:YS SmBbbM+2 /2b 2zQ`ib 2tiû`B2m`b

(1)

+@UCja3

9 SmBbbM+2 2i ûM2`;B2

:YS SmBbbM+2 /2b 2zQ`ib 2tiû`B2m`b

O

#»x

#»y

#»z

E 0μP

# » V_P/_R bRCj nN 3Nc3L$I3 LjāaC3I V2W. 3N LRnq3L3Nj Ua aUA

URaj © nN a3Uěa3RY

Hȕ3Nc3L$I3 LjāaC3I V2W 3cj cRnLCc © nN3 ,jCRN Lā,A NC\n3 VURN,jn3II3. 03 Ua3ccCRN. © 0CcjN,3. 3j,YW a3Uaāc3Njā3 Ua nN3 03NcCjā 03 8Ra,3 # »

f(P)VRn ,@LU 03 8Ra,3 W a3IjCq3

f(P)a3IjCq3L3Nj © 0μ0Nc I3 LRnq3A L3Nj 03 V2W Ua aUURaj n a3Uěa3R. 3cj -

Pf# »(P)→E/R =

E

# » f(P)·# »

V_P/_R 0μY

0μa3Uaāc3Nj3 cRCj nN āIāL3Nj 03 Lcc3 V0mW cRCj 03 cna8,3 V0sW Rn 03 qRInL3 V 0vW cnCqNj I Njna3 03 I 03NcCjā 03 8Ra,3Y

H UnCccN,3 cȕ3uUaCL3 3N rjjY

H UnCccN,3 0āU3N0 0n aā8āa3NjC3I. IRac\n3 I3 aā8āa3NjC3I 0ȕājn03 3cj nN aā8āa3NjC3I <ICIā3N. RN UaI3 IRac 03 UnCccN,3 <ICIā3NN3Y

[n3I\n3c UnCccN,3c -

SmBbbM+2 /ûp2HQTTû2 T` H T2bMi2m` H3 ,@LU <aqCjjCRNN3I 3cj nN ,@LU qRInLC\n3. CI <Cj cna ,@\n3 āIāL3Nj 03 Lcc3 0m03 Iȕ3Nc3L$I3 LjāaC3IEY H 03NcCjā 03 8Ra,3 cȕā,aCj # »

f(P) =ρ(P)·

# » g(P)q3,

ġ ρ(P)- I 03NcCjā 0n cwcjěL3 LjāaC3I n URCNj T d

ġ # »

g(P)- I3 ,@LU <aqCjjCRNN3I n URCNj TY

H UnCccN,3 0āq3IRUUā3 Ua I U3cNj3na cna Iȕ3Nc3L$I3 LjāaC3I 2 3cj -

P#»g→E/R=

E

ρ(P)·# » g(P)·# »

V_P/_R 0vY

SmBbbM+2 /ûp2HQTTû2 T` H2b +iBQMb /2 T`2bbBQM H3c ,jCRNc 03 Ua3ccCRN cRNj nN3 03NcCjā 03 8Ra,3 cna8,C\n3. IȕāIāL3Nj 0ȕCNjā<ajCRN 3cj 0RN, 0μ = 0sY Hȕ,jCRN 03 I Ua3ccCRN 3cj 0ā~NC3 Ua -

# »

f(P) = −p(P)·# » n(P)q3,

ġ p(P)- I Ua3ccCRN n URCNj T d ġ # »

n(P)- I NRaLI3 © I cna8,3 n URCNj TY

H UnCccN,3 0āq3IRUUā3 Ua I3c ,jCRNc 03 Ua3ccCRN cȕ3uUaCL3 -

P#»p→E/R=

E

−p(P)·# »

n(P)·V# »_P/_R 0sY

SzO

(2)

:Yl *b /m bQHB/2 BM/û7Q`K#H2

:YlYS

^úMQM+û

H UnCccN,3 Lā,NC\n3 0āq3IRUUā3 Ua I3c ,jCRNc Lā,NC\n3c <CccNj cna nN cRIC03 b n ,Rnac 03 cRN LRnq3L3Nj Ua aUURaj © nN a3Uěa3R3cj ā<I3 n ,RLRL3Nj 0n jRac3na ,CNāLjC\n3 0n cRIC03 b 0Nc cRN LRnq3L3Nj Ua aUURaj n aā8āa3NjC3IR3j 0n jRac3na 03c ,jCRNc Lā,NC\n3c 3ujāaC3na3c

<CccNj cna bY

Pf# »(P)→S/R = V_S/_R

⊗{F_f_→_S}

V .ûKQMbi`iBQM

bRCj nN cRIC03 b 3N LRnq3L3Nj Ua aUURaj © nN a3Uěa3RY

H3 LRnq3L3Nj 03 b Ua aUURaj ©R3cj ,a,jāaCcā Ua I3 jRac3na ,CNāLjC\n3 - V_S/_R

=

Ω# »_S/_R

# » V_A_∈_S/_R

A

Y

H3 cRIC03 b 3cj cRnLCc 3N ,@\n3 URCNj T © nN3 ,jCRN Lā,NC\n3 ,a,jāaCcā3 Ua I 03NcCjā 03 8Ra,3

# »

f(P)Y +3jj3 ,jCRN Lā,NC\n3 āIāL3NjCa3 3cj 0ā,aCj3 Ua I3 jRac3na - # »

0F= # »

f(P)0μ

#»0

P

Y

Hȕ,jCRN Lā,NC\n3 <IR$I3 cna I3 cRIC03 b 3cj 0āj3aLCNā3 3N CNjā<aNj Iȕ,jCRN āIāL3NjCa3 3N ,@\n3 URCNj cna I jRjICjā 0n cRIC03 0ȕRɵ -

{F_f_→_S}=

⎧⎪

⎨

⎪⎩

# » R_f_→_S=

S

# » f(P)0μ

# » KA.f→S=

S

# »

AP∧# »

f(P)0μ

⎫⎪

⎬

⎪⎭

A

Y

Ta 0ā~NCjCRN. I UnCccN,3 0āq3IRUUā3 Ua ,3jj3 ,jCRN Lā,NC\n3 cna I3 cRIC03 b cȕ3uUaCL3 - Pf# »(P)→S/R =

S

# »

f(P)·V# »_P_∈_S/_R0μY

+RLUj3 j3Nn 03 I a3IjCRN 03 ,RLURcCjCRN 03c qCj3cc3c 0n cRIC03 -

# »

V_P_∈_S/_R = # »

V_A_∈_S/_R+ # »

Ω_S/_R∧# »

AP I UnCccN,3 0āq3IRUUā3 03qC3Nj -

Pf# »(P)→S/R =

S

# »

f(P)·# »

V_A_∈_S/_R+# »

Ω_S/_R∧# »

AP

0μ

=

S

# »

f(P)·V# »_A_∈_S/_R0μ+

S

# »

f(P)·Ω# »_S/_R∧AP# »

0μ

3N U3aLnjNj I3c j3aL3c 0n UaR0nCj LCuj3 UnCc 3N cRajNj 03c CNjā<aI3c I3c j3aL3c ,RNcjNjc URna I

SSz

(3)

:Yk TnCccN,3 03c 3{Rajc CNjāaC3nac

qaC$I3 0ȕCNjā<ajCRNY

Pf# »(P)→S/R =

S

# »

f(P)·# » V_A_∈_S/_R0μ+

S

# »

Ω_S/_R·# »

AP∧# »

f(P) 0μ

= # » V_A_∈_S/_R·

S

# »

f(P)0μ+# » Ω_S/_R·

S

# »

AP∧# »

f(P) 0μ

bRnc ,3jj3 8RaL3. RN a3,RNNţj I3 ,RLRL3Nj 0n jRac3na ,CNāLjC\n3 3j 0n jRac3na 03c ,jCRNc Lā,A NC\n3c jaNcLCccC$I3c -

Pf# »(P)→S/R =

# » Ω_S/_R

# » V_A_∈_S/_R

A

⊗

⎧⎪

⎨

⎪⎩

S

# » f(P)0μ

S

# »

AP∧# »

f(P)0μ

⎫⎪

⎬

⎪⎭

A

= V_S/_R

⊗{F_f_→_S}

`3La\n3 S - H3 ,RLRL3Nj 03c jRac3nac N3 0āU3N0 Uc 0n URCNj ,@RCcC LCc I3c 03nu jRac3nac 0RCq3Nj ćja3 aā0nCjc 3N nN LćL3 URCNj qNj 0ȕ3{3,jn3a I3 ,I,nIY QN ,@RCcCj I3 URCNj 03 aā0n,jCRN \nC U3aL3j I3 ,I,nI I3 UInc cCLUI3 URccC$I3Y

`3La\n3 l - H UnCccN,3 ,I,nIā3 0āU3N0 0n a3Uěa3 0Nc I3\n3I RN I ,I,nI3Y bC I3 a3Uěa3 03 ,I,nI 3cj <ICIā3N. RN UaI3 IRac 03 UnCccN,3 <ICIā3NN3Y

:Yk SmBbbM+2 /2b 2zQ`ib BMiû`B2m`b

:YkYS

SmBbbM+2 /2b 2zQ`ib /2 HBBbQM QN c3 UaRURc3 LCNj3NNj 03 0āj3aLCN3a I UnCccN,3 03c 3{Rajc CNjāaC3nac © nN cwcjěL3 03 cRIC03c CN0ā8RaL$I3cY

bRC3Nj I3 cwcjěL3 LjāaC3IΣ,RNcjCjnā 03 03nu cRIC03cS₁ 3jS₂ 3N LRnq3L3Nj Ua aUURaj © nN a3Uěa3R3j ICāc 3Nja3 3nu Ua nN3 ICCcRNL₁₂Y

H3c UnCccN,3c 0āq3IRUUā3c Ua I3c ,jCRNc 3uA jāaC3na3c ©S₁3jS₂a3cU3,jCq3L3Nj cna ,@,nN 03 ,3c cRIC03c 3N LRnq3L3Nj Ua aUURaj n a3Uěa3 Rcȕā,aCq3Nj -

S₁

S₂ L₁₂

Σ

7ϔόЛЁζ :YS Ģ TnCccN,3 03c BNj3aĢ3{Rajc P(^S¹^→^S¹/R)=P(^Σ^→^S¹/R)+P₍_S₂_→_S₁_/_R)

P(^S²^→^S²/R)=P(^Σ^→^S²/R)+P₍_S₁_→_S₂_/_R) 3N cRLLNj ,3c 03nu ā<ICjāc

P(^S¹^→^S¹/R)+P(^S²^→^S²/R)=P(^Σ^→^S¹/R)+P(^Σ^→^S²/R)+P₍_S₂_→_S₁_/_R)+P₍_S₁_→_S₂_/_R) q3,P_(S₂_→_S₁_/_R)=

F_S₂_→_S₁

⊗

V_S₁_/_R

3jP_(S₁_→_S₂_/_R)=

F_S₁_→_S₂

⊗

V_S₂_/_R

P(^S¹^→^S¹/R)+P(^S²^→^S²/R)=P(^Σ^→^Σ/R)+

FS2→S1

⊗

V_S₁_/_R +

FS1→S2

⊗

V_S₂_/_R P(^S¹^→^S¹/R)+P(^S²^→^S²/R)=P(^Σ^→^Σ/R)+

F_S₂_→_S₁

⊗

V_S₁_/_R

−

F_S₂_→_S₁

⊗

V_S₂_/_R

SSS

(4)

P(^S¹^→^S¹/R)+P(^S²^→^S²/R)=P(^Σ^→^Σ/R)+

FS2→S1

⊗

V_S₁_/_R

−

V_S₂_/_R P(^S¹^→^S¹/R)+P(^S²^→^S²/R)=P(^Σ^→^Σ/R)+

F_S₂_→_S₁

⊗

V_S₁_/S₂

QN a3,RNNţj I UnCccN,3 03c 3{Rajc 3ujāaC3nac cna I3 cwcjěL3 LjāaC3IΣ P(^Σ→Σ/R)

3j I UnCccN,3 0CccCUā3 0Nc I ICCcRN 3Nja3 I3c 03nu cRIC03c 03Σ P₍_S₂_→_S₁_/_R)+P₍_S₁_→_S₂_/_R)=

FS2→S1

⊗

V_S₁_/S₂ Y

+3jj3 UnCccN,3 3cj CN0āU3N0Nj3 0n a3Uěa3 03 ,I,nIY QN NRLL3 ,3jj3 UnCccN,3. UnCccN,3 03c CNj3aĢ3{Rajc 3j RN I NRj3 -

P₍_S₁_↔_S₂₎=P₍_S₂_→_S₁_/_R)+P₍_S₁_→_S₂_/_R)

P₍_S₁_↔_S₂₎=

FS2→S1

⊗

V_S₁_/S₂

RnP₍_S₁_↔_S₂₎=

FS1→S2

⊗

V_S₂_/S₁

`3La\n3 - H UnCccN,3 03c CNj3aA3{Rajc 03 ICCcRN 3cj CN0āU3N0Nj3 0n a3Uěa3 3j 0n URCNj 03 aā0n,jCRN ,@RCcC URna I ,I,nI3a. ,RLL3 URna jRnj ,RLRL3Nj. RN ,@RCcCa nN URCNj En0C,C3nu URna Iȕā,aCjna3 03c jRac3nacY

:YkYl

GBBbQM ûM2`;ûiB[m2K2Mi T`7Bi2

QN 0Cj \nȕnN3 ICCcRN 3Nja3 cRIC03 3cj āN3a<ājC\n3L3Nj Ua8Cj3 IRac\n3 I UnCccN,3 03c CNj3aA3{Rajc 03 ICCcRN 3cj NnII3 -

P_S₁_↔_S₂=0Y

:YkYk

*QMi+i TQM+im2H `û2H

I

#»n

#»t

#»n∧#»t

# » R1→2

# » V_I_∈_2/1

+ǃN3 03 8aRjj3L3Nj

S₁ S2

7ϔόЛЁζ :Yl Ģ +RNj,j aā3I QN c3 UaRURc3 03 0āj3aLCN3a © \n3II3c ,RN0CjCRNc nN3

ICCcRN URN,jn3II3 3cj āN3a<ājC\n3L3Nj Ua8Cj3Y

bRC3Nj 03nu cRIC03c S1 3j S2 3N ,RNj,j URN,jn3I 3N I V~<na3 :YlWY H3 jRac3na 03c ,jCRNc jaNcLCccC$I3c Ua I ICCcRN URN,jn3II3 aā3II3 3N B 0n cRIC03S₁ cna I3 cRIC03S₂ cȕā,aCj -

{A₁_→₂}=

# »

R₁_→₂ =N₁₂·n#»+# » T₁₂

# »

KI.1→2 =Mp₁₂·n#»+# » Mr₁₂

I

ġ n#». I NRaLI3 n UIN jN<3Nj n ,RNj,j RaC3Njā3 03S₁q3acS₂.

ġ N₁₂. I UaRE3,jCRN cna #»n03 I aācnIjNj3 0n jRac3na

# » R₁_→₂.

ġ # »

T₁₂. I ,RLURcNj3 0Nc I3 UIN jN<3Nj 03# » R₁_→₂VI 0Ca3,jCRN 3cj © UaCRaC CN,RNNn3W.

ġ Mp₁₂. I UaRE3,jCRN cna #»n 0n LRL3Nj 0n jRac3na VLRL3Nj 03 UCqRj3L3Nj njRna 03 Iȕu3(I.#»n)W.

ġ # »

Mr12. I ,RLURcNj3 0Nc I3 UIN jN<3Nj VLRL3Nj 03 aRnI3L3NjWY

SSl

(5)

:Yk TnCccN,3 03c 3{Rajc CNjāaC3nac

H3 LRnq3L3Nj 03S₂Ua aUURajS₁3cj 0ā~NC3 Ua I3 jRac3na ,CNāLjC\n3 cnCqNj - V_2/1

=

# »

Ω_2/1 =Ωp₁₂·#»n+ # »

Ωr₁₂

# » V_I_∈_2/1

I

ġ Ωp12- ,RLURcNj3 03 UCqRj3L3Nj njRna 03(I.n#»).

ġ # »

Ωr₁₂- ,RLURcNj3 03 aRnI3L3Nj 0Nc I3 UIN jN<3NjY V .ûi2`KBMiBQM /2 H `ûbmHiMi2

H3c IRCc 03 +RnIRL$ U3aL3jj3Nj 03 0āj3aLCN3a I aācnIjNj3 03 Iȕ,jCRN aā3II3 3Nja3 03nu cRIC03c 3N ,RNj,j URN,jn3I. 3N 8RN,jCRN 03c jaRCc ,c cnCqNj -

#b2M+2 /2 7`Qii2K2Mi , IRac I aācnIjNj3 N3 ,RLURaj3 \nȕnN3 ,RLURcNj3 NRaLI3. I ,RLURA cNj3 jN<3NjC3II3 3cj NnII3 \n3I\n3 cRCj I3 LRnq3L3Nj -

# »

R₁_→₂ =N₁₂·#»n

# » T₁₂= #»

0

6`Qii2K2Mi 2i ;HBbb2K2Mi , I qCj3cc3 03 <ICcc3L3Nj 3cj NRN NnII3 V # » V_I_∈_2/1 = #»

0 3j # »

V_I_∈_2/1·n#»=0WY H3c IRCc 03 +RnIRL$ Uaā,Cc3Nj IRac \n3 ,RLURcNj3 jN<3NjC3II3 03 I aācnIjNj3 3cj ,RICNāCa3 n q3,j3na # »

V_I_∈_2/1 LCc 03 c3Nc RUURcā VI3c 8aRjj3L3Njc cȕRUURc3Nj n 0āUI,3L3NjW 3j \n3 I3 LR0nI3 03 Iȕ3{Raj jN<3NjC3I 3cj UaRURajCRNN3I © I ,RLURcNj3 NRaLI3 -

# » V_I_∈_2/1∧# »

T₁₂= #»

0 3j # » V_I_∈_2/1·# »

T₁₂< 0 # »

T₁₂=f·|N₁₂|

f3cj I3 ,R3|,C3NjV8,j3naW 03 8aRjj3L3Nj 3Nja3 I3c 03nu cRIC03c. CI 0āU3N0 03 I Njna3 03c LjāaCnu 3N ,RNj,j. 03 I \nICjā 03c cna8,3c 8aRjjNj3c 3j 03 I In$aC~,jCRNY H aācnIjNj3 03 Iȕ,jCRN 03 ,RNj,j 3Nja3 I3c 03nu cRIC03c 3cj cna I3 ,ǃN3 03 8aRjj3L3NjV~<na3 :YlWY bC RN NRj3φI3 03LCAN<I3 n cRLL3Nj IRacf=jNφY

6`Qii2K2Mi bMb KQmp2K2Mi # » V_I_∈_2/1 = #»

0. I3 LR0nI3 03 I ,RLURcNj3 jN<3NjC3II3 Nȕ3cj IRac ,RNNn

\n3 Ua nN3 CNā<ICjā.

# »

T12f·|N12|

3j c 0Ca3,jCRN N3 U3nj ćja3 0āj3aLCNā3 VI aācnIjNj3 3cj 0Nc I3 ,ǃN3 03 8aRjj3L3NjWY TRna 0āA j3aLCN3a I3c ,RLURcNj3c. RN c3 UI,3 © I ICLCj3 0n <ICcc3L3Nj. RN U3nj IRac ā,aCa3 -

# »

T₁₂=f·|N₁₂|Y

H 0Ca3,jCRN 3cj 0ā0nCj3 03 I 0Ca3,jCRN cnUURcā3 0n LRnq3L3Nj q3,

# »

V_I_∈_2/1∧n#»= #»

0 3j # »

V_I_∈_2/1·n < 0#» 3N URcNj # »

V_I_∈_2/1I qCj3cc3 cnUURcā3 03 <ICcc3L3Nj 3N BY

¨ ,3c jaRCc ,c RN U3nj aERnj3a I3 ,c _QmH2K2Mi bMb ;HBbb2K2Mi , # »

V_I_∈_2/1 = #»

0. cC I3c 8aRjj3L3Njc N3 cRNj Uc NnIc. IRac RN c3 jaRnq3 0Nc I3 ,c Uaā,ā03Nj q3,

# »

T₁₂f·|N₁₂|Y

# V .ûi2`KBMiBQM /m KQK2Mi # » KI.1→2

Ta NIR<C3 q3, I3 8aRjj3L3Nj 03 <ICcc3L3Nj. RN 0ā~NCj nN ,RnUI3 03 aācCcjN,3 n UCqRj3L3Nj 3j nN ,RnUI3 03 aācCcjN,3 n aRnI3L3NjY +3c ,RnUI3c aācCcjNjc CNj3aqC3NN3Nj 0ěc \n3 I3 ,RNj,j N3 U3nj

SSk

(6)

UInc ćja3 ,RNcC0āaā ,RLL3 URN,jn3I LCc cnCqNj nN3 cna8,3 IR,ICcā3 Vā,ac3L3NjW. I aāUajCjCRN NRN @RLR<ěN3 03c ,jCRNc āIāL3NjCa3c 03 ,RNj,j ,aāNj IRac ,3c LRL3Njc aācCcjNjcY

H3c IRCc 03 ,RNj,j 3Nja3 03nu cRIC03c cRNj ,RLUI3u3c. 3j 03c IRCc c3L$I$I3c nu IRCc 03 +RnIRL$

URna I3c 8aRjj3L3Njc 03 <ICcc3L3Nj RNj ājā 8RaLnIā3c URna LR0āICc3a ,3c U@āNRLěN3cY _ûbBbiM+2 m `QmH2K2Mi , cC# »

Ωr₁₂= #»

0. IRac# »

Mr₁₂=h·|N₁₂|q3,hI3 ,R3|,C3Nj 03 8aRjj3L3Nj 03 aRnI3L3Nj d

_ûbBbiM+2 m TBpQi2K2Mi , cCΩp₁₂ = 0. IRac|Mp₁₂| = k·|N₁₂|q3,kI3 ,R3|,C3Nj 03 8aRjj3L3Nj 03 UCqRj3L3NjYY

`3La\n3 - I3c 03nu ,R3|,C3Njch3jkcRNj @RLR<ěN3c © nN3 IRN<n3naY + V SmBbbM+2 /BbbBTû2 T` mM +QMi+i TQM+im2H `û2H

MRnc cnUURc3aRNc \n3 I3c LRL3Njc aācCcjNjc cRNj NnIc # » KI.1→2 = #»

0Y

Ta 0ā~NCjCRN I UnCccN,3 03c CNj3aĢ3{Rajc 0CccCUā3 Ua nN3 ,jCRN 03 ICCcRN 3cj - P₍_S₁_↔_S₂₎=

AS2→S1

⊗

V_S₁_/S₂

P₍_S₁_↔_S₂₎=

# »

R₁_→₂ =N₁₂·n#»+# » T₁₂

# » KI.1→2 = #»

0

I

⊗

# » Ω_2/1

# » V_I_∈_2/1

I

P₍_S₁_↔_S₂₎= # » V_I_∈_2/1·

N₁₂·#»n+ # » T₁₂

q3, # »

V_I_∈_2/1·#»n =0 P₍_S₁_↔_S₂₎= # »

V_I_∈_2/1·# » T₁₂

7CNI3L3Nj ,3jj3 UnCccN,3 3cj NnII3 IRac\n3 - ġ I qCj3cc3 03 <ICcc3L3Nj 3cj NnII3 # »

V_I_∈_2/1 = #»

0. ġ I ,RLURcNj3 jN<3NjC3II3 3cj NnII3 # »

T₁₂= #»

0 VUc 03 8aRjj3L3NjWY / V GBBbQM TQM+im2HH2 MQ`KHBbû2

mN3 ICCcRN URN,jn3II3 3N B 03 NRaLI3 #»x 3cj 0ā~NC3 Ua I3 jRac3na ,CNāLjC\n3 - V_2/1

=

⎧⎨

⎩

ω_x 0 ω_y V_y ω_z V_z

⎫⎬

⎭I (#»x.#»y.#»z)

H3 jRac3na 03c 3{Rajc jaNcLCccC$I3c 3cj 0ā,aCj Ua I3 jRac3na \n3I,RN\n3 cnCqNj - {A₁_→₂}=

⎧⎨

⎩ X L Y M Z N

⎫⎬

⎭I (#»x.y.#»#»z)

/āj3aLCNRNc I UnCccN,3 03c CNj3aA3{RajcY

P₍_S₁_↔_S₂₎=

A_S₂_→_S₁

⊗

V_S₁_/S₂

P₍_S₁_↔_S₂₎=

⎧⎨

⎩ X L Y M Z N

⎫⎬

⎭

(#»x.#»y.#»zI)

⊗

⎧⎨

⎩

ω_n 0 ω_t V_t ωz Vz

⎫⎬

⎭

(#»x.y.#»#»zI)

P₍_S₁_↔_S₂₎=Y·Vy+Z·Vz+L·ωx+M·ωy+N·ωzY

SS:

(7)

:Y: iaqCI 3j āN3a<C3

+3jj3 UnCccN,3 3cj NnII3 \n3I \n3 cRCj I3 LRnq3L3Nj cC

Y=0.Z=0.L=0.M=03jN=0 H3 jRac3na 03c ,jCRNc jaNcLCccC$I3c cȕā,aCj IRac -

{A₁_→₂}=

⎧⎨

⎩ X 0

0 0 0 0

⎫⎬

⎭

(#»x.y.#»#»zI)

Y

QN a3jaRnq3 I3 jRac3na 03c ,jCRNc jaNcLCccC$I3c Ua nN3 ICCcRN URN,jn3II3 VNN3u3 YSYSWY Ta 0ā~NCjCRN nN3 ICCcRN NRaLICcā3 3cj āN3a<ājC\n3L3Nj Ua8Cj3Y

:YkY:

GBBbQMb MQ`KHBbû2b `û2HH2b

H3c ICCcRNc NRaLICcā3c. j3II3c \n3II3c cRNj 0ā~NC3c 0Nc I3 j$I3n 3N NN3u3 YSYS cRNj. Ua 0ā~A NCjCRN. Ua8Cj3cY bC RN cRn@Cj3 0RUj3a nN LR0ěI3 UInc aāICcj3. CI 3cj Nā,3ccCa3 03 LR0C~3a I3 jRac3na 03c ,jCRNc jaNcLCccC$I3cY

Ta 3u3LUI3. URna nN3 ICCcRN UCqRj 0ȕu3 (O.#»x) I3c 03nu jRac3nac NRaLICcā3c V,CNāLjC\n3 3j 3{Rajc jaNcLCccC$I3cW cRNj -

V_2/1

=

⎧⎨

⎩ ω_x 0

0 0 0 0

⎫⎬

⎭

(x#».y.#»O#»z)

3j {A1→2}=

⎧⎨

⎩ X 0 Y M Z N

⎫⎬

⎭

(#»x.y.#»O#»z)

Y

H3 jRac3na 03c ,jCRNc jaNcLCccC$I3c aā3I cȕR$jC3Nj 3N ERnjNj nN3 ,RLURcNj3 NRN NnII3 © I UI,3 0n yāaR -

{A₁_→₂}=

⎧⎨

⎩ X H8 Y M Z N

⎫⎬

⎭

(#»x.#»y.O#»z)

Y

/ȕRɵ I UnCccN,3 0CccCUā3 Ua I ICCcRN - P₍_S₁_↔_S₂₎=

A_S₂_→_S₁

⊗

V_S₁_/S₂

P₍_S₁_↔_S₂₎=

⎧⎨

⎩ X H₈ Y M Z N

⎫⎬

⎭

(#»x.#»y.O#»z)

⊗

⎧⎨

⎩ ω_x 0

0 0 0 0

⎫⎬

⎭

(x#».y.#»O#»z)

P₍_S₁_↔_S₂₎=H₈·ω_xY

:Y: h`pBH 2i ûM2`;B2

bRCj nN 3Nc3L$I3 LjāaC3I 2 cRnLCc © Iȕ,jCRN Lā,NC\n3 a3Uaāc3Njā3 Ua I 03NcCjā 03 8Ra,3f(P) 3N ,@\n3 URCNjPY

:Y:YS

^h`pBH

QN UU3II3 jaqCI 0ȕnN3 ,jCRN Lā,NC\n3 3Nja3 IȕCNcjNjt₁ 3j IȕCNcjNjt₂. I \nNjCjā R$j3Nn3 3N cRLLNj I UnCccN,3 0āq3IRUUā3 Ua ,3jj3 ,jCRN Lā,NC\n3 3Nja3 ,3c 03nu CNcjNjc -

W_t^t₁²(^f^{# »}⁽^P^)→^E/^R) = _t₂

t1

P(^f^{# »}⁽^P^)→^E/^R/Rg)0t [J]

SS9

(8)

:Y:Yl

úM2`;B2 TQi2MiB2HH2

HRac\n3 Iȕ,jCRN Lā,NC\n3 3cj nN3 ,jCRN ,RNc3aqjCq3 VnN3 8Ra,3 3cj 0Cj3 ,RNc3aqjCq3 IRac\n3 I3 jaqCI UaR0nCj Ua ,3jj3 8Ra,3 3cj CN0āU3N0Nj 0n ,@3LCN cnCqC Ua cRN URCNj 0ȕ,jCRNW. IRac I3 jaqCI 03 ,3jj3 8Ra,3 U3nj c3 L3jja3 cRnc I 8RaL3 0ȕnN3 0C{āa3NjC3II3 jRjI3 3u,j3Y H3 jaqCI N3 0āU3N0 UInc IRac \n3 03c ājjc CNCjCnu 3j ~Nnu 03 IȕāN3a<C3 URj3NjC3II3 -

W_t^t₁²(^f^{# »}(P)→E/R) = − (E_p(t₂) −E_p(t₁))Y H UnCccN,3 0āq3IRUUā3 Ua # »

f(p)cȕR$jC3Nj 0RN, Ua 0āaCqjCRN 03 IȕāN3a<C3 URj3NjC3II3 - 0Ep

0j =P(^f^{# »}⁽^P^)→^E/^R/Rg)Y QN 0Cj \n3 I UnCccN,3 ŋ 0āaCq3 Ō 03 IȕāN3a<C3 URj3NjC3II3Y

QN N3 U3nj 0ā~NCa IȕāN3a<C3 URj3NjC3II3 \n3 cC Iȕ,jCRN Lā,NC\n3 3cj ,RNc3aqjCq3 V<aqCjā. ,jCRN 0ȕnN a3ccRaj.ĞWY

HȕāN3a<C3 URj3NjC3II3 3cj IRac nN3 UaCLCjCq3 03 I UnCccN,3. 3II3 Nȕ3cj 0ā~NC3 \nȕ© nN3 ,RNcjNj3 UaěcY

:Y9 h?ûQ`ĕK2 /2 HǶûM2`;B2 +BMûiB[m2

:Y9YS

^úMQM+û

TRna jRnj LRnq3L3Nj 0ȕnN cwcjěL3 03 cRIC03cΣ. I 0āaCqā3 03 IȕāN3a<C3 ,CNājC\n3 <ICIā3NN3 03 Σ3cj ā<I3 © I cRLL3 03 I UnCccN,3 <ICIā3NN3 0āq3IRUUā3 Ua I3c ,jCRNc Lā,NC\n3c 3ujāaC3na3c cȕ3u3aÓNj cnaΣ3j 03 I UnCccN,3 03c CNj3aA3{Rajc 3Nja3 I3c cRIC03c 03 2Y

0 0j

Ec₍_Σ/_R_g₎

=P(^Σ^→^Σ/Rg)+P_intΣY

:Y9Yl

.ûKQMbi`iBQM /Mb H2 +b /ǶmM b2mH bQHB/2

Og

x# »_g y# »_g

z# »_g

; S

7ϔόЛЁζ :Yk bRCj nN cRIC03S03 Lcc3m3N LRnq3L3Nj Ua aUURaj © nN

a3Uěa3 <ICIā3NRgY H3 TaCN,CU3 7RN0L3NjI 03 I /wNLC\n3 UUIC\nā © ,3 cRIC03 cȕā,aCj -

D_S/_R_g

=

F_S_→_S

⎧⎨

⎩

S # » Γ₍_P/_R_g₎0m

S

# »

AP∧Γ# »₍_P/_R_g₎0m

⎫⎬

⎭A

=

# » R_S_→_S

# » K_A.S_→_S

A

Y

KnIjCUICRNc ,@\n3 L3L$a3 03 Iȕā<ICjā Ua I3 jRac3na ,CA NāLjC\n3 03 b Ua aUURaj n a3Uěa3 <ICIā3N

V_S/_R_g # » =

Ω_S/_R_g

# » V_A_∈_S/_R_g

A

Y

D_S/_R_g

⊗

V_S/_R_g

=

F_S_→_S

⊗

V_S/_R_g

⎧⎨

⎩

S # » Γ₍_P/_R_g₎0m

S

# »

AP∧Γ# »₍_P/_R_g₎0m

⎫⎬

⎭A

⊗

# » Ω_S/_R_g

# » V_A_∈_S/_R_g

A

=

R# »_S_→_S

# » K_A.S_→_S

A

⊗

# » Ω_S/_R_g

# » V_A_∈_S/_R_g

A

SSf

(9)

:Y9 i@āRaěL3 03 IȕāN3a<C3 ,CNājC\n3

H3 j3aL3 03 0aRCj3 a3Uaāc3Nj3 I UnCccN,3 <ICIā3NN3 0āq3IRUUā3 Ua I3c ,jCRNc Lā,NC\n3c 3ujāA aC3na3c © b cna b -

P(^S^→^S/R^g)=

# » R_S_→_S

# » K_A.S_→_S

A

⊗

# » Ω_S/_R_g

# » V_A_∈_S/_R_g

A

Y

/āq3IRUURNc Iȕnja3 j3aL3Y

D_S/_R_g

⊗

V_S/_R_g

=

⎧⎨

⎩

S# » Γ₍_P/_R_g₎0m

S

# »

AP∧Γ# »₍_P/_R_g₎0m

⎫⎬

⎭A

⊗

# » Ω_S/_R_g

# » V_A_∈_S/_R_g

A

=

S

# » Γ₍_P/_R_g₎0m

·# » V_A_∈_S/_R_g+

⎛

⎝

S

# »

AP∧# » Γ₍_P/_R_g₎0m

⎞

⎠·# » Ω_S/_R_g

# »

V_A_∈_S/_R_g3cj CN0āU3N0Nj 03 I Lcc3. RN U3nj 0RN, I3 L3jja3 cRnc IȕCNjā<aI3 cNc ,@N<3a I3 aācnIjj.

D_S/_R_g

⊗

V_S/_R_g

=

S

# »

Γ₍_P/_R_g₎·# » V_A_∈_S/_R_g0m+

⎛

⎝

S

# »

AP∧# » Γ₍_P/_R_g₎0m

⎞

⎠·# » Ω_S/_R_g

3N a3LUIÓNj # »

V_A_∈_S/_R_g = # »

V_P_∈_S/_R_g+ # »

Ω_S/_R_g∧# »

PA D_S/_R_g

⊗

V_S/_R_g

=

S

# »

Γ₍_P/_R_g₎·# »

V_P_∈_S/_R_g+# »

Ω_S/_R_g∧# »

PA

0m +

⎛

⎝

S

# »

AP∧# » Γ₍_P/_R_g₎0m

⎞

⎠·# » Ω_S/_R_g

D_S/_R_g

⊗

V_S/_R_g

=

S

# »

Γ₍_P/_R_g₎·# » V_P_∈_S/_R_g0m+

S

# »

Γ₍_P/_R_g₎·# »

Ω_S/_R_g∧# »

PA

0m +

⎛

⎝

S

# »

AP∧Γ# »₍_P/_R_g₎0m

⎞

⎠·Ω# »_S/_R_g

H cRLL3 03c 03nu 03aNCěa3c CNjā<aI3c 3cj NnII3 VUaR0nCjc LCuj3c RUURcācW D_S/_R_g

⊗

V_S/_R_g

=

S

# »

Γ₍_P/_R_g₎·# » V_P_∈_S/_R_g0m

Ta 0ā~NCjCRN 0

0j

# » V_P_∈_S/_R_g

R^g =Γ# »₍_P/_R_g₎. 3N a3LUIÓNj D_1S/_R_g

⊗

V_S/_R_g

=

S

0 0j

# » V_P_∈_S/_R_g

R^g·# » V_P_∈_S/_R_g0m

QN a3,RNNţj cRnc I3 cC<N3 CNjā<aI3 I 8RaL3 0C{āa3NjC3II3 0u²

0j =2·u·0u 0j Y D_S/_R_g

⊗

V_S/_R_g

=

S

1 2

0# » V_P_∈_S/_R_g²

0j 0m

SSe

(10)

+RLUj3 j3Nn 0n UaCN,CU3 03 ,RNc3aqjCRN 03 I Lcc3 RN U3nj CNq3ac3a IȕCNjā<ajCRN 3j I 0āaCqjCRNY D_S/_R_g

⊗

V_S/_R_g

= 0 0j

S

1 2

# » V_P_∈_S/_R_g²0m

QN a3,RNNţj I 0ā~NCjCRN 03 IȕāN3a<C3 ,CNājC\n3Y D_S/_R_g

⊗

V_S/_R_g

= 0

0j[T S/Rg]

QN a3jaRnq3 0RN, I 0ā~NCjCRN 0n j@āRaěL3 03 IȕāN3a<C3 ,CNājC\n3 URna nN cRIC03 VUc 03 UnCccN,3 03c CNj3aĢ3{Rajc URna nN c3nI cRIC03W -

0

0j[T S/Rg] =P(^S^→^S/R^g)Y

:Y9Yk

.ûKQMbi`iBQM /Mb H2 +b /2 /2mt bQHB/2b

GË₁ S₁ GË₂

S₂ L₁₂

Σ

O_g

x# »_g y# »g

z# »g

7ϔόЛЁζ :Y: Ģ i@āRaěL3 03 IȕāN3a<C3 ,CNāA jC\n3

bRCj nN cwcjěL3 LjāaC3IΣ,RLURcā 03 03nu cRIC03cS₁3j S₂3N LRnq3L3Nj Ua aUURaj © nN a3Uěa3 <ICIā3NRg3j 3N ICCcRN IȕnN q3, Iȕnja3Y H3 j@āRaěL3 03 IȕāN3a<C3 ,CNājC\n3 UUIC\nā ©S₁cȕā,aCj -

0 0j

T₍_S₁_/_R_g)

=P(^S¹^→^S¹/Rg). 03 LćL3 URnaS₂

0 0j

T₍_S₂_/_R_g)

=P(^S²^→^S²/Rg)Y

H UnCccN,3 03c ,jCRNc 3ujāaC3na3c cnaS₁3cj I cRLL3 03 I UnCccN,3 03c ,jCRNc 3ujāaC3na3c ©Σ<CccNj cnaS₁ 3j 03c ,jCRNc 03 ICCcRNc 03S₂cnaS₁Y

0 0j

T₍_S₁_/_R_g₎

=P(^S¹^→^S¹/Rg)=P(^Σ^→^S¹^//Rg)+P₍_S₂_→_S₁_/_R_g₎

03 LćL3 URnaS₂ 0 0j

T₍_S₂_/_R_g₎

=P(^S²^→^S²/Rg)=P(^Σ^→^S²/Rg)+P₍_S₁_→_S₂_/_R_g₎

2N 00CjCRNNNj I3c 03nu ā<ICjāc 0

0j

T₍_S₁_/_R_g₎ + 0

0j

T₍_S₂_/_R_g₎

=P(^Σ^→^S¹^//R^g)+P_(S₂_→_S₁_/_R_g₎+P_(Σ_→_S₂_/_R_g₎+P_(S₁_→_S₂_/_R_g₎ 0

0j

T₍_Σ/_R_g₎ =

P(^Σ^→^S¹^//Rg)+P₍_Σ_→_S₂_/_R_g₎ +

P₍_S₂_→_S₁_/_R_g₎+P₍_S₁_→_S₂_/_R_g₎ 0

0j

T₍_Σ/_R_g₎

=P(^Σ^→^Σ/Rg)+P₍_S₁_↔_S₂₎

QN a3jaRnq3 0RN, I3 j@āRaěL3 03 IȕāN3a<C3 ,CNājC\n3 0Nc I3 ,c 03 03nu cRIC03cY

SS4

(11)

:Y9 i@āRaěL3 03 IȕāN3a<C3 ,CNājC\n3

:Y9Y:

:ûMû`HBbiBQM ¨ M bQHB/2b

H3 j@āRaěL3 03 IȕāN3a<C3 ,CNājC\n3 URna nN 3Nc3L$I3 LjāaC3I 03 N cRIC03c cȕR$jC3Nj 3N <āNāaICcNj I a3IjCRN URna 03nu cRIC03cY

0 0j

T₍_Σ/_R_g₎

=P(^Σ^→^Σ/Rg)+P_intΣY

:Y9Y9

^liBHBbiBQM

H3 j@āRaěL3 03 IȕāN3a<C3 ,CNājC\n3 U3aL3j 0ȕR$j3NCa nN3 ā\njCRN 0C{āa3NjC3II3 0n c3,RN0 Ra0a3 ,A a,jāaCcjC\n3 0n LRnq3L3Nj. ,3jj3 ā\njCRN Nȕ3cj Uc CN0āU3N0Nj3 03c f ā\njCRNc R$j3Nn3c © UajCa 0n T7/Y

H3 j@āRaěL3 03 IȕāN3a<C3 ,CNājC\n3 3cj 3|,,3 URna 0āj3aLCN3a Iȕā\njCRN 0C{āa3NjC3II3 0n LRnq3A L3Nj 0Nc I3 ,c 0ȕnN Lā,NCcL3 © nN c3nI 03<aā 03 LR$CICjāY

H3 j@āRaěL3 3cj 0C|,CI3 © L3jja3 3N Ǖnqa3 cC I3c UnCccN,3c CNjāaC3na3c N3 cRNj Uc NnII3c Rn N3 0āaCq3Nj Uc 0ȕnN3 8RN,jCRN 03 8Ra,3 CNqaC$I3 VāN3a<C3 URj3NjC3II3WY

:Y9Yf

AMiû;`H2 T`2KBĕ`2 /2 HǶûM2`;B2 +BMûiB[m2

HRac\n3 I3c UnCccN,3c 03c 3{Rajc 3ujāaC3nac 3j CNjāaC3nac © nN 3Nc3L$I3 03 cRIC03cΣcRNj NnII3c Rn 0āaCq3Nj 0ȕnN3 8RN,jCRN 03 8Ra,3 VāN3a<C3 URj3NjC3II3 n cC<N3 UaěcW. ,3c UnCccN,3c U3nq3Nj IRac ćja3 LCc3c cRnc I 8RaL3 0ȕnN3 0C{āa3NjC3II3 03 IȕāN3a<C3 URj3NjC3II3 -

P(^Σ→Σ/R^g)+P_intΣ= −0

0j[Ep(Σ)]Y H3 j@āRaěL3 03 IȕāN3a<C3 ,CNājC\n3 cȕā,aCj 0RN, -

0 0j

T_Σ/_R_g

= −0

0j[E_p(Σ)]Y 2N CNjā<aNj ,3jj3 ā\njCRN RN R$jC3Nj -

T_Σ/_R_g = −E_p(Σ) +K

q3,K,RNcjNj3 0ȕCNjā<ajCRNY +3jj3 ā\njCRN 3cj IȕCNjā<aI3 Ua3LCěa3 03 IȕāN3a<C3 ,CNājC\n3. ,ȕ3cj nN3 ā\njCRN 0C{āa3NjC3II3 0n LRnq3L3Nj 0n Ua3LC3a Ra0a3Y

QN ā,aCj UInjǃj ,3jj3 a3IjCRN cRnc I 8RaL3 -

T_Σ/_R_g+E_p(Σ) =KY

QN a3,RNNţj 3N URcNjK = E_m(Σ)I a3IjCRN ,a,jāaCcjC\n3 03 I ,RNc3aqjCRN 03 IȕāN3a<C3 LāA ,NC\n3Y HȕāN3a<C3 Lā,NC\n3 jRjI3 3cj I cRLL3 03 IȕāN3a<C3 ,CNājC\n3 <ICIā3NN3 3j 03 IȕāN3a<C3 URj3NjC3II3 -

T_Σ/_R_g+Ep(Σ) =Em(Σ)Y

SSO

(12)

:Yf 62mBHH2 /2 i`pmt /B`B;ûb Mê9

2u3a,C,3 Sk A TRNj āIāqj3na 03 <a<3

0ȕUaěc 2Mb2 #ib lzzk +RaaC<ā U<3 SkS

7ϔόЛЁζ :Y9 Ģ TRNj āIāqj3na H3 URNj āIāqj3na 3cj ,RNcjCjnā 03 03nu ,RIRNN3c q3ajC,I3c ~uā3c

n cRIY H3 qā@C,nI3 © cRnI3q3a 3cj LCc 3N URcCjCRN 3Nja3 I3c 03nu ,RA IRNN3c. 3j LCNj3Nn Ua 03nu UCa3c 03 $ac. ~uā3c cna 03nu ,@A aCRjcY +@\n3 ,@aCRj 3cj <nC0ā 3N jaNcIjCRN q3ajC,I3 cna I3 ,aj3a 0ȕnN3 ,RIRNN3Y

H3 LRj3na āI3,jaC\n3 3cj ~uā 3N @nj 03 I ,RIRNN3 LRjaC,3Y H ,@ţN3 \nC a3IC3 I3c qCc 03c 03nu ,RIRNN3c Ucc3 n ac 0n cRI. cRnc I3 qā@C,nI3 cRnI3qā 3j 0āq3IRUU3 nN ,RnUI3 LRj3na NRjāC_mY

H ~<na3 :Yf Uaāc3Nj3 I3 c,@āL ,CNāLjC\n3 0n URNj āIāqj3naY +a,jāaCcjC\n3c ,CNāLjC\n3c

ġ 2N @nj 03 I ,RIRNN3. I URnIC3 LRjaC,3 nN 0CLěja3 03 φ_m=100 mm3j I URnIC3 aā,3UjaC,3 nN 0CLěja3 03

ġ H3c qCc RNj nN 0CLěja3d=25 mm3j nN3 IRN<n3naL= 2.5 m. cRNj 3N ,C3a ja3LUā. nN c3nI

~I3j 3j nN Uc 03p=3 mmd

ġ H3c ā,aRnc cRNj 3N $aRNy3 3j RN Nā<IC<3 I3 8aRjj3L3Nj n ,RNj,j 3Nja3 I qCc 3j Iȕā,aRn d ġ H ,Rnac3 0n ,@aCRj 3cj 032 mY

+a,jāaCcjC\n3c ,CNājC\n3c

ġ H Lcc3 LuCLI3 0n qā@C,nI3 cRnI3qā 3cj 03Mv = 2 000 kg3j I Lcc3 03 ,@\n3 UCa3 03

$ac 3cj 03M_b=200 kgd

ġ H3 LRL3Nj 0ȕCN3ajC3 0n LRj3na njRna 03 cRN u3 03 aRjjCRN 3cj NRjāJ_md ġ H3 LRL3Nj 0ȕCN3ajC3 03 I qCc LRjaC,3 njRna 03 cRN u3 03 aRjjCRN 3cj NRjāJ_vd ġ H3c Lcc3c 3j CN3ajC3c 03 I ,@ţN3. 03c URnIC3c. 03 I ,RnaaRC3 cRNj Nā<IC<3$I3cY

iRnj3c I3c ICCcRNc cRNj Ua8Cj3c @RaLCc I3c 03nu ICCcRNc @āIC,Rŧ0I3c. 0RNj I3 a3N03L3Nj 3cj 03 4z XY H3 a3Uěa3 ccR,Cā n ,@ccCc 3cj cnUURcā <ICIā3NY QN NRj3 z# »_g. I3 q3,j3na nNCjCa3 q3ajC,I RaC3Njā q3ac I3 @njY

#ac k #ac :

pCc S pCc l +@ccCc 3j

cRI z

7ϔόЛЁζ :Yf Ģ b,@āL ,CNāLjC\n3 0n URNj āIāqj3na [SY Taā,Cc3a I3 jRac3na ,CNāLjC\n3 03 ,@,nN3 03c ICCcRNcY

[lY /āj3aLCN3a IȕāN3a<C3 ,CNājC\n3T_Σ/R_g <ICIā3NN3 0n Lā,NCcL3 ,RLUI3jY

[kY K3jja3 IȕāN3a<C3 ,CNājC\n3 cRnc I 8RaL3T_Σ/R_g = ¹₂ ·Jeq·ω²_mY /āj3aLCN3a I3 LRL3Nj 0ȕCN3ajC3 ā\nCqI3NjJ_eqaL3Nā cna Iȕa$a3 LRj3naY

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