Hw,ā3 +@aI3L<N3ATaCc 9e

(1)

SzY:Yl **^*Q``2+iBQM**

+RaY 9 - +RIRNN3 03 I3q<3 bnE3j U<3 ::

[SY /āj3aLCN3a I aācnIjNj3# »

Rs→C03 Iȕ,jCRN Lā,NC\n3 0n cRI cna I ,RIRNN3. 3N 8RN,jCRN 03q₁.q₂3j 03c 0CL3NcCRNcY

QN cCj \n3# »

dRs→C=q(y)·ds#»z q3,ds=dx·dy

q3,x ∈[a−b,a]3jx∈ [−a,−(a−b)]3jy∈ [0,L]3jq(y) = q₂−q₁

L ·y+q₁

QN ,I,nI3 Iȕ,jCRN 0n cRI URna URna I3 UC30 q3,x>0. Iȕ,jCRN 0n c3,RN0 3cj 0āj3aLCNā3 Ua NIR<C3Y

# » R¹_s_→_C= ^a

x=a−b _L

Y=0q(y)·dx·dy#»z

# » R¹_s_→_C= ^a

x=a−b _L

Y=0

q₂−q₁ L ·y+q₁

·dx·dy#»z

# » R¹_s_→_C=b·

q₂−q₁ L · ^L²

2 +q₁·L

#»z =b·^q²+q₁ 2 ·L#»z Ua NIR<C3 URna Iȕnja3 UC30

# »

R²_s_→_C=b·^q²+q₁ 2 ·L#»z

0ȕRɵ

# »

Rs→C=b·(q₂+q₁)·L#»z

[lY /āj3aLCN3a I3 LRL3Nj 3NO.M# »O,s→C. 03 ,3jj3 ,jCRN Lā,NC\n3.

UnCc 3NP.M# »_P,s_→CY

QN 0āj3aLCN3 0Nc nN Ua3LC3a j3LUc URna I3 UC30 q3,x>0 bRCj nN URCNjQq3,OQ# »=x·^#»x+y·^#»y

# » M_O,s→C1=^a

x=a−b _L

Y=0

# »

OQ∧(q(y)·dx·dy#»z)

# » MO,s→C1=^a

x=a−b _L

Y=0(x·^#»x+y·^#»y)∧(q(y)·dx·dy#»z)

# » MO,s→C1=^a

x=a−b _L

Y=0−x·q(y)·dx·dy#»y+ ^a

x=a−b _L

Y=0y·q(y)·dx·dy#»x

# » MO,s→C1=^a

x=a−b _L

Y=0−x· q₂−q₁

L ·y+q₁

·dx·dy#»y +^a

x=a−b _L

Y=0y· q₂−q₁

L ·y+q₁

·dx·dy#»x

BI Nȕ3cj Uc njCI3 03 ,I,nI3a IȕCNjā<aI3 cnCqNj#»y. ,RLUj3 j3Nn 03 I cwLājaC3 03 I aāUajCjCRN 03c ,jCRNc Lā,NC\n3c cna I3c 03nu UC30c.

I3 LRL3Nj njRna 03(O,#»y)N3 U3nj ćja3 \n3 NnI. E3 qRnc ICcc3 qāA

aC~3aY QN N3 ,I,nI3 \n3 I3 LRL3Nj cnCqNj(O,#»x)Y

# » MO,s→C1=^a

x=a−b _L

Y=0y· q₂−q₁

L ·y+q₁

·dx·dy#»x

# » MO,s→C1=b

_L Y=0

q₂−q₁

L ·y²+q₁·y

·dy#»x

# » MO,s→C1=b·

q₂−q₁ L · ^L³

3 +q₁·^L² 2

·^#»x =b·^q² 3 +^q¹

6

·L²·^#»x

Ua NIR<C3. RN 0ā0nCj I3 LRL3Nj 03c 03nu UC30c

# »

MO,s→C=2·b·^q² 3 +^q¹

6

·L²·^#»x

2NP,3 LRL3Nj cȕā,aCj -

# »

MP,s→C=M# »O,s→C+PO^{# »}∧R^{# »}_s_→_C

# »

M_P,s→C=2·b·^q² 3 +^q¹

6

·L²·^#»x+ ((e−d)·^#»y+h·^#»z)∧b·(q₂+q₁)·L#»z

# »

M_P,s_→C=2·b·^q² 3 +^q¹

6

·L²+ (e−d)·b·(q₂+q₁)·L#»x

[kY 3N 0ā0nCa3 I3 jRac3na 03 Iȕ,jCRN Lā,NC\n3 0n cRI.

T_s_→_C. cna I ,RIRNN3 3N TY

{Ts→C}=

# »

Rs→C=b·(q₂+q₁)·L#»z

# »

MP,s→C=2·b·^q² 3 +^q¹

6

·L²+ (e−d)·b·(q₂+q₁)·L#»x

P

[:Y /āj3aLCN3aq₁3jq₂3N 8RN,jCRN 03FT3j 03d

QN ā,aCj Iȕā\nCIC$a3 03 I ,RIRNN3 3N TY 2II3 3cj cRnLCc3 © 03nu ,jCRNc Lā,NC\n3c -

T_s_→_C^3jA_T_→_C=

−FT·^#»z

#»0

QN 3N 0ā0nCj I3c 03nu ā\njCRNc 03 Iȕā\nCIC$a3 - P

⎧⎨

⎩

−FT+b·(q₂+q₁)·L=0

2·b·^q² 3 +^q¹

6

·L²+ (e−d)·b·(q₂+q₁)·L

=0

q₁=FT·²·L+3·e−3·d b·L² q₂=−FT·²·L+3·e−3·d

b·L²

[9Y TRna āqCj3a I 0ā8RaLjCRN 0n cRI. I3c qI3nacq₁3jq₂N3 0RCq3Nj ELCc ćja3 NnII3cY 2N 0ā0nCa3 I3c qI3nac LCNC 3j LuC 03dY

QN aācRn0

q₁=F_T·²·L+3·e−3·d

b·L² =0⇒dmax=e+² 3·L 3j

q₂=−FT·²·L+3·e−3·d

b·L² =0⇒d_min=e+¹ 3·L

+RaY f - 2,Inc3 03 +NI bnE3j U<3 :9

[SY ia,3a I3 <aU@3 03c ICCcRNc 0n Lā,NCcL3 ,RLUI3j ,RNcjCjnā3 Ua I3 $ERw3a. I3 ,RaUc 0n qāaCN. I jC<3 0n qāaCN 3j I3 qNjCIY

Hw,ā3 +@aI3L<N3ATaCc 9e

(2)

z S k l

Sph(O)

Sph(C) PG(C,y#»₂)

Sph(B)

SC(A,z#»₀)

P_g_→₁ P_eau_→₁ A_p,2_→₃

[lY Taā,Cc3a cna I3 <aU@3 I3c ,jCRNc Lā,NC\n3c 3N aRn<3

ġ ,jCRN 03 I <aqCjā -

P_g_→₁=^P^#»¹=−M₁·g·z^#»₀

#»0

G₁

ġ ,jCRN 03 Iȕ3n cna VSW -

P_eau_→₁= R# »_e_→₁

# » MO,e→1

O

ġ ,jCRN 03 I Ua3ccCRN 0Nc I3 qāaCN - A_p,2_→₃=^R^{# »}²^→³=R₂₃·y^#»₂

#»0

C

[kY Taā,Cc3a I3c 0C{āa3Njc jRac3nac 0ȕ,jCRN jaNcLCccC$I3c Ua I3c ICCcRNcY

ġ bU@āaC\n3 3N Q 3Nja3 VzW 3j VSW

A^O₀_→₁=

⎧⎨

⎩ X_O 0 YO 0 ZO 0

⎫⎬

⎭

O∀B

d

ġ bU@ěa3 ,wICN0a3 3N 3Nja3 VzW 3j VSW

A^A₀_→₁ =

⎧⎨

⎩ XA 0 YA 0

0 0

⎫⎬

⎭ (^#»^{? ,}^#»^{? ,}^z^#»A0)

d

ġ bU@āaC\n3 3N + 3Nja3 VSW 3j VkW A₁_→₃=

⎧⎨

⎩ XC 0 YC 0 ZC 0

⎫⎬

⎭

C∀B

d

ġ bU@āaC\n3 3N # 3Nja3 VzW 3j VlW{A₀_→₂}=

⎧⎨

⎩ XB 0 YB 0 ZB 0

⎫⎬

⎭

B∀B

d

ġ TCqRj <ICccNj 0ȕu3(C,y#»₂)3Nja3 VlW 3j VkW {A₂_→₃}=

⎧⎨

⎩ X₂₃ L₂₃

0 0

Z₂₃ Z₂₃

⎫⎬

⎭ (^#»^{? ,}^y^#»2,#»O

?) d

[:Y bRCj P nN URCNj 0n qNjCI 03 ,RRa0RNNā3c (x, 0,z) 0Nc (O,x#»₁,y#»₁,#»z). 3uUaCL3a c qCj3cc3 Ua aUURaj n $ERw3aV# »_P_∈_1/03N 8RN,jCRN 03ω1Y

# » VP∈1/0=

d dt

# » OP

=

dx·x^#»₁+z·z^#»₀

# » dt

V_P_∈_1/0=Ω^{# »}_1/0∧(x·^#»x₁+z·z^#»₀)

# »

VP∈1/0=ω1·z^#»₀∧(x·x^#»₁+z·z^#»₀) =x·ω1·y^#»₁ [9Y 2uUaCL3a# »

dFeau→13N 8RN,jCRN 03ω13jxY Taā,Cc3a IȕāIāL3Nj 03 cna8,3dsCNcC \n3 I3c $RaN3c 0ȕCNjā<ajCRNY

# »

dFeau→v=−pr·ds·y^#»₁=−k·ρ·V# »_P_∈_v/b²·ds·y^#»₁

=−k·ρ·x²·ω²₁·ds·y^#»₁

=−k·ρ·x²·ω²₁·dx·dz·y^#»₁ q3,x∈[0,L]3jz∈[0,he]

[fY /āj3aLCN3a # »

Feau→1 3N 8RN,jCRN 03 ω1 3j 03c 0C{āa3Njc UaA Lěja3c <āRLājaC\n3cY 7Ca3 IȕUUIC,jCRN NnLāaC\n3Y

# » Feau→v=

S

# » dFeau→v=

S

−k·ρ·x²·ω²₁·ds·y^#»₁= L 0

H2

0

−k·ρ·x²·ω²₁·dxdz·y^#»₁

=−k·ρ·ω²₁·^L³ 3 ·^H

2 ·y^#»₁

[eY /āj3aLCN3aM# »_O,eau→1=

S

# »

OP∧dF# »eau→1Y

# » MO,eau→v=

S

# »

OP∧# » dFeau→v=

S

(x·x^#»₁+z·z^#»₀)∧ −k·ρ·x²·ω²₁·ds·y^#»₁

=−k·ρ·ω²₁·

S

x³·x^#»₁∧ ·y^#»₁·ds

−k·ρ·ω²₁

S

x²·z·z^#»₀∧y^#»₁·ds

=−k·ρ·ω²₁· L 0

H2

0

x³·dxdz·z^#»₀

+k·ρ·ω²₁ L 0

H2

0

x²·z· ·dxdz·x^#»₁

=−k·ρ·ω²1·^L⁴ 4

H

2 ·z^#»₀+k·ρ·ω²1

L³ 3

H² 8 ·x^#»₁

[4Y 2uUaCL3a I3 jRac3na 03 Iȕ,jCRN Lā,NC\n3 03 Iȕ3n cna I3 qNjCI 3N QY

{Aeau→v}=

⎧⎪

⎨

⎪⎩

# »

Feau→v=−k·ρ·ω²₁·^L³ 3 ·^H

2 ·y^#»₁

# »

M_O,eau_→v=−k·ρ·ω²₁·^L⁴ 4

H

2 ·z^#»₀+k·ρ·ω²₁L³ 3

H² 8 ·x^#»₁

⎫⎪

⎬

⎪⎭

O

[OY /āj3aLCN3a I3 URCNjP0n qNjCI URna I3\n3IM# »P,eau→1=^#»0Y

# » MP,eau→1=^#»0

# »

MP,eau→1=# »

MO,eau→1+PO^{# »}∧F# »eau→v

# »

MP,eau→1=−k·ρ·ω²₁·^L⁴ 4

H

2 ·z^#»₀+k·ρ·ω²₁L³ 3

H² 8 ·x^#»₁

−(x·x^#»₁+z·z^#»₀)∧ −k·ρ·ω²₁·^L³ 3 ·^H

2 ·y^#»₁=^#»0 cRCj

−^L⁴ 4

H 2 ·z^#»₀+^L³

3 H²

8 ·x^#»₁−(x·x^#»₁+z·z^#»₀)∧ −^L³ 3 · ^H

2 ·y^#»₁=^#»0

−^L 4·z^#»₀+¹

3 H

4 ·x^#»₁−(x·x^#»₁+z·z^#»₀)∧ −¹ 3·y^#»₁=^#»0

−^L 4·z^#»₀+¹

3 H 4 ·x^#»₁+¹

3·x·z^#»₀−¹

3·z·x^#»₁=^#»0

−^L 4+¹

3·x

·z^#»₀+ 1

3 H

4 −¹ 3·z

·x^#»₁=^#»0

~NI3L3Nj

−^L 4+¹

3·x=0⇒ x=³ 4·L 1

3 H 4 −¹

3·z=0⇒ z= ^H 4

[SzY /āj3aLCN3a I3 LRL3Nj 3N Q 0n jRac3na 03 Iȕ,jCRN Lā,NC\n3 jaNcLCccC$I3 Ua I ICCcRN cU@ěa3 ,wICN0a3 3Nja3 VzW 3j VSWY

94 Hw,ā3 +@aI3L<N3ATaCc

(3)

QN cCj

A^A₀_→₁=

⎧⎨

⎩ XA 0 YA 0

0 0

⎫⎬

⎭ (^#»^{? ,}^#»^{? ,}^z^#»A0)

# »

MO,0→1A=M# »A,0→1A+OA^{# »}∧(X_A·x^#»₀+Y_A·y^#»₀)

# »

MO,0→1A=H·z^#»₀∧(XA·x^#»₀+YA·y^#»₀)

# »

M_O,0→1A=H·X_A·y^#»₀−H·Y_A·y^#»₀

0ȕRɵ

A^A₀_→₁=

⎧⎨

⎩

XA −H·YA

Y_A H·X_A

0 0

⎫⎬

⎭O (x^#»₀,y#»₀,#»z₀)

[SSY /āj3aLCN3a I3 jRac3na aācnIjNj 03c 03nu ICCcRNc 3Nja3 I3 $A ERw3a VzW 3j I3 qNjCI VSW 3N QY

{A₀_→₁}=A^O₀_→₁+A₀^A_→₁ {A₀_→₁}=

⎧⎨

⎩ XO 0 YO 0 ZO 0

⎫⎬

⎭ (x^#»₀,y#»₀,Oz#»₀)

+

⎧⎨

⎩

XA −H·YA

YA H·XA

0 0

⎫⎬

⎭ (x^#»₀,y#»₀,O#»z₀)

{A₀_→₁}=

⎧⎨

⎩

XO+XA −H·YA

Y_O+Y_A H·X_A

Z_O 0

⎫⎬

⎭ (^#»x₀,y#»₀,O#»z₀)

QN a3,RNNţj I3 jRac3na 03c ,jCRNc jaNcLCccC$I3c 0ȕnN3 ICCcRN TCqRjY

[SlY 2N CcRINj. Iȕ3Nc3L$I3 'l.k(. EncjC~3a \n3 I aācnIjNj3 03 Iȕ,A jCRN Lā,NC\n3 3N 03 I jC<3 0n qāaCN cna I3 qNjCI cȕā,aCj -R# »₃_→₁= F·y^#»₂Y

Hȕ3Nc3L$I3 'l.k( 3cj cRnLCc © Iȕ,jCRN 03 03nu <ICcc3nac VcU@āA aC\n3 3N # 3j +WY QN cCj \n3 Iȕ3Nc3L$I3 3cj 3N ā\nCIC$a3 cC I3c 03nu aācnIjNj3c cRNj RUURcā3c 3j ,RICNāCa3c URajā3c Ua I 0aRCj3 UccNj Ua I3c 03nu URCNjc 0ȕUUIC,jCRN 03c ,jCRNc Lā,NC\n3c V# 3j + C,CWY I 0aRCj3 V#+W URna q3,j3na nNCjCa3y#»₂. RN 0 0RN, $C3N -

# »

R₃_→₁=F·y^#»₂ VSzYSW

QN 0RN, A₃_→₁=

⎧⎨

⎩ 0 0 F 0 0 0

⎫⎬

⎭ (^#»x₂,y#»₂,#»zC₀)

[SkY /āj3aLCN3a I3 LRL3Nj 3N Q 03 ,3jj3 ,jCRN# » MO,3→1Y

# »

MO,3→1=^#»0+OC^{# »}∧F·y^#»₂

# »

M_O,3_→₁= (H·z^#»₀+a·x^#»₁)∧F·y^#»₂

# »

MO,3→1=−H·F·x^#»₂+a·F·sin(x^#»₁,y#»₂)·z^#»₀

# »

M_O,3→1=−H·F·x^#»₂+a·F·sin(^π

2 +β−α)·z^#»₀

# »

MO,3→1=−H·F·x^#»₂+a·F·cos(β−α)·z^#»₀

I3 jRac3na 03qC3Nj

A₃_→₁=

⎧⎨

⎩

0 −H·F

F 0

0 a·F·cos(β−α)

⎫⎬

⎭ (x^#»₂,#»y₂,Oz#»₀) [S:Y /āj3aLCN3aF3N 8RN,jCRN 03 I Ua3ccCRNpvY

2N CcRINj. I jC<3 0n qāaCN. 3II3 3cj cRnLCc3 © I Ua3ccCRN. Iȕ,A jCRN 0n ,RaUc 3j Iȕ,jCRN 0n qNjCIY 2N ā,aCqNj I3 j@āRaěL3 03 I aācnIjNj3 cnCqNjy#»₂. RN 0ā0nCj -

F=pv·Su

[S9Y Taā,Cc3a I3c nja3c ,jCRNc Lā,NC\n3c 3ujāaC3na3c cna I3 qNA jCI. 3j I3na LRL3Nj 3N Q 3N UaRE3,jCRN cnaz#»₀Y

H 03aNCěa3 ,jCRN 3ujāaC3na3 cna I3 URajCI 3cj I3 URC0cY C,C I3 URC0c 3cj URajā Uaz#»₀I3 LRL3Nj 3N Q 3N UaRE3,jCRN cna#»z(0] 3cj 0RN, NnIY

[SfY ĀNRN,3a I3 T7bY +8 +Rnac

URna I3 qNjCI. RN

{A₀_→₁}+{Aeau→1}+P_g_→₁+{A₃_→₁}=0 [SeY [n3II3 ā\njCRN 0RCjARN ā,aCa3 URna R$j3NCa nN3 a3IjCRN 3Nja3 Iȕ,jCRN 03 Iȕ3n 3j Iȕ,jCRN 0n qāaCN cna I3 qNjCI. EncjC~3a ]

QN ,@3a,@3 nN3 a3IjCRN 3Nja3 Iȕ,jCRN 03 Iȕ3n 3j Iȕ,jCRN 0āq3A IRUUā3 Ua I3 qāaCNY Hȕ,jCRN 0n qāaCN 0RCj 3NjaţN3a 3N aRjjCRN I3 qNjCI njRna 03(O,z#»₀). Iȕ,jCRN 03 Iȕ3n cȕRUURcNj © ,3 LRnq3A L3NjY BI c3L$I3 0RN, U3ajCN3Nj C,C 0ȕā,aCa3 Iȕā\njCRN 0n LRL3Nj 3N UaRE3,jCRN 3NOcnCqNjz#»₀

[S4Y /āj3aLCN3a I a3IjCRN 0RNNNjF3N 8RN,jCRN 03 I qCj3cc3 03 aRjjCRNω10n qNjCI. 3N 0ā0nCa3pv3N 8RN,jCRN 03ω1Y

# »

MO,0→1+# »

MO,eau→1+# »

MO,g→1+# » MO,3→1

·^#»z(0] =0

0−k·ρ·ω²₁·^L⁴ 4

H

2 +0+a·F·cos(β−α) =0 0ȕRɵ

F= ^k·ρ·ω²₁

a·cos(β−α)·^H·L⁴ 8

+RaY e - #aa<3 0n +Rn3cNRN bnE3j U<3 :4

[SY ia,3a I3 <aU@3 03 cjan,jna3 0n Lā,NCcL3 0n Lā,NCcL3 ,RLUI3jY Taā,Cc3a I3c jRac3nac ,CNāLjC\n3c 03 I $Rn,I3(O₁,A₁,B₁)^Y

z - a0C3a S - qNN3

kS - ,RaUc lS - jC<3

L₀₃₋₁-bU@āaC\n3 3N(B₁) L₃₂₋₁- TCqRj ;ICccNj 0ȕu3(B₁,x# »₂₁)

L₂₁₋₁- bU@āaC\n3 3N(A₁)

L01−1-TCqRj0ȕu3(O1,#» z0)

kl - ,RaUc ll - jC<3

L₀₃₋₂-bU@āaC\n3 3N(B₂)

L₃₂₋₂- TCqRj ;ICccNj 0ȕu3(^B2,x# »₂₂) L₂₁₋₂- bU@āaC\n3 3N(A₂)

L01−1-TCqRj0ȕu3(O1, #»z0)

Hw,ā3 +@aI3L<N3ATaCc 9O

(4)

[lY DncjC~3a \n3 Iȕ,jCRN āIāL3NjCa3 03 Iȕ3n cna I qNN3 n URCNj Pcȕā,aCj -

# »

dFe→1(P) =−R₁·ρ·g·h·ds·^#»n

q3, ds=R₁·dα·dz 3j h=R₁·sinα

# »

dFe→1(P) =−R²₁·ρ·g·sinα·dα·dz·^#»n [kY /āj3aLCN3a# »

Fe→1=Fex·x^#»₀+Fey·y^#»₀Y [kY 7Ca3 IȕUUIC,jCRN NnLāaC\n3Y

# » Fe→1=⁻⁶⁰

0

L

−2L 2

−R²₁·ρ·g·sinα·dα·dz·^#»n

# » Fe→1=⁻⁶⁰

0

L

−2L 2

−R²₁·ρ·g·sinα·dα·dz·(cosα·x^#»₀+sinα·y^#»₀)

# » Fe→1=⁻⁶⁰

0

L

−2L 2

−R²₁·ρ·g·sinα·cosα·dα·dz·x^#»₀

+⁻⁶⁰

0

L

−2L 2

−R²₁·ρ·g·sin²α·dα·dz·y^#»₀

# »

Fe→1=−R²₁·ρ·g·L·⁻⁶⁰

0 sinα·cosα·dα·x^#»₀−R²₁·ρ·g·⁻⁶⁰

0 sin²α·dα·y^#»₀

# »

Fe→1=−R²₁·ρ·g·L·

1−cos²α 2

−60 0

·x^#»₀−R²₁·ρ·g·

t−cosα·sinα 2

₋₆₀

0

·y^#»₀

# » Fe→1=³

8·L·ρ·g·R²₁·x^#»₀−L·ρ·g·R²₁·¹ 8·√

3−¹ 6·π

·y^#»₀

[:Y DncjC~3a \n3 I3 jRac3na 03 Iȕ,jCRN Lā,NC\n3 03 Iȕ3n 3N Q cȕā,aCj -

A_e_→₁=

⎧⎨

⎩ Fex 0 Fey 0

0 0

⎫⎬

⎭ (^#»x,#»y,O#»z) H3 LRL3Nj 3cj NnI ,a# »

OM∧# » dFe→1(P) =^#»0Y [9Y ia,3a I3 <aU@3 03 cjan,jna3 03 ,3 Lā,NCcL3Y

[9Y TI,3a I3c ,jCRNc Lā,NC\n3c. 03 Iȕ3n. 03 I <aqCjā 3j 03 I Ua3ccCRN VRN Nā<IC<3a I Lcc3 03 I jC<3 3j 0n ,RaUc 0n qāaCN 03qNj I Lcc3 03 I qNN3 VSW 3j 03c ,jCRNc Lā,NC\n3cY

[9$Y `UU3I3a I3 jRac3na 0ȕ,jCRN Lā,NC\n3 jaNcLCccC$I3 Ua ,@\n3 ICCcRN 0Nc I3 ,c 03 Iȕ@wURj@ěc3 0ȕnN LR0ěI3 UINY

[9,Y +RL$C3N 0ȕCN,RNNn3c 03 ICCcRNc URccě03 ,3 Lā,NCcL3 ] [90Y +RL$C3N 0ȕā\njCRN U3njARN ā,aCa3 ]

[93Y +RN,Ina3Y

z

S l

k

P ( O, z #»

₀

) P ( B, z #»

₀

) G z #»

₀

P ( A, z #»

₀

)

A

_e_→₁

P

_g_→₁

{ PS

₂_→₃

}

,jCRNc 03 ICCcRN

{A₀_→₁}=

⎧⎨

⎩ X₀₁ 0 Y₀₁ 0

0 0

⎫⎬

⎭ (^#»? ,#»O

? ,#»z₀) {A₁_→₂}=

⎧⎨

⎩ X₁₂ 0 Y₁₂ 0

0 0

⎫⎬

⎭ (^#»^{? ,}^#»^{? ,}^#»^zB0) {A₂_→₃}=

⎧⎨

⎩

0 0

Y₂₃ 0 0 N₂₃

⎫⎬

⎭∀P (^#»x₃,y#»₃,#»z₃)

{A₀_→₃}=

⎧⎨

⎩ X₀₃ 0 Y₀₃ 0

0 0

⎫⎬

⎭ (^#»^{? ,}^#»^{? ,}^z^#»A0)

,jCRNc Lā,NC\n3c

{PS₂→3}=

⎧⎨

⎩ p·S 0

0 0

⎫⎬

⎭∀Pin(A,x#»₃) (^#»x₃,y#»₃,#»z₃) Pg→1

=

⎧⎨

⎩

0 0

−m₁·g 0

0 0

⎫⎬

⎭ (^#»^{? ,}^#»^{? ,}^z^#»G0) {Ae→1}=

⎧⎨

⎩ Fex 0 Fey 0

0 0

⎫⎬

⎭ (^#»x,#»y,O#»z)

H3 Lā,NCcL3 UIN ,RLURaj3ns=8CN,RNNn3cY 0Nc I3 UIN RN U3nj ā,aCa3ne=3·(n−1) =9)ā\njCRNcY

H3 cwcjěL3 ,RLURaj3 0RNc8CN,RNNn3c URna9ā\njCRNc. CI 3cj

[fY DncjC~3a ,3jj3 cjajā<C3Y

<ICcc3nac. I3c 03nu <ICcc3nac cRNj RUURcāc 3j URajāc Ua I 0aRCj3(AB)Y

lY RN CcRI3 3NcnCj3 'l( - I jC<3 'l( 3cj cRnLCc3 © 03nu <ICcc3nac VI3 Uaā,ā03Nj 3j I Ua3ccCRNW 3j I ICCcRNc <ICccCěa3. IȕCcRI3L3Nj q U3aL3jja3 03 0āj3aLCN3a I aācnIjNj3 03 Iȕ,jCRN 031→2 3N 8RN,jCRN 03 I Ua3ccCRNY

kY RN CcRI3 ~NI3L3Nj 'S(

[eY 2N CcRINj 'l.k( UnCc 'l(. 3N 0ā0nCa3 Iȕ,jCRN 3NB3Nja3 I3c cRIC03c l 3j S 3N 8RN,jCRN 03PH3j 03c 0CL3NcCRNc njCI3c 0n qāaCNY PM BbQH2 &k-j' ,_⎧ bRnLCc © 03nu <ICcc3nac {A₁_→₂} =

⎨

⎩ X₁₂ 0 Y₁₂ 0

0 0

⎫⎬

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3j{A₀_→₃}=

⎧⎨

⎩ X₀₃ 0 Y₀₃ 0

0 0

⎫⎬

⎭ (^#»^{? ,}^#»^{? ,}^#»^zA0)

Y

+3c 03nu <ICcc3nac cRNj 0RN, RUURcāc. I3 cnUURaj 03c <ICcA c3nac 3cj I 0aRCj3 0ȕ,jCRN(A,x#»₃)Y

QN 0RN, 0Nc I $c3(x^#»₃,y#»₃,z#»₃)VURna I3 0ājCI 03c ,IA ,nIc. qRCa I3 ,Rnac 6W -{A₁_→₂}=

⎧⎨

⎩ X₁₂ 0

0 0

⎫⎬

⎭ (^#»x₃,y#»₃,#»zB₀)

3j{A₀_→₃}=

⎧⎨

⎩

−X₁₂ 0

0 0

⎫⎬

⎭ (x^#»₃,y#»₃,zA#»₀)

Y

⎧⎨

⎩ X₁₂ 0

0 0

⎫⎬

⎭ (^#»x₃,y#»₃,#»zB₀)

.{PS₂_→₃} =

−

⎧⎨

⎩ p·S 0

0 0

⎫⎬

⎭∀Pin(A,#»x₃) (x^#»₃,y#»₃,#»z₃)

3j{A₁_→₂}=

⎧⎨

⎩ X₁₂ 0

0 0

⎫⎬

⎭ (^#»? ,#» B

? ,z#»₀) Y

2N ā,aCqNj I3 j@āRaěL3 03 I aācnIjNj3 cjjC\n3 3N UaRE3,A jCRN cnCqNjx#»₃. RN R$jC3Nj

X₁₂=p·S

BI Nȕ3cj Uc njCI3 0ȕā,aCa3 I3c nja3c ā\njCRNc 6

fz Hw,ā3 +@aI3L<N3ATaCc

(5)

[4Y QN CcRI3 LCNj3NNj 'S(

⎧⎨

⎩

−p·S 0

0 0

⎫⎬

⎭ (x^#»₃,y#»₃,#»zB₀)

.

A₀_→₁ =

⎧⎨

⎩ X₀₁ 0 Y₀₁ 0

0 0

⎫⎬

⎭ (^#»? ,#»O

? ,#»z₀) .

P_g_→₁=

⎧⎨

⎩

0 0

−m₁·g 0

0 0

⎫⎬

⎭ (x^#»₀,#»y₀,zG#»₀)

3j A_e_→₁=

⎧⎨

⎩ Fex 0 Fey 0

0 0

⎫⎬

⎭ (x^#»₀,y#»₀,O#»z₀)

Y

[4Y [n3II3 ā\njCRN 8njACI ā,aCa3 URna R$j3NCa 0Ca3,j3L3Nj nN3 a3IjCRN 3Nja3p_H3j I3c 3{Rajc 3ujāaC3nacY

B,C c3nI3 Iȕā\njCRN 03c LRL3Njc 3NO3N UaRE3,jCRN cnaz#»₀3cj njCI3. 3II3 U3aL3j 03 N3 Uc 8Ca3 CNj3aq3NCa I3c CN,RNNn3c 03 I ICCA cRN

A₀_→₁Y

# »

MO,2→1·z^#»₀+# »

MO,0→1·z^#»₀+# »

MO,G→1·z^#»₀+# » MO,E→1·z^#»₀=0

# »

OB∧(−p·S·x^#»₃)·z^#»₀+^#»0+OG^{# »}∧(−m₁·g·y^#»₀)·z^#»₀+^#»0 =0 (a·x^#»₁+b·y^#»₁)∧(−p·S·x^#»₃)·z^#»₀+ (c·x^#»₁+d·y^#»₁)∧(−m₁·g·y^#»₀)·z^#»₀=0

−e·p·S·sin(β+θ)−f·p·S·cos(β+θ)−c·m₁·g·cosβ+d·m₁·g·sinβ=0

−p·S·(^e·sin(β+θ) +f·cos(β+θ)) +m₁·g·(−c·cosβ+d·sinβ) =0

p·S=^m¹·g·(−c·cosβ+d·sinβ) e·sin(β+θ) +f·cos(β+θ) q3,

tanθ= ^f−a·sinβ−b·cosβ e−a·cosβ+b·sinβ

[OY [n3I 3cj Iȕ3{3j 03 Iȕ,jCRN 03 Iȕ3n cna I Ua3ccCRN ] naCjARN Un UaāqRCa ,3 ,RLURaj3L3Nj ]

Tc 0ȕ3{3j 0Ca3,j cna I Ua3ccCRN 0Nc I3 qāaCN. I 8RaL3 03 I qNN3 ājā ,@RCcC3. URna Encj3L3Nj URnqRCa c3 0āUI,3a 0Nc Iȕ3n cNc \n3 I @nj3na 0ȕ3n cRCj nN UaR$IěL3Y

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+RaY 4 - `R$Rj `RLāR bnE3j U<3 9l

[SY ~N 03 ,@RCcCa I3 ,Uj3na 03 8Ra,3 Nā,3ccCa3 © ,3jj3 ,LU<N3 03 L3cna3c. 0RNN3a nN Ra0a3 03 <aN03na 03 Iȕāj3N0n3 03 L3cna3c Nā,3ccCa3. CNcC \nȕnN Ra0a3 0ȕC0ā3 03 I Uaā,CcCRN a3\nCc3Y

TRna aāICc3a ,3c 3ccCc. CI Nȕ3cj Uc Nā,3ccCa3 0ȕqRCa nN3 <aN03 Uaā,CcCRNY +3c L3cna3c RNj URna c3nI $nj 0ȕqRCa nN3 C0ā3 03 Iȕ3{Raj

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[lY ¨ UajCa 0ȕnN 3Na3<Ccja3L3Nj 03 Iȕ3{Raj 03 a3Iěq3L3Nj 3N 8RN,A jCRN 0n j3LUc VcCLnIā IRac 0ȕnN3 3uUāaC3N,3W. 0RNNā 3N NN3u3 ]].

Hȕ3{Raj 0RCj ćja3 LCNj3Nn nN U3n UInc 033 sY

[kY TRna I $Rn,I3 <n,@3 0n <aU@3 03c ICCcRNc V~<na3 ]]W . 0RNN3a I3c jRac3nac ,CNāLjC\n3c 3j I3c jRac3nac 03c ,jCRNc jaNcLCccC$I3c Ua I3c ICCcRNcY

ġ HCCcRN2Dg z -

V_2D/0=Ω# »2D/0=ω2D/0·y^#»₀

#»0

C_D

.

A₀_→_2D=

⎧⎨

⎩

X_02D L_02D Y_02D 0 Z_02D N_02D

⎫⎬

⎭

C_D (x^#»₀,#»y₀,z#»₀)

ġ HCCcRN3Dg2D-

V_3D/2D=Ω# »3D/2D=ω3D/2D·y^#»₀

#»0

BC_D

. A_2D_→_3D=

⎧⎨

⎩

X_2D3D L_2D3D Y_2D3D 0 Z_2D3D N_2D3D

⎫⎬

⎭

B_D (x^#»₀,y#»₀,z#»₀)

d

ġ HCCcRN4Dg3D-

V_4D/3D=

⎧⎨

⎩ ωx43 0 ωy43 0 ωz43 0

⎫⎬

⎭

A_D (x^#»₀,y#»₀,z#»₀)

.

A_3D_→_4D=

⎧⎨

⎩

X_3D4D 0 Y_3D4D 0 Z_3D4D 0

⎫⎬

⎭A_D (x^#»₀,y#»₀,#»z₀)

ġ HCCcRN4Dg0-

V_4D/0=

⎧⎨

⎩

0 V_x43 0 V_y43 ωz43 0

⎫⎬

⎭

O_D (^#»x₀,y#»₀,z#»₀)

.

A₀_→_4D=

⎧⎨

⎩

0 L_04D 0 M_04D Z_04D 0

⎫⎬

⎭

G_D (x^#»₀,#»y₀,z#»₀)

Y

ġ N$ N,RNNn3c -Ic =8CN,RNNn3c ,CNāLjC\n3c.Is =16CNA ,RNNn3c 03 ICCcRN

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H Ua3LCěa3 LR$CICjā 3cj I aRjjCRN 0n UC30 njRna 03 Iȕu3 (OD,z#»₀)Y H 03nuCěL3 ,Raa3cURN0 n LRnq3L3Nj 0n UC30. 03 I EL$3 3j 03 I ,nCcc3 R$j3Nn 3N 8CcNj <ICcc3a I3 UC30 cna I3 cRI VqRCa I ~<na3 ]]WY

C_D

B_D

AD

OD

C_D

B_D

AD

OD

[9Y Taā,Cc3a I3 NRL$a3 0ȕCN,RNNn3c 03 ICCcRNc 03 ,3 LR0ěI3 cCLUICA

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H3 Lā,NCcL3 ,RLURaj3Is =16CN,RNNn3c. I3 Lā,NCcL3 ,RLA URaj3N=4cRIC03c cRCjEs= (N−1)·6=18ā\njCRNc. I3 cwcjěL3 ,RLURaj3m=2LR$CICjāc. CI 3cj 0RN, URccC$I3 03 aācRn0a3 ,RLUIěA j3L3Nj I3 Lā,NCcL3h=Es−Is−m=0Y

[fY DncjC~3a \n3 I3c ICCcRNc 3Nja3 I3c cRIC03c Vk/W 3j Vk;W 3j I3 cRI VzW U3nq3Nj ćja3 LR0āICcā3c Ua 03c ICCcRNc cU@ěa3AUINY

Hw,ā3 +@aI3L<N3ATaCc 9e

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z

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A

P

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fz Hw,ā3 +@aI3L<N3ATaCc

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