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# » A_Σ/R

# » δ_A,Σ/Rg

A

=

# » R_Σ→Σ

# » M_A,Σ→Σ

A

VkYSW q3,

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A_Σ/Rd

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ke

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# »

A_Σ/R= # » R_Σ→Σ

# »

δ_A,Σ/Rg = # »

M_A,Σ→Σ VkYlW

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A_Σ/R = # »

R_Σ→Σ. \n3 IȕRN ā,aCj -

m_Σ·Γ# »G_Σ,Σ/Rg = # »

R_Σ→Σ VkYkW

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d dt

# » VG_Σ,Σ/R

Rg

Y

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m_Σ· d

dt

# » VG_Σ,Σ/R

Rg

= # »

R_Σ→Σ VkY:W

Hw,ā3 +@aI3L<N3ATaCc k4

jXkXjX h?ûQ`ĕK2 /m KQK2Mi /vMKB[m2

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# »

δ_A,Σ/Rg = # »

M_A,Σ→Σ VkY9W

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H3 LRL3Nj 0wNLC\n3 cȕā,aCjδ# »G_Σ,Σ/Rg = d

dt

# » σG_Σ,Σ/Rg

Rg

. n ,3Nja3 0ȕCN3ajC3G_Σ0ȕRɵ d

dt

# » σG_Σ,Σ/Rg

Rg

= # »

M_GΣ,Σ→Σ VkYfW

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dt

# » σ_A,Σ/Rg

Rg

= # »

M_A,Σ→Σ VkYeW

jXjX liBHBbiBQM /m SX6X.X

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Hw,ā3 +@aI3L<N3ATaCc kO

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MRnc cqRNc \n3 -

# »

V_P,E/Rg = # »

V_P,E/R1+ # » V_P,E1/Rg

# »

V_P,E/Rg = # »

V_P,E/R1+ # »

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URaj n j3LUc 0Nc I3 a3Uěa3 <ICA Iā3NRg-

Og

x#»g

y#»g

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x#»₁ y#»₁

z#»₁ O1

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#»x

#»y

#»z

×^P E

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d dt

# » V_P,E/Rg

Rg

= d

dt

# » V_P,E/R1

Rg

+ d

dt

# » VO₁,R₁/Rg

Rg

+ d

dt

# » ΩR₁/Rg ∧O^{# »}₁P

Rg

Ta 0ā~NCjCRN -Γ# »P,E/Rg = d

dt

# » V_P,E/Rg

Rg

3jΓ# »O₁,R₁/Rg = d

dt

# » VO₁,R₁/Rg

Rg

H a3IjCRN 03qC3Nj -

# » Γ_P,E/Rg =

d dt

# » V_P,E/R1

Rg

+Γ# »O₁,R1/Rg +Ω# »R₁/Rg∧ d

dt

# » O₁P

Rg

+ d

dt

# » ΩR₁/Rg

Rg

∧O^{# »}₁P q3,

d dt

# » O₁P

Rg

= d

dt

# » O₁P

R₁

+Ω# »R₁/Rg∧O^{# »}₁P= # »

V_P,E/R1+Ω# »R₁/Rg ∧O^{# »}₁P 3j

d dt

# » V_P,E/R1

Rg

= d

dt

# » V_P,E/R1

R₁

+Ω# »R₁/Rg∧ # »

V_P,E/R1 =Γ# »_P,E/R1+Ω# »R₁/Rg ∧# » V_P,E/R1 /ȕRɵ ~NI3L3Nj I a3IjCRN 03 ,RLURcCjCRN 03c ,,āIāajCRNc -

# »

Γ_P,E/Rg =Γ# »_P,E/R1 +Ω# »R₁/Rg∧ # »

V_P,E/R1+Γ# »O₁,R1/Rg

+Ω# »R₁/Rg∧# »

V_P,E/R1+Ω# »R₁/Rg ∧O^{# »}₁P +

d dt

# » ΩR₁/Rg

Rg

∧O^{# »}₁P

# »

Γ_P,E/Rg =Γ# »_P,E/R1 +Γ# »O₁,R₁/Rg+Ω# »R₁/Rg ∧Ω# »R₁/Rg∧O^{# »}₁P

+ d

dt

# » ΩR₁/Rg

Rg

∧O^{# »}₁P+2·Ω# »R₁/Rg ∧# »

V_P,E/R1 VkY4W

QN NRj3 -

ġ Γ# »_P,E/Rg - ,,āIāajCRN $cRIn3 0n URCNjP03EUa aUURaj n a3Uěa3 <ICIā3NRgd

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Hw,ā3 +@aI3L<N3ATaCc :z

ġ Γ# »O₁,R₁/Rg+# »

ΩR₁/Rg∧# » ΩR₁/Rg∧O^{# »}₁P

+ d

dt

# » ΩR₁/Rg

Rg

∧O^{# »}₁P- ,,āIāajCRN 0ȕ3NjaţN3L3Nj 0n URCNj

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# »

Γ_P,E/Rg = Γ# »_P,E/R1+ Γ# »_P,R1/Rg+ 2·Ω# »R₁/Rg∧ # » V_P,E/R1

# »

Γabs = Γ^{# »}rel+ Γ^{# »}ent+ Γ^{# »}cor VkYOW

jX9XkX *QKTQbBiBQM /m iQ`b2m` /vMKB[m2

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D_E/Rg=

⎧⎪

⎨

⎪⎩

# » A_E/Rg =

P∈E

# » Γ_P/Rg·dm

# » δA,E/Rg =

P∈E

# »

AP∧Γ# »P/Rg·dm

⎫⎪

⎬

⎪⎭

A

TRna I3 ,3Nja3 0ȕCN3ajC3GI 0ā,RLURcCjCRN 03 Iȕ,,āIāajCRN 0RNN3 -

# »

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ΩR₁/Rg ∧# » V_G,E/R1 /ā,RLURcRNc. I3 LRL3Nj 0wNLC\n3 -

# » δ_A,E/Rg =

p∈E

# »

AP∧Γ^{# »}_P/R·dm

=

p∈E

# »

AP∧Γ# »_P,E/R1+Γ# »_P,R1/Rg+2·Ω# »R₁/Rg∧ # » V_P,E/R1

·dm

# » δ_A,E/Rg =

p∈E

# »

AP∧Γ# »_P,E/R1·dm+

p∈E

# »

AP∧Γ# »_P,R1/Rg·dm +2

p∈E

# »

AP∧Ω# »R₁/Rg∧ # » V_P,E/R1

·dm VkYSzW

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# »

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Hw,ā3 +@aI3L<N3ATaCc :S

D_E/R=

⎧⎪

⎨

⎪⎩

p∈E

# » ΓP/R·dm

p∈E

# »

AP∧Γ^{# »}_P/R·dm

⎫⎪

⎬

⎪⎭

A

D_E/R=

⎧⎪

⎨

⎪⎩

p∈E

# » Γ_P,E/R1·dm

p∈E

# »

AP∧Γ# »_P,E/R1·dm

⎫⎪

⎬

⎪⎭

A

+

⎧⎪

⎨

⎪⎩

p∈E

# » Γ_P,R1/Rg ·dm

p∈E

# »

AP∧Γ# »_P,R1/Rg ·dm

⎫⎪

⎬

⎪⎭

A

+

⎧⎪

⎨

⎪⎩

p∈E2·Ω# »R₁/Rg ∧# » V_P,E/R1 ·dm +2

p∈E

# »

AP∧Ω# »R₁/Rg ∧# » V_P,E/R1

·dm

⎫⎪

⎬

⎪⎭

A

Ua NIR<C3

D_E/R=D_E/R1+D_E,R1/Rg+D_cor,E/Rg

={D_rel}+{Dent}+{Dcor}

jX9XjX S`BM+BT2 7QM/K2MiH /Mb mM `2Tĕ`2 MQM ;HBHû2M

bRCj E nN 3Nc3L$I3 LjāaC3I.Rg I3 a3Uěa3 <ICIā3N 3j R₁ I3 a3Uěa3 0ȕājn03Y QN c3 UaRURc3 0ȕā,aCa3 I3 UaCN,CU3 8RN0L3NjI 03 I 0wNLC\n3 0Nc I3 a3Uěa3R1. Ua 0ā~NCjCRN I3 TY7Y/Y cȕā,aCj -

D_E/Rg=A_E→E

2N 0ā,RLURcNj I3 jRac3na 0wNLC\n3 cna I3 a3Uěa3R₁-

D_E/R1+D_E,R1/Rg+D_cor,E/Rg=A_E→E

7CNI3L3Nj I3 TY7Y/ Ua aUURaj n a3Uěa3 NRN <ICIā3NR₁03qC3Nj -

D_E/R1=A_E→E−D_E,R1/Rg−D_cor,E/Rg

/Nc nN a3Uěa3 NRN <ICIā3N. CI 8nj cRncjaCa3 nu 8Ra,3c 3ujāaC3na3c UUIC\nā3c © Iȕ3Nc3L$I3 LjāaC3IE I3 jRac3na 03c 8Ra,3c 0ȕCN3ajC3 0ȕ3NjaţN3L3Nj 3j I3 jRac3na 03c 8Ra,3c 0ȕCN3ajC3 03 +RaCRICcY

`3La\n3 - cC R13cj 3N jaNcIjCRN nNC8RaL3 Ua aUURaj n a3Uěa3 <ICIā3N. IRac

D_E,R1/Rg = 0 3j

D_cor,E/Rg= 0

0RN,

D_E/R1=A_E→E.R₁3cj 0RN, nccC nN a3Uěa3 <ICIā3NY

jX8X TTHB+iBQM Ĝ ú[mBHB#`;2 /ǶmM bQHB/2

jX8XRX S`Q#HĕK2 ;ûMû`H /2 HǶû[mBHB#`;2

/Nc I3 ,c 0ȕnN LRnq3L3Nj 03 aRjjCRN. I3c qC$ajCRNc 0n3c © nN3 LnqCc3 aāUajCjCRN 03c Lcc3c Ua aUURaj © Iȕu3 03 I aRjjCRN CN0nCc3Nj nN3 ncna3 3j nN3 0ājāaCRajCRN aUC03 03c UIC3ac 3j ,aā3Nj nN3 <ćN3 URna IȕnjCICcj3na V$anCjc. qC$ajCRNcWY

HȕR$E3j 03 Iȕā\nCIC$a<3 3cj 03 cnUUaCL3a ,3c qC$ajCRNcY

MRnc IIRNc. āqIn3a IȕCNn3N,3 03 I aāUajCjCRN 03c Lcc3c VURcCjCRN 0n ,3Nja3 0ȕCN3ajC3. cwLājaC3 0n cRIC03W cna ,3c qC$ajCRNcY

Hw,ā3 +@aI3L<N3ATaCc :l

VX .QMMû2b

Q

x#»₁ y#»₁

z#»0

Q

x#»₀

×G θ

7ϔόЛЁζ kYkY Ģ Ā\nCIC$a<3

bRCj nN cRIC03 S₁ 03 Lcc3 K 3N ICCcRN UCA qRj 0ȕu3(O,z#»0)Ua aUURaj n $‘jCS0Y +3 cRA IC03 NȕwNj n,nN3 UajC,nIaCjā <āRLājaC\n3 VNC UIN 03 cwLājaC3. NC u3 03 aāqRInjCRNW. I LjaC,3 0ȕCN3ajC3 0n cRIC03 3N Q 3cj 03 I 8RaL3 -

IO(S₁) =

⎛

⎝ A −F −E

−F B −D

−E −D C

⎞

⎠

O(^x#»1 ,y#»1 ,z#»1)

H3 a3Uěa3R₁= (O,x#»₁,y#»₁,z#»₁)3cj ICā n cRIC03 3N aRjjCRN q3,# » (x^#»₀,x#»₁) =θ. URna j5z.θ =0Y OG =xg·x^#»1+zg·z^#»0

R₀nN a3Uěa3 <ICIā3N.z#»₀3cj q3ajC,I c,3N0NjY mN ,RnUI3 LRj3na # »

Cm =Cm·z^#»₀U3aL3j I aRjA jCRNY

H ICCcRN UCqRj 3cj Ua8Cj3Y

# VX úim/2 /vMKB[m2

AMp2MiB`2 /2b +iBQMb 2tiû`B2m`2b UUIC\nā3c n cRIC03 3N aRjjCRN ġ ,jCRN 03 I U3cNj3na cna I3 cRIC03 -

Pg→S₁

=

−M·g·z^#»₀

#»0

G

=

−M·g·z^#»₀ M·g·xg·y^#»₁

O

ġ +RnUI3 LRj3na -

CMot→S₁

= #»

0 Cm·z^#»₀

∀P

d

ġ ,jCRNc jaNcLCccC$I3c Ua I ICCcRN UCqRj -

L_S0→S1=

⎧⎨

⎩

X₀₁ L₀₁ Y₀₁ M₀₁ Z₀₁ 0

⎫⎬

⎭∀P∈(O,z#»₀)

(^{#»? ,#»? ,z#»0}) Y

.ûi2`KBMiBQM /m iQ`b2m` /vMKB[m2 3N Q 0n cRIC03S10Nc cRN LRnq3L3Nj Ua aUURaj ©R0Y

/āj3aLCNRNc 0Nc nN Ua3LC3a j3LUc I3 jRac3na ,CNājC\n3 3N Q 0n cRIC03S₁ 0Nc cRN LRnq3L3Nj Ua aUURaj ©R₀-

ġ `ācnIjNj3 ,CNājC\n3 - p# »S₁/R0 = M·# »

VG∈S₁/R0 = M·xg·θ^˙·y^#»₁ ġ KRL3Nj ,CNājC\n3. Q 3cj nN URCNj ~u3 0Nc I3 aā8āa3NjC3I. 0RN, -

# »

σO,S₁/Rg =IO(S₁)·Ω# »S₁/R₀ =

⎛

⎝ A −F −E

−F B −D

−E −D C

⎞

⎠

OB₁

·

⎛

⎝0 0˙ θ

⎞

⎠

=−E·θ^˙·x^#»₁−D·θ^˙·y^#»₁+C·θ^˙·z^#»₀

=−E·ω·x^#»1−D·ω·y^#»1+C·ω·z^#»0q3,ω=θ^˙

0ȕRɵ I3c ,RLURcNj3c 0n jRac3na 0wNLC\n3 -

D_S1/R0=

# » AS₁/R0

# » δO,S₁/R₀

O

ġ # »

AS₁/R0. aācnIjNj3 0wNLC\n3. Ua 0āaCqjCRN 03 I aācnIjNj3 ,CNājC\n3 -

# »

AS₁/R0 = M·xg·θ^¨·y^#»₁−M·xg·θ^˙2·x^#»₁

Hw,ā3 +@aI3L<N3ATaCc :k

ġ δ# »_O,S1/R0. LRL3Nj 0wNLC\n3 3NO.O3cj nN URCNj ~u3 0NcR00RN, -

# » δ_O,S1/R0 =

d dt

# » σ_O,S1/R0

R₀

= −E·θ^¨·x^#»₁−D·θ^¨·y^#»₁−E·θ^˙2·y^#»₁+D·θ^˙2·x^#»₁+C·θ^¨·z^#»₀

= D·θ^˙2−E·θ^¨

·x^#»₁+−D·θ^¨−E·θ^˙2

·y^#»₁+C·θ^¨·z^#»0

S`BM+BT2 7QM/K2MiH /2 H /vMKB[m2 UUIC\nā n cRIC03S1Y D_S1/R0=A_S

1→S₁

D_S1/R0=Pg→S₁

+CMot→S₁

+L_S0→S1 # »

AS₁/R0

# » δ_O,S1/R0

O

=

−M·g·z^#»0

M·g·xg·y^#»₁

O

+ #»

0 Cm·z^#»0

∀P

+

⎧⎨

⎩

X₀₁ L₀₁ Y₀₁ M₀₁ Z₀₁ 0

⎫⎬

⎭∀P∈(O,z#»₀)

(^{#»? ,#»? ,z#»}0) BI 3cj En0C,C3nu C,C. 0ȕā,aCa3 I3 jRac3na 03c 3{Rajc jaNcLCccC$I3c Ua I ICCcRN UCqRj

L_S0→S1 ^{0Nc I}

$c3(x^#»1,y#»1,z#»1). 03 0āj3aLCN3a I3c ,RLURcNj3c 03 I ICCcRN 0Nc ,3jj3 $c3 UnCc 03 a3q3NCa 0Nc I $c3 (x^#»0,y#»0,z#»0)Y

QN R$jC3Nj 0RN, I3c 03nu ā\njCRNc q3,jRaC3II3c cnCqNj3c - ġ i@āRaěL3 03 I aācnIjNj3 0wNLC\n3

# »

AS₁/R0 =−M·g·z^#»₀+^#»0 +X₀₁·x^#»₁+Y₀₁·y^#»₁+Z₀₁·z^#»₀ M·xg·θ^¨·y^#»1−M·xg·θ^˙2·x^#»1 =−M·g·z^#»0+^#»0 +X01·x^#»1+Y01·y^#»1+Z01·z^#»0

ġ i@āRaěL3 0n LRL3Nj 0wNLC\n3

# »

δO,S₁/R0 = M·g·xg·y^#»₁+Cm·z^#»₀+L₀₁·x^#»₁+M₀₁·y^#»₁ D·θ^˙2−E·θ^¨

·x^#»₁+−D·θ^¨−E·θ^˙2

·y^#»₁+C·θ^¨·z^#»₀= M·g·xg·y^#»₁+Cm·z^#»₀ +L₀₁·x^#»₁+M₀₁·y^#»₁

H UaRE3,jCRN 03 ,3c 03nu ā\njCRNc 0RNN3 I3c f ā\njCRNc c,ICa3c cnCqNj3c -

⎧⎪

⎨

⎪⎩

−M·xg·θ^˙2=X₀₁ M·xg·θ^¨=Y01

0=−M·g+Z₀₁ 3j

⎧⎪

⎪⎨

⎪⎪

⎩

D·θ^˙2−E·θ^¨ =L01

−D·θ^¨−E·θ^˙2 = M·g·xg+M01

C·θ^¨ =Cm

.ûi2`KBMiBQM /2b 2zQ`ib /Mb H HBBbQM TRna ,RNjCNn3a 3j cCLUIC~3a I3c ,I,nIc. NRnc cnUURc3aRNc \n3 I3 aRjRa jRnaN3 © qCj3cc3 ,RNcjNj3ω˙ =θ^¨=0. I3c f ā\njCRNc 03qC3NN3Nj -

⎧⎪

⎨

⎪⎩

−M·xg·θ^˙2= X₀₁ 0=Y₀₁ M·g= +Z₀₁

3j

⎧⎪

⎨

⎪⎩

D·θ^˙2= L01

−E·θ^˙2−M·g·xg= M₀₁ 0=Cm

Hw,ā3 +@aI3L<N3ATaCc ::

H3 jRac3na 03c ,jCRNc jaNcLCccC$I3c 0Nc I ICCcRN UCqRj cȕā,aCj 0Nc I $c3 ICā3 n cRIC03 3N aRjjCRN (x^#»₁,y#»₁,z#»₁)-

L_S0→S1=

⎧⎨

⎩

X01=−M·xg·θ^˙2 L01 =D·θ^˙2

Y01 =0 M01=−E·θ^˙2−M·g·xg

Z₀₁= M·g 0

⎫⎬

⎭

(x^#»₁,y#»₁,Oz#»₁)

QN cȕU3aÓRCj \n3 I3c 3{Rajc VaācnIjNj3 3j LRL3NjW 0Nc I ICCcRN UCqRj cRNj 8RN,jCRN 03 I qCj3cc3 03 aRjjCRN θY 2N UaRE3,jCRN 0Nc I $c3 <ICIā3NN3.˙ R0. RN U3nj LC3nu āqIn3a IȕCNn3N,3 03c UaLěja3c ,CNājC\n3c cna I3c 3{Rajc 0Nc I ICCcRNY

L_S0→S1=

⎧⎨

⎩

X₀₁·cosθ L₀₁·cosθ−M₀₁·sinθ X₀₁·sinθ L₀₁·sinθ+M₀₁·cosθ

Z₀₁ 0

⎫⎬

⎭

(x^#»₀,y#»₀,Oz#»₀)

q3,θ =ω·t

L_S0→S1=

⎧⎨

⎩

X₀₁·cos(ω·t) L₀₁·cos(ω·t)−M₀₁·sin(ω·t) X₀₁·sin(ω·t) L₀₁·sin(ω·t) +M₀₁·cos(ω·t)

Z01 0

⎫⎬

⎭

(x^#»₀,y#»₀,Oz#»₀)

QN ,RNcjj3 0RN, \n3 I3c 3{Rajc jaNcLCc n $‘jC Ua I ICCcRN UCqRj N3 cRNj Uc ,RNcjNjc 3j 0āU3N03Nj 0n j3LUcY TRna a3N0a3 ,3c 3{Rajc CN0āU3N0Njc 0n j3LUc. CI 8nj \n3 -

⎧⎪

⎨

⎪⎩

X₀₁ =0 L₀₁ =0 M₀₁ =0

,ȕ3cj © 0Ca3

⎧⎪

⎪⎨

⎪⎪

⎩

−M·xg·θ^˙2 =0 D·θ^˙2−E·θ^¨ =0

−D·θ^¨−E·θ^˙2−M·g·xg =0 0ȕRɵ

⎧⎪

⎨

⎪⎩ xg=0

D=0 E=0

pRnc URnaa3y qāaC~3a \n3 ,3c ,RN0CjCRNc cRNj nccC cn|cNj3c cC I qCj3cc3 Nȕ3cj Uc ,RNcjNj3Y jX8XkX ú[mBHB#`;2

VX ú[mBHB#`;2 biiB[m2

QN 0Cj \nȕnN cRIC03 3N aRjjCRN 3cj ā\nCIC$aā cjjC\n3L3Nj IRac\n3 I3 ,3Nja3 0ȕCN3ajC3 3cj cna Iȕu3 03 aRjjCRN V0Nc Iȕ3u3LUI3 Uaā,ā03Njxg =0WY

# VX ú[mBHB#`;2 /vMKB[m2

QN 0Cj \nȕnN cRIC03 3cj ā\nCIC$aā 0wNLC\n3L3Nj. cȕCI 3cj ā\nCIC$aā cjjC\n3L3Nj 3j \n3 I3c UaR0nCjc 0ȕCN3ajC3 ,RLURajNj Iȕu3 03 aRjjCRN cRNj NnIc V0Nc Iȕ3u3LUI3 Uaā,ā03NjD=03jE=0WY

+ VX S`BM+BT2 /2 HǶû[mBHB#`;2

Ā\nCIC$a3a nN cRIC03 3N aRjjCRN a3qC3Nj 0RN, © NNnI3a I3c 0C{āa3Njc j3aL3c ,C 03ccncY /3nu cjajā<C3c cRNj 3NqCc<3$I3c

ġ ERnj3a 03c Lcc3c n cRIC03 ~N 03 LR0C~3a ,3c ,a,jāaCcjC\n3c ,CNājC\n3c d ġ mcCN3a I3 cRIC03 VU3aÓ<3. L3nI<3W ~N 03 LR0C~3a I aāUajCjCRN 03c Lcc3cY

H Ua3LCěa3 cRInjCRN 3cj njCICcā3 URna aāICc3a Iȕā\nCIC$a<3 03c aRn3c 03 qā@C,nI3c. QN a3jaRnq3 UInjǃj I c3,RN03 IRac 0ȕā\nCIC$a<3 aāICcā cna 03c UCě,3c LccCq3c VqRINj 0ȕCN3ajC3W. ,3c ncCN<3c cRNj IRac 3{3,jnāc 3N ncCN3. IRac 03 I 8$aC,jCRNY

/n URCNj 03 qn3 03c ,I,nIc © aāICc3a. I3c 03nu Lāj@R03c cRNj NIR<n3c. I c3,RN03 a3qC3Nj © ERnj3a 03c Lcc3c Nā<jCq3cY

Hw,ā3 +@aI3L<N3ATaCc :9

jX8XjX ú[mBHB#`;2 ¨ k Kbb2b

bRCj nN cRIC03S₁. 3N aRjjCRN Ua aUURaj n a3Uěa3 <ICIā3N R₀Y QN cRn@Cj3 ā\nCIC$a3a ,3 cRIC03Y TRna ,3I RN aERnj3 n cRIC03 © ā\nCIC$a3a 3N aRjjCRN 03nu Lcc3c URN,jn3II3cM₁3jM₂V~<na3 3j 0RNNā3c kY:WY H3 NRnq3I 3Nc3L$I3 3cj 0RN, -Σ={S₁,M₁,M2}^Y

MRnc IIRNc a3,@3a,@3a I Lcc3 3j I URcCjCRN 0Nc I3 a3Uěa3 ICā n cRIC03 S₁ 03 ,@,nN3 03c Lcc3c URN,jn3II3c URna \n3 Iȕ3Nc3L$I3ΣcRCj ā\nCIC$aāY

S₁. I3 cRIC03 © ā\nCIC$a3a 03 Lcc3 M 03 LjaC,3 0ȕCN3ajC3 -

IO(S₁) =

⎛

⎝ A −F −E

−F B −D

−E −D C

⎞

⎠

O(^x#»1 ,y#»1 ,z#»1)

03 ,3Nja3 0ȕCN3ajC3 -# » OG= xg·x^#»1+zg·z^#»0d

M₁ I Lcc3 URN,jn3II3 03 Lcc3 m₁ . q3, # » OM₁ = x1·x^#»1+y1·y^#»1+z1·z^#»0d

M₂ I Lcc3 URN,jn3II3 03 Lcc3 m₂ . q3, # » OM₂ = x2·x^#»1+y2·y^#»1+z2·z^#»0Y

VW 0RNNā3c

Q

x#»₁ y#»₁

z#»₀

Q

x#»0

×G θ M₁

M₂

V$W c,@āL

7ϔόЛЁζ kY:Y Ģ Ā\nCIC$a<3 © 03nu Lcc3c

VX .ûi2`KBMiBQM /2b +`+iû`BbiB[m2b +BMûiB[m2b /2 HǶ2Mb2K#H2

H Lcc3 jRjI3 03Σ3cjm_Σ=m+m₁+m₂Y H LjaC,3 0ȕCN3ajC3 03 Iȕ3Nc3L$I3 3cj - IO(Σ) =IO(S₁) +IO(M₁) +IO(M₂)

`3La\n3 - I LjaC,3 0ȕCN3ajC3 0ȕnN3 Lcc3 URN,jn3II3 3N cRN ,3Nja3 0ȕCN3ajC3 3cj NnII3 VI3 qRInL3 3cj NnI 6W -IM₁(M₁) =

⎛

⎝0 0 0 0 0 0 0 0 0

⎞

⎠

M1

2N UUIC\nNj I3 j@āRaěL3 03 ?nw<3Nc. RN R$jC3Nj I LjaC,3 3N∀B O03 I Lcc3m₁-

IO(M1) =m1·

⎛

⎝y²₁+z²₁ −x₁·y₁ −x₁·z₁

−x₁·y₁ z²₁+x₁² −y₁·z₁

−x₁·z₁ −y₁·z₁ x²₁+y²₁

⎞

⎠

O(^x#»1 ,y#»1 ,z#»1)

H LjaC,3 0ȕCN3ajC3 03 Iȕ3Nc3L$I3 LjāaC3IΣcȕā,aCj ~NI3L3Nj - IO(Σ) =

⎛

⎝ A_Σ −F_Σ −E_Σ

−F_Σ B_Σ −D_Σ

−E_Σ −D_Σ C_Σ

⎞

⎠

O(^x#»_{1 ,}^y#»_{1 ,}^z#»₁)

Hw,ā3 +@aI3L<N3ATaCc :f

q3,

A_Σ = A+m1·y²₁+z²₁

+m2·y²₂+z²₂

−D_Σ=−D−m1·y1·z1−m2·y2·z2

B_Σ =B+m1·z²₁+x²₁

+m2·z²₂+x²₂

−E_Σ=−E−m1·x1·z1−m2·x2·z2

C_Σ =C+m1·x²₁+y²₁

+m2·x₂²+y²₂

−F_Σ=−F−m1·x1·y1−m2·x2·y2

# VX ú[mBHB#`;2 biiB[m2

Hȕ3Nc3L$I3 3cj ā\nCIC$aā cjjC\n3L3Nj cC I3 ,3Nja3 0ȕCN3ajC3 03 Iȕ3Nc3L$I3 3cj cna Iȕu3 03 aRjjCRNY

# » OG_Σ = ¹

M_Σ

M·OG^{# »}+m₁·OM^{# »}₁+m₂·OM^{# »}₂ Hȕā\nCIC$a3 cjjC\n3 3cj 0RN, aāICcā cC# »

OG_Σ·x^#»₁=03j # »

OG_Σ·y^#»₁ =0 /ȕRɵ I3c 03nu Ua3LCěa3c ā\njCRNc © a3cU3,j3a -

M·xg+m₁·x₁+m₂·x₂ =0 VkYSlW

m₁·y₁+m₂·y₂ =0 VkYSkW

+ VX ú[mBHB#`;2 /vMKB[m2

H3c UaR0nCjc 0ȕCN3ajC3 ,RLURajNj Iȕu3 03 aRjjCRN(O,z#»₀)0RCq3Nj ćja3 NnIc VC,CD_Σ3jE_ΣW. 0ȕRɵ I3c 03nu ā\njCRNc cnCqNj3c -

−D_Σ =−D−m₁·y₁·z₁−m₂·y₂·z₂=0 VkYS:W

−E_Σ= −E−m₁·x₁·z₁−m₂·x₂·z₂=0 VkYS9W H3 cwcjěL3 © aācRn0a3 3cj nN cwcjěL3 03 : ā\njCRNc 3j 4 CN,RNNn3c Vm₁.m₂.x₁.x₂.y₁.y₂.z₁.z₂WY BI 3uCcj3 0RN, © UaCRaC nN3 CN~NCjā 03 cRInjCRNcY

/ VX TTHB+iBQM , `Qm2

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QN 0RN, - ġ

x₁²+y²₁= R3jz₁ =0VRnz₁= LW URna I Ua3LCěa3 Lcc3 d ġ

x₂²+y²₂= R3jz2 =LVRnz2=0W URna I c3,RN03Y

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M·xg+m1·x1+m2·x2 =0 m₁·y₁+m₂·y₂ =0

−D−m₁·y₁·z₁−m₂·y₂·z₂ =0

−E−m₁·x₁·z₁−m₂·x₂·z₂ =0

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x₁ =R·cosθ₁ y1 =R·sinθ1

3j

x2= R·cosθ2

y2= R·sinθ2

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M·xg+m₁·R·cosθ1+m₂·R·cosθ2=0 m₁·R·sinθ₁+m₂·R·sinθ₂=0

−D−m2·R·sinθ2·L=0

−E−m2·R·cosθ2·L=0 ,3 \nC U3aL3j 03 0ā0nCa3 -

⎧⎪

⎪⎨

⎪⎪

⎩

tanθ2= ^D E m₂=

√D²+E² L·R

3j

⎧⎪

⎪⎨

⎪⎪

⎩

tanθ1= ^D E−M·xg·L m1= ^D

R·L· ¹ sinθ₁

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L_S0→S1=

⎧⎨

⎩

X₀₁=−M·xg·θ^˙2 L₀₁ =D·θ^˙2

Y₀₁ =0 M₀₁=−E·θ^˙2−M·g·xg

Z₀₁= M·g 0

⎫⎬

⎭

(^x#»1,y#»₁,Oz#»₁)

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