313233 34 35

31 1. ()

2. 3.

32 1)

2 1 2 3nNn(n-1)/2

31. 2.

P21 P 31 P 32

1.2.3.Nn(n-1)/26 n=4

Nn(n-1)/215 n=61.2.3.

1.1P13 P23 P12 V2V P12l(P13P12)1P13P12 nnP12

2.642P24 VP24l(P24P14)4 4 2 (P24P12)/ P24P14 a)2244 VP24l(P24P12)2: CW, 2

b)2233 : P23 P23 :VP23l(P23P13)3 32(P13P23/P12P23): CCW, 2VP23l(P23P12)2

3.3 /2 P12P23 / P13P23 i /j P1jPij / P1iPij:

4.; V,V

33 1.

2. 1) v m/s/mmpVAvpa VBAvab VBvpb, BA? ?p c a c

VCv pcVCAv acVCBv bcp c a c b c ? ? ? ? CA CB

VBA/LBAvab/l AB vca/l CApabc) pab/ABbc/ BCca/CA abcABC CWvcb/l CB

:p p bc VCBVBC abcABCabcABC 90pabc PABCp

BCEVEbceEpeVEAD

2) aBapba m/s2/mmpaAapaAaBatBAabb: b baBAab a: a b ?BA?BA2lAB

: atCAacc atCBaccc c c c p c ? ? ? ? ? ? 2lCACA? CA ? ?2lCBCB?CBaCapc

atBA/ lABab/ lABbc/ lBC a c/ lCApabc p abcABC p pCWa bb /l ABaaba aca bc

ab aBAaAB bc aCB ca aAC abcABCabcABC pabcPABC p :BCEaEbceEpeaE

2. 1) 2) VB3B2 : b2 b3 3 = vpb3 / lCB ? ?BC

aB3 apb3, akB3B2VB3B2 3 90 3atB3 /lBCab3b3 /lBCarB3B2 akb3 B C??23lBC BC?l121BA ?BC2VB3B23

21) VBLAB2 VVB /pb VFaF345345345VxX3X4X535I3I535Q3Q5I3I5 Q3 Q5 ? CD ?BC

VCB Vbc VCVpc bcCW4 VC /lCDCCWepef6 VFE v ef e f pf 5VFE /lFECW ?//DF3 VCB /lCBpc ?EFVF v pf

??24 lCDCD? CD23 lCB CB ?BC: 4= atC / lCD 3 = atCB/ lCB CCW CCW aC =a pc BCeeaBC =a bc bcpc aE =a pe

c6?//DF25 lFE FE ?BC: 5 = atFE/ lFE CCW aF =a pf atFE =a ff ffpf ef

345VxX3X4X5bcxBCX3 X335I3I5 cexCEX4 X4 efxEFX5 X5bcpBCI3 I3efpEFI5 I5

35Q3Q5I3I5aI3aQ5CaI3=a pi3aI5=a pi5bcpBCQ3 Q3 efpEFQ5 Q5bci3BCI3 efpEFQ5

1. VE=VF+VEF VG= VB+VGB ? ? ? VC=VB+VCB ? ? VC+VGC = VG ? ? ? : ? ? ? ? ?

B ? ? ? ? ? ? (a)(b)

(b)(C)B! ? ?

2.ak ak ak ak ak ak ak ak ak Bak ak

34 24C

35

1.l----

ej sin- cos (2 1 ) cos (2 1 ) 1 ei cos- sin (2 1 )

l,

2. : 1 ,232322 l2 cos2l3 cos3+ l4 cos4l1 cos1 (2) 2? 3? l2 sin2l3 sin3+ l4 sin4l1 sin1 (3)

(2)(3)l22l23+ l24+ l212 l3 l4cos3 2 l1 l3(cos3 cos1- sin3 sin1)2 l1 l4cos1 Asin3+Bcos3+C=0 (4)A=2 l1 l3 sin1B=2 l3 (l1 cos1- l4)C= l22l23l24l212 l1 l4cos1 tg(3 / 2)=[Asqrt(A2+B2C2)] / (BC) 2

l3 cos3l1 cos1+ l2 cos2l4 (6) (6)(7)l23l21+ l22+ l242 l1 l2cos1 2 l1 l4(cos1 cos2 - sin1 sin2 )2 l1 l2cos1 Dsin2+Ecos2+F=0 (8)D=2 l1 l2 sin1E=2 l2 (l1 cos1- l4 )F= l21+l22+l24l23- 2 l1 l4 cos1 tg(2 / 2)=[Dsqrt(D2+E2F2)] / (EF)l3 sin3l1 sin1+ l2 sin20 (7)

3 l3 sin (3 2 ) = 1 l1 sin (1 2 )3 = 1 l1 sin (1 2 ) / l3 sin (3 2 ) -2 l2 sin (2 3 ) = 1 l1 sin (1 3 )2 = - 1 l1 sin (1 3 ) / l2sin (23 )

9 -32 l3 cos (3 2 ) -3 l3 sin (3 2 ) = - 12 l1 cos (1 2 ) - 22 l2 3 =12 l1 cos (1 - 2 ) + 22 l2 -32 l3 cos (3 - 2 ) / l3 sin (3 2 ) 2 =12 l1 cos (1 - 3 ) + 32 l3 -22 l2 cos (2 - 3 ) / l2 sin (2 3 )

1.1,:232322 xpypvp ap

P2.

[A]{} =1{B}PP

3.15{}={}[A]+ 1

P

[A]{}{B}1 {}[A]{} =1{B}:

1. 2. 3., 4.