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`2pBbBQM A +BMĀKiB[m2 /vMKB[m2

2u3a,C,3 SA 2bTA +RNjaǃI3 0wNLC\n3 03 cj$CICjā 03c qā@C,nI3c

+RaaC<ā U<3 Sz

X S`ûb2MiiBQM

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ġ +Uj3na qCj3cc3 aRn3cY ġ +Uj3na N<I3 03 $a\n<3Y

ġ +Uj3na 0ȕ,,āIāajCRN jaNcq3acI3Y

H ,Raa3,jCRN 03 jaE3,jRCa3 3cj ,RNjaǃIā3 Ua I3 ,I,nIj3na <a‘,3 nu CN8RaLjCRNc 8RnaNC3c Ua I3 ,UA j3na <waRc,RUC\n3 0ȕN<I3 03 I,3jY

+3jj3 ājn03 qCc3 © L3jja3 3N āqC03N,3 I3c UaCN,CU3c U@wcC\n3c LCc 3N Ǖnqa3 0Nc I3 0CcURcCjC8 2bTY 2II3 c3 0ā,RLURc3 ,RLL3 cnCj -

SY Ājn03 UaāI$I3Y

lY bCjnjCRN 03 ,RLURaj3L3Nj ,aCjC\n3 0n qā@C,nI3Y kY /āj3aLCNjCRN 03 I 0āaCq3 0n qā@C,nI3Y

:Y +Raa3,jCRN 03 jaE3,jRCa3 XRX .QMMû2bX (6B;X RXk) +RN0CjCRNc 0ȕājn03 -

ġ H3 qā@C,nI3 03 jwU3 ja,jCRN VaRn3c p LRjaC,3cW 0ā,aCj nN a, 03 ,3a,I3. 03 awRN ,RNcjNj ā<I ©r.

cna nN3 aRnj3 @RaCyRNjI3 0Nc I3 UIN(O,x0,y0)Y

ġ H3 jN<<3 VaRjjCRN 0n qā@C,nI3 Ua aUURaj © Iȕu3(G,x1)W c3a ,RNcC0āaā NnIY H3 aRnICc VaRjjCRN 0n qā@C,nI3 Ua aUURaj © Iȕu3(G,y1)W c3a ,RNcC0āaā NnIY

ġ H3c aācCcjN,3c UccCq3c CNcC \n3 IȕCN3ajC3 03c āIāL3Njc 03 jaNcLCccCRN c3aRNj Nā<IC<ā3cY H LjaC,3 0ȕCN3ajC3 0n qā@C,nI3 VbW n URCNj ; 3uUaCLā3 0NcR23cj -

IG(S) =

IGx 0 0 0 IGy 0 0 0 IGz

(Gx2 ,y2 ,z2)

.

S

(2)

VW ,c 0n cna qCa<3 V$W ,c 0n cRnc qCa<3

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7ϔόЛЁζ SYS Ģ ,jCRN 0n ,RNjaǃI3 0wNLC\n3 03 cj$CICjā

TaLāja<3 - )7C<Y SYl U<3 k *

H URcCjCRN 0n ,3Nja3 0ȕCN3ajC3 ; 0n qā@C,nI3 VbW 3cj ICā3 n a3Uěa3(G,x1,y1,z1)Y H3 a3Uěa3(G,x2,y2,z2) 3cj ICā n qā@C,nI3Y

QN NRj3 -Ω# »R1/R0 = dα

dt ·z0=α˙ ·z0 =ω·z0Y

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(3)

VW TaLāja<3

V$W a3Uěa3c

H3 qā@C,nI3 a3Uaāc3Njā 3N jaCj CNj3aaRLUn VICā n a3Uěa3 R1W a3Uaāc3Nj3 I3 qā@C,nI3 3N jaE3,jRCa3 C0āI3Y H3 qā@C,nI3 3N jaCj ,RNjCNn VICā n a3Uěa3 R2W a3Uaāc3Nj3 I3 qā@C,nI3 3N cCjnjCRN ,aCjC\n3Y H cCjnjCRN ,aCjC\n3 3cj LR0āICcā3 Ua IȕN<I3 03 I,3j βY

7ϔόЛЁζ SYl Ģ TaLāja<3

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Hw,ā3 +@aI3L<N3ATaCc k

(4)

"X úim/2 T`ûH#H2

"XRX úim/2 ;`T?B[m2

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[SY ia,3a 3NA.C3jD. I 0Ca3,jCRN 03 # »

VAV/S. # »

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VBV/S3j # »

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VGV/SUa nN3 0CL3NcCRN 033 cm. ja,3a jRnj3c I3c qCj3cc3cY

"XkX úim/2 MHviB[m2 [lY /āj3aLCN3a # »

VGS/R0 qCj3cc3 0n URCNj ; UUaj3NNj n qā@C,nI3 Ua aUURaj ©R03uUaCLā3 0Nc I

$c3(x1,y1,z1)

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QN URc3 0Nc I3 a3Uěa3R1 - Γ# »GS/R0 = γx1·x1+γy1·y1 q3, γx1·x1 5,,āIāajCRN jaNcq3acI3 3j γy1·y15 ,,āIāajCRN IRN<Cjn0CNI3 VUa aā8āa3N,3 © I jaE3,jRCa3 C0āI3WY

[:Y /RNN3a Iȕ3uUa3ccCRN ICjjāaI3 03γx13N 8RN,jCRN 03r3j 03α˙ UnCc 03v3j 03rVv5 L3cna3 I<ā$aC\n3 0n q3,j3na # »

VGS/R0 3jr5 awRN 03 I jaE3,jRCa3 ,Ca,nICa3WY [9Y 2uUaCL3a # »

ΩS/R0 0Nc I $c3(x1,y1,z1)3N 8RN,jCRN 03α˙ 3j 03βY˙

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·z1Y Ā,aCa3 0Nc I $c3(x1,y1,z1). I3 jRac3na 0wNLC\n3 n URCNj ; 0n qā@C,nI3 03 Lcc3 L. 0Nc cRN LRnq3L3Nj Ua aUURaj ©R0Y

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H3c 0CL3NcCRNc 0n qā@C,nI3 CNcC \n3 I LR0āICcjCRN 03c ,jCRNc cRIgaRn3 V,c <āNāaIW cRNj 0RNNā3c cna I3c 0R,nL3Njc j3,@NC\n3c )~<na3 SYk U<3 : 3j ~<na3 SY: U<3 f*Y

VW b,@āL

ġ m=1 600 kg ġ L=2,95 m ġ a=1,25 m ġ b=1,70 m ġ e=0,81 m ġ h=0,47 m ġ IGz =1 780 kgm2 cna I3 c,@āL. R2= R1Y

V$W 0RNNā3c

7ϔόЛЁζ SYk Ģ +a,jāaCcjC\n3c 0n qā@C,nI3 QN 0RNN3

(5)

ġ I3c jRac3nac 0ȕ,jCRNc 0n cRI cna I3c aRn3c 3N . #. +. / 3uUaCLāc 0Nc I $c3(x1,y1,z1)- Asolroue =

⎧⎨

TAx 0

0 0

NA 0

⎫⎬

AB1

.

Bsolroue =

⎧⎨

TBx 0

0 0

NB 0

⎫⎬

BB1

.

Csolroue =

⎧⎨

TCx 0

0 0

NC 0

⎫⎬

CB1

.

Dsolroue =

⎧⎨

TDx 0

0 0

ND 0

⎫⎬

DB1

d

ġ I3 jRac3na 0wNLC\n3 0n qā@C,nI3 3uUaCLā 0Nc I $c3(x1,y1,z1)--

DS/R0=

⎧⎨

m·γx1 0

0 0

0 0

⎫⎬

GB1

Y

[eY BcRI3a I3 qā@C,nI3. 8Ca3 IȕCNq3NjCa3 03c ,jCRNc 3ujāaC3na3c. UUIC\n3a I3 UaCN,CU3 8RN0L3NjI 03 I 0wNLC\n3 3N ; 3j 3N 0ā0nCa3 I3c f ā\njCRNcY

+RN0CjCRN 0ȕ0@āa3N,3 jaNcq3acI3Y QN aUU3II3 \n3 - μtransersal =μt = −TAx

NA = −TBx

NB = −TCx

NC = −TDx

ND .

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[OY pCj3cc3 LuCLI3 0LCccC$I3Y HRac\n3μtransMAXI = 0,8. ,I,nI3a I qCj3cc3 LuCLI3 0LCccC$I3 0Nc ,3c ,RN0CjCRNc cNc \n3 I3 qā@C,nI3 c3 jaRnq3 3N cCjnjCRN ,aCjC\n3 03 0āaU<3Y QN aUU3II3 \n3 γx1 = −v2

r q3, awRN 03 I jaE3,jRCa3r =40 mY

[SzY `3jaRnq3a. © UajCa 03c ā\njCRNc 03 I 0wNLC\n3 3j 03 Iȕā\njCRN cnUUIāL3NjCa3. I3 cwcjěL3 0ȕā\njCRNc ,CA03ccRncY

NA+NB+NC+ND =m.g (NA−NB+NC−ND) =h·m·γx1

(NA+NB)−b·(NC+ND) =0

~N 03 URnqRCa āqIn3a I3c ,jCRNc 03 ,Raa3,jCRN UUIC,$I3c © ,@\n3 aRn3. CI 3cj Nā,3ccCa3 03 ,RNNţja3 I ,@a<3 cȕ3u3aÓNj cna ,@,nN3 0ȕ3Nja3 3II3cY QN 0ā~NCj nN jnuK03 aāUajCjCRN 03c ,@a<3c 3Nja3 I3c aRn3c 3ujāaC3na3c 3j CNjāaC3na3c 0ȕnN qā@C,nI3 3N qCa<3 j3I \n3K= NB

NA = ND NC

[SSY /āj3aLCN3a. Iȕ3uUa3ccCRN ICjjāaI3 03c ,RLURcNj3c NRaLI3cNA NB NC3j ND3N 8RN,jCRN 03a.b.

L.m.g3jKY

[SlY KRNja3y \n3K= g·e−h·γx1

g·e+h·γx1. UnCc ,I,nI3a © UajCa 03c ,a,jāaCcjC\n3c 0n qā@C,nI3. I3c qI3nac 03NA NB NC3jNDURna nN qā@C,nI3 aRnINj ©60 km h1cna nN3 jaE3,jRCa3 ,Ca,nICa3 03 awRN40 mY [SkY bCjnjCRN ,aCjC\n3 -

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VLćL3 cCjnjCRN URna I3c aRn3c `WY

+b # © UajCa 03 I cCjnjCRN 0n ,c W. I3 ,RN0n,j3na ,,āIěa3 3j UUIC\n3 nN ,RnUI3 LRj3na nu aRn3c LRjaC,3c d CNcC 03c ,RLURcNj3c jN<3NjC3II3c IRN<Cjn0CNI3c qC3NN3Nj cȕERnj3a n NCq3n 03c ,A jCRNc cRIgaRn3c LRjaC,3cY

[SkY KR0āICc3a 0Nc I3c 03nu ,c V 3j $W d I3c ,jCRNc 03 ,RNj,j jN<3NjC3II3c n NCq3n 0ȕnN3 aRn3 LRjaC,3 3N a3UaR0nCcNj cna qRja3 83nCII3 03 ,RUC3 I3 LR0ěI3 <aU@C\n3 UaRURcā cna I ~<na3 SY:Y +RN,Ina3

Hw,ā3 +@aI3L<N3ATaCc 9

(6)

VW b,@āL 0n ,RNj,j cRI aRn3

H 0ā,RLURcCjCRN 03 jRnj3c I3c ,jCRNc cRIgA aRn3 c3 83a 0Nc I3 a3Uěa3R1 VN<I3 03 $aA

\n<3 03c aRn3c qNj Nā<IC<āW CNcC URna I aRn3 3N . RN NRj3 -

# »

Asol→roue =TAx·x1+TAy·y1+NA·z1

q3,

ġ TAx - ,RLURcNj3 jN<3NjC3II3 jaNcq3acI3

ġ TAy- ,RLURcNj3 jN<3NjC3II3 IRN<Cjn0CNI3

ġ NA - ,RLURcNj3 NRaLI3 QN 0RNN3 -

/Nc I3 ,c 0ȕnN qCa<3 © <n,@3 Ua aUURaj n a3Uěa3R1V,c ājn0CāW -

μtransversal = TAx NA

0Nc I3 ,c 03c aRn3c LRjaC,3c Vqā@C,nI3 3N ,,āIāajCRNW -

μlongitudinal= TAy NA

?wURj@ěc3 -

μtransversal =μlongitudinal =μMAXIsol/roues

=μmax

2N 3{3j I3 cwcjěL3 2bT LCNjC3Nj I3c UN3nA LjC\n3c 0Nc nN3 UI<3 03 X 03 <ICcc3L3Nj 8C$I3 Rɵ ,3jj3 @wURj@ěc3 3cj qI$I3Y

+RN0CjCRN 0ȕ0@āa3N,3 - TA μmaxNA q3, # »

TA =T# »Ax+T# »Ay

3jμmax =0,8

V$W 0RNNā3c 3j @wURj@ěc3c

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cna Iȕ0@āa3N,3 03 I aRn3 0Nc I3 ,c $Y

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#. + 3j /Y

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.X .ûi2`KBMiBQM /2 H /û`Bp2 /m pû?B+mH2

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(7)

[S:Y TaCN,CU3 0n ,I,nI 03γx1th =v2

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[S:$Y āj$ICa I a3IjCRN 0RNNNj a 3N 8RN,jCRN 03L.θroue3je. 3N ,RNcC0āaNj \n3r= IS/R0C+eY [S9Y TaCN,CU3 03 I L3cna3 03γx3rel

H3 qā@C,nI3 3cj ā\nCUā 0ȕnN ,Uj3na 0ȕ,,āIāajCRN jaNcq3acI3 LR0āICcā ~<na3 SY9Y

H Lcc3 VkW 3cj 3N ICCcRN <ICccCěa3 0ȕu3 x2

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n LRL3Nj 03 I L3cna3. I Lcc3 VkW cRnLCc3 © Iȕ,,āIāajCRNγx3rel 3cj 3N ā\nCIC$a3 Ua aUURaj n ,@‘ccCc VbWY

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+RN,IncCRN - 2N ,RLUaNjγx3relL3cnaā3 3jγx1th,I,nIā3. I3 ,I,nIj3na 0āj3,j3 nN3 cCjnjCRN ,aCjC\n3 qIC0ā3 Ua I3 ,Uj3na 0ȕN<I3 03 I,3j Vβ = 0WY H3 cwcjěL3 RUěa3 IRac nN3 U@c3 03 ,Raa3,jCRN 03 jaA E3,jRCa3 Ua nN3 ,jCRN 03 8a3CN<3 ,C$Iā3 cna nN3 aRn3 0ȕnN3 Uaj 3j Ua I aā0n,jCRN 0n ,RnUI3 LRj3na 0ȕnja3 UajY

1X *Q``2+iBQM /2 i`D2+iQB`2

+RN0CjCRNc 0ȕājn03 - qā@C,nI3 3N qCa<3 © <n,@3 Vβ=0WY

H3 ,I,nIj3na 0āj3,jā nN3 cCjnjCRN 03 cRncAqCa<3Y H3 ,RnUI3 LRj3na cna I3c aRn3c p 3cj cnUUaCLā 3j I aRn3 ` <n,@3 c3nI3 a3ÓRCj nN ,RnUI3 03 8a3CN<3 ,RNjaǃIā \nC CN0nCj nN3 ,RLURcNj3 jN<3NjC3II3 IRN<Cjn0CNI3TCyn NCq3n 03 Iȕ,jCRN 0n cRI cna I aRn3 `;Y

QN 0RNN3 I3 jRac3na 0wNLC\n3 0n qā@C,nI3 -

DS/R0=

⎧⎨

m·γx1 0 m·γy1 0

0 IGz·α¨ +β¨

⎫⎬

GB1

Y

[SeY BcRI3a I3 qā@C,nI3. 8Ca3 IȕCNq3NjCa3 03c ,jCRNc 3ujāaC3na3c UnCc LR0āICc3a ,3c ,jCRNc Ua 03c jRaA c3nac 0RNj I3c ,RLURcNj3c c3aRNj 3uUaCLā3c 0NcR2UnCc 0NcR1Y

Hȕ2bT <Cj 0ěc I3 0ā$nj 03 I cCjnjCRN 03 cRncAqCa<3 0ěc \n3β¨ = 0. RN U3nj 0RN, ,RNcC0āa3a \n3β 3cj U3jCjY

[S4Y Ā,aCa3 IRac I3c ā\njCRNc. Cccn3c 03 I UaRE3,jCRN cnax13j cnaz1. 0n j@āRaěL3 0n LRL3Nj 0wNA LC\n3. UUIC\nā n qā@C,nI3 3N ; 0Nc cRN LRnq3L3Nj Ua aUURaj ©R03N ,RNcC0āaNj \n3β3cj U3jCjY

Hw,ā3 +@aI3L<N3ATaCc e

(8)

KRNja3a \n3 IȕRN R$jC3Nj -

(NA+NB)−b·(NC+ND) =−h·TCy

(TCx+TDx)−a·(TAx+TBx)−e·TCy = IGz·α¨ +β¨ [SOY 2N 0L3jjNj \nȕCI w Cj ā\nCA0@āa3N,3 jaNcq3acI3

μt=μt = −TAx

NA = −TBx

NB = −TCx

NC = −TDx

ND

.

/āj3aLCN3a © IȕC03 03c 03nu ā\njCRNc ,CA03ccnc Iȕ3uUa3ccCRN 03 I ,RLURcNj3 jN<3NjC3II3 03 8a3CN<3 TCy3N 8RN,jCRN 03μt.IGz.α.¨ β¨3j I3c 0CL3NcCRNch3jeY

2N U@c3 03 ,Raa3,jCRN RN ,RNcC0ěa3α¨ Nā<IC<3$I3 03qNjβY QN Ua3N0a URna I cnCj3 03 Iȕājn03¨ α¨ =0Y [lzY

[lzY H ,RLURcNj3 jN<3NjC3II3 03 8a3CN<3TCy3cj 03 cC<N3 Nā<jC8Y /āj3aLCN3a IRac I3 cC<N3 03βY¨ [n3 U3nj RN 0Ca3 03 I qaCjCRN 03 I qCj3cc3 03 I,3jβ˙ 0Nc I3 ,c Rɵβ˙ <0Y +RN,Ina3 cna IȕRUURajnNCjā 03 I ,Raa3,jCRN \nC 3N aācnIj3Y

[lz$Y H3 ,@C3a 03c ,@a<3c 0n cwcjěL3 CLURc3 ,RLL3 ,aCjěa3 03 ,Raa3,jCRN 03 jaE3,jRCa3 β¨ = 0,4 rad s2Y +I,nI3a © UajCa 03c 0RNNā3c ,CA03ccnc 3j 03c ,a,jāaCcjC\n3c I qI3na 03 I ,RLURcNj3 03 8a3CN<3TCyY

[lz,Y QN 0L3j \n3 NC = 1 960 N.TCx = 1 390 N3jTCy = 600 NY +I,nI3aTC3j 3N 0ā0nCa3 I3 ,R3|,C3Nj 0ȕ0@āa3N,3 cRIgaRn3 Nā,3ccCa3Y

(9)

7ϔόЛЁζ SYf Ģ /` A /āj3aLCNjCRN 0n +B`

Hw,ā3 +@aI3L<N3ATaCc O

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