^O,^#»x,#»y,#»z)^{cRNj NnIcY}

#»x

#»y

#»z

x y z P1

P2

7ϔόЛЁζ lYeY Ģ bRIC03 q3, S UIN 03 cwLājaC3

E= Pxz=

P∈S

x·z· 0m3jD= Pyz =

P∈S

y·z· 0m 2N 0ā,RLURcNj IȕCNjā<ajCRN cna I3c 03nu 03LCĢcRIC03c cwLājaC\n3cS13jS2-

E= Pxz =

P∈S₁

x·z· 0m+

P∈S2

x·z· 0m

H3 UIN(O,#»x,#»y)3cj UIN 03 cwLājaC3Y QN 3{3,jn3 I3 ,@N<3L3Nj 03 qaC$I3z → −zURna ,I,nI3a I 03nuCěL3 CNjā<aI3Y +RLUj3 j3Nn 0n UIN 03 cwLājaC3. I3c $RaN3c 0ȕCNjā<ajCRN ,@N<3NjP∈ S2→P∈ S1

0ȕRɵ -

P∈S2

x·z· 0m=−

P∈S1

x·z· 0m⇒E=Pxz =0 QN ,RNcjj3 0RN, \n3E=03j RN 0āLRNja3 03 LćL3D=0Y

H LjaC,3 0ȕCN3ajC3 0n cRIC03 Sn URCNjO0Nc I $c3 B = (^#»x,#»y,#»z)q3, #»z I NRaLI3 n UIN 03 cwLājaC3.03qC3Nj -

IO(S) =

⎛

⎝IOx Pxy 0 Pxy IOy 0

0 0 IOz

⎞

⎠

O,B

=

⎛

⎝ A −F 0

−F B 0

0 0 C

⎞

⎠

O,B

bC I3 cRIC03 URccě03 nN UIN 03 cwLājaC3. IRac I LjaC,3 0ȕCN3ajC3. ā,aCj3 3N nN URCNj 03 ,3 UIN 3j 0Nc nN3 $c3 0RNj nN q3,j3na 3cj I NRaLI3 n UIN. ,RLURaj3 03nu UaR0nCjc 0ȕCN3ajC3 NnIcY H3c 03nu UaR0nCjc 0ȕCN3ajC3 NnIc cRNj ,3nu ,RNj3NNj I NRaLI3 n UINY

Hw,ā3 +@aI3L<N3ATaCc Sk

(14)

aQHB/2 p2+ /2mt THMb /2 bvKûi`B2 bC nN cRA IC03 URccě03 03nu UINc 03 cwLājaC3. 3N ,@RCcCcA cNj 0ȕā,aCa3 I LjaC,3 0ȕCN3ajC3 3N nN URCNjO 03 I 0aRCj3 0ȕCNj3ac3,jCRN 03c 03nu UINc 3j 0Nc nN3

$c3Ba3cU3,jNj ,3jj3 cwLājaC3. IRac I3c jaRCc UaRA 0nCjc 0ȕCN3ajC3c cRNj NnIcY

IO(S) =

⎛

⎝IOx 0 0

0 IOy 0

0 0 IOz

⎞

⎠

O,B

#»x

#»y

#»z

#»x

#»z

#»y

x y Pz1

P2

7ϔόЛЁζ lY4Y Ģ bRIC03 q3, l UINc 03 cwLājaC3 aQHB/2 p2+ mM2 bvKûi`B2 /2 `ûpQHmiBQM bC Iȕu3

(O,#»z)3cj nN u3 03 aāqRInjCRN LjāaC3II3. I3 cRIC03 URccě03 IRac nN3 CN~NCjā 03 UIN 03 cwLājaC3 Raj@RA

<RNnuY H3c UaR0nCjc 0ȕCN3ajC3 cRNj 0RN, jRnc NnIc 3j I LjaC,3 3cj 0C<RNI3 0Nc jRnj3 $c3 ,RNj3NNj Iȕu3 03 aāqRInjCRN 3j 3N jRnj URCNj 03 ,3j u3Y

H LjaC,3 0ȕnN cRIC03 03 aāqRInjCRN 3uUaCLā3 3N nN URCNjO03 cRN u3 03 aāqRInjCRN 3j 0Nc nN3 $c3 a3cU3,jNj ,3jj3 cwLājaC3 cȕā,aCj -

IO(S) =

⎛

⎝A 0 0

0 A 0

0 0 C

⎞

⎠

O,B

#»z

#»x

#»y

7ϔόЛЁζ lYOY Ģ bRIC03 03 aāqRInjCRN

+RLUj3 j3Nn 03 I cwLājaC3 03 aāqRInjCRN I3c LRL3Njc 0ȕCN3ajC3 Ua aUURaj nu (^O,^#»x)^3j(^O,^#»y)^cRNj ā<nuY

A=

P∈S

y²+z²

· 0m=B=

P∈S

x²+z²

· 0m

C=

P∈S

x²+y²

· 0m=2·A−2·

P∈S

z²· 0m

Hw,ā3 +@aI3L<N3ATaCc S:

(15)

aQHB/2 THM /ǶûTBbb2m` Mû;HB;2#H2 QN c3 UI,3 cna nN URCNj O0n UIN q3, (O,#»z)I NRaLI3 n UINY HȕCNjā<ajCRN cnCqNj I 0Ca3,jCRN 03 I NRaA LI3 n UIN 3cj NnII3 VI3c $RaN3c 0ȕCNjā<ajCRN cRNj NnII3cW 0ȕRɵ -

IO(S) =

⎛

⎝ A −F 0

−F B 0

0 0 A+B

⎞

⎠

O,B

Q

#»z #»x

#»y

7ϔόЛЁζ lYSzY Ģ bRIC03 0ȕāUCcc3na Nā<IC<3$I3

A=

P∈Sy²+z² 0m=

P∈Sy²0m B=

P∈Sx²+z²0m=

P∈Sx²0m C=

P∈Sx²+y²0m= A+B D=

P∈Sy·z· 0m=0 E=

P∈Sx·z· 0m=0

.Bb[m2 THM /ǶûTBbb2m` Mû;HB;2#H2 TRna nN 0Cc\n3 UIN. 3NO,3Nja3 0n 0Cc\n3 3j 0Nc nN3 $c3Bj3II3

\n3 #»z 3cj I NRaLI3 n UIN

IO(S) =

⎛

⎝A 0 0

0 A 0

0 0 2·A

⎞

⎠

O,B

Hw,ā3 +@aI3L<N3ATaCc S9