:

1 1-1 2-1 3-1 4-1

( ) 5-1

2 1-2 2-2 3-2 4-2 5-2

( ) 6-2

( ) : ( ) 1

( ) 1-1 2-1

3-1 4-1

.

.

.

5

1 . 2

. .

.

... ...

.

!

. :

.

. 2=1+1

!

(8 ) 1 (82 ) 2

6

...

.

. :

: : ! . ! 2=1+1

.

: .

.

. .

. . .... :

.

. .

7

-1

1-1

- . - ( )

. .

.

.

: .

.

.

. .

.

8

.

.

. ! ( 1)

. .

() () .

.

. .

. .

. -

. . -

. " " " "

9

. .

.

...

.

. : .

.

( ) .

.

: (2) 1 .

.

r

-1

01

( ) : .

: ( 3)

. .

.

: ( 54)

( )

.

. . .

: ( 6)

. .

. .

{ s3= s2= s1= } :

11

. v = = k 1s1+ k 2s2+ k3 s3= +

=++ vsss 110 123 :

=

011

sv

s( ) v :

s1 ,1=s2 , t=s3t=2 : ( 7) . vtt =++ 2 5012

=

=

===

=++=++=++

5012

5012

5012

3

2

1

3

2

1

22123

112233

vvv

v

vvv

vvtvttt

vvsvsvs

s v s v vvv ,, 123) ( s v s v

:

112233

3

2

1

vvsvsvs :vvv

==++ sv

=

21

2 : ( 8) s122,1 =) ( s111,1 =) ( ( "1" )

. 1, vxy =) (

=+ vvsvs 1122

21

121

1 =+ vvsvs 1

+=+=

+

=

vvyvvx

vvyx

12

1212

212

1 1

=

yx

v1 v

2

1

11(9) 12

=

yx

vv

2

1

11 12

(01)

=

yx

vv

1112

2

1

s v vv ,12) ( .

11222

vvsvs : 1vv

==+ sv

=

-

.

...= st 322= st s= 11 n : 1-1n

. = vft() . = st n

: (01) (9)

11 11 sss vvTv (11)= 12

=

31

11111 ss vvTv (21)= 12

=

: s s2 s1 .

ss20,1 =) ( ss11,0 =) (

. : s 12 11

s212,1 =) ( s111,1 =) (

:

= sTss 11112 [] (31) = Tsss 112 [11] (41) ss TT = 111 (51)

(51) (41) (31) .

1,0,0) (: . 0,1) ( 1,0) (

. 0,0,1) ( 0,1,0) ( :

.

41

t ( ) (8) :( 61)

. 1t2 (=-)1,1 1t1 (=-,1-)1 . s t

:

=

=1112

,1111

1 ts TT 1

(71)

=

==0213

1111

11112

t TTT 1ss

t

2-1 ( )

. n : . n

.

.

.

! .

( )

: s .

51

(1)==

==

=vssvbvssva

ba

vss

sss

()()

()()

22

11

. v

( ) .

:

(2)cvsdvsacbd

vwvcsdsvcsvdsss

sss

=+=+=+=+

()()

()(())()

12

1212

:

cadb (3)ba

wvcddc

=+ ssTssTs vwvwab

==

()[][] ==

.

: (1) (41-1-1) (31-1-1) ] [ (4)

==

()()

()()

2122

1112tsts 12

tstsTss

tt

ttttt

s

] [ (5)

==

()()

()()

1222

1121tsts 12

tstsTtt

ss

sssss

t

.) !(

61

.

.

n : 2-1

00

2 . =0 se njtn T= .

( 6)

. .

bab []22 ) ( (7)a

=+ sssTs vvvvvab

=== ( 8)

.

. =+= []0 ) ( (9)

cadb ==dc

ssTs vwvwab

. :

71

. .

. .

!

. ( 01)

.

. 2

. 2 .

.

. .

. .

(5) (4) .

81

. :

sttt Csststs tsts 121112 2122 == ] [ (11) tsss Ctttsts tsts 121121 1222 == ] [ (21)

= CC sttsT (31) 1= CC ststT (41)

.

.

. t : 3-1 s = 2[0.50.53] s tT = 1[20] s tT

s t . . s t DCBA

==== 00101101 ABCD tTtTtTtT] [ ] [ ] [ ] [ 3-1

( ) .

. .

91

w v w . v

w v v w v w v

. w . w

()() =+ vwvwwvw (1)

w : (1) w . w :

()()() =+ wwvwvwwvw (2) .

:

() wvwvw

wv

() wvw

-2

02

wv ] [ ) (( 3)vvv

wwwwww

vvvwwwttt

wvwvwvwvwvwv

= ttt wv

=

=

=3

3

1

21

31

32

123

123

123

1221

3113

2332

00

0 ted

.

. .

= [][] tststs rCrC : : 4-1

4-1. ( )

: -1 -2 -3 -4

() .

.

( 1) :

12

: (: )

. 1 1 2. 2

2 . 1 .

! 1 2 .

: . 1

1 2. 2 2 . 1

2 . 3 .

2 . ! 1

( ) ( 2)

.

. - .

.

22

( )

.

( ) ( 3) ) (

.

: (11-2-1) .

] [

=+

==

(2)()()(2)

(,)(,)(,)(,)

2122

111212

soCsoCsoCsoC

soCtssoCtssoCtssoCts

sttt Css

(4)

=

SCCS

. 1

enisoC lanoitceriD 1

1s

1t

-3

2s 2t

32

22 . (4)

33 . 1

1 .

:

== tstss vCvv (5).

. ( 6)

K t . s

K " .

. ". K :

. K Q . . 'Q

=++ ()(1()) QQCKQSCKQK (7)

42

(),() QKQKKQK Q

. . KQ

.

- KQ . S C .

() QKQKC ) ( (8) () KQS (9)

Q

K

(K .Q)K

Q (K .Q )K (=KQ) K

(Q (K .Q)K C)

(KQ) S

-4

Q'

52

( 9) ( 8) . (7)

KQKCQCKQS

QKQKQKQKCKQS

()(1)()

()(())()

=++=++

. : s1 t1

] [

+

+

=

=++

3

2

1

123

21

31

32

,1

,1

,11

001

(1)001

00

0

001

()(1())

kkk

SCkkkkk

kkkk

C

ttsttsttst stCKtSCKtK

(01)

++

+=

213

312

21

1

(1)

(1)

(1)

kSCkkkSCkk

CCkts

:

(11)] [

+++++++++

=

=

22131233

12323122

3122132

1

123

(1)(1)(1)

(1)(1)(1)

(1)(1)(1)

kSCkkkSCkkCCkkSCkkCCkkSCkkCCkkSCkkkSCkk

stttt Csss

. ( 11)

v .

: vC

=== (,)() tCtKsttKt vvCvCv (21)

62

== vCvCv ttstKKtK () (,)(,) (31) : K

==123 KKkkk tsT] [ (41)

9 . 9 6 .

: (11)

(51)(2)

21

(1)2

()soc1

1221

3113

2332

1112233

132333

122232

112131

=

=++

=

cccccc

SK

ccc

ccccccccc

KC

: .

CCC KKK == ()()(2) (61)

( 71) 4 4

:

4soc2 (71) =

72

-2 :

2)soc

2(soc

2soc2

2 == soc

:

(3)(81)2

(2),nis2

(1),nis2

112233 nis === kkk

:

TT +++=== 122232421234 1,,1 ] [(91)

: (11)

(02)

+++

=2

22

132423141

23142

32

12341

123413242

32

2

2()2()122

2()1222()

1222()2()

C

(12)

(4)4

(3,)4

(2,)4

1(1,)21

4

12213

4

13312

4

23321

4112233

cc

cc

cc

ccc

=

=

=

=+++

: 5-1 . .

82

: 6-1 12c

. 2/1

12 1212

. Q Q : 7-1

: K (1)2 stCIcKsK =++] [ ] [

: ()() = QKQKKQK

. : 8-1

Q Q2 K1 Q Q1 . K1+ K2 Q Q1+ Q2 K2

: : 9-1 = abcdacbdadbc) () ( ) () ( ) ( ) (

j2 = jP P : 01-1

} {

232332

133113

121221

431221

423113

412332

444411223312, 2

PPccPPccPPccPPccPPccPPcc

jjjst PcccecarTCccc

=+=+=+===

# =+==++

92

. : 11-1 .

: tstststststs ,, 112211332233) ( ) ( ) ( ) ( ) ( ) (

.

: 21-1 :

.22 cccssss

== 22 . 7-1

. 2/ = 2/ =

.

5-1 ( )

. .

( 1)

.

03

: (11-4-1)

(2)

=

SCCCS

00

100 1()

(3)

=

SC

CSC

0010

0 2()

(4)

=

00100

3()

SC CS

C

. t s Cst ( 5)

1 t t 2 . A

s t 3 . B (4) ( 3) ( 2) .

. s t : (21-4-1)

= (1,)1() tt vCv (6)

(7) = tt vCv () (1,;2,)2(1,) = tt vCv () (1,;2,;3,)3(1,;2,) (8) (6)(7)(8) (1,;2,;3,)321 ()()() == ttstt vCCCvCv (9)

13

== stst CCCCC 321321 ()()()(,,) (01)

.

21 . .

( 11)

3 t . E 2 . E

F 1 . F . s

23

s t (4) ( 3)(2) : (21-1-1) (11-1-1) .

= 1() Fs vCv (21) = 2() EF vCv (31) = 3() tE vCv (41) 321 ()()() == tssts vCCCvCv (51) (41)(31)(21)

# 321321 (,,)()()() == stst CCCCC (61)

1t

3E, 3t

2F,2E 1E

2t

1s , 1F

3s

3F

2s

-5

33

. t

21 .

. 21 21

. :

=== ststst CCCCCC 321321321 (,,)(,,)()()() (71)

(81)

++

=

=

SCSCCSCSSSCCSSCCSCCCSSSCCSCSS

SCCS

SC

CSSCCS

stC00

100

0010

0

00100

. -1) ( )

. ( ) (4-4

.

. . . htumizA elgna waY elgna hctiP ()

43

elgna lloR . noitavelE : . knaB

nat(1,)nis(2,)nat(3)33

12313

1

11

112

ccc

c === c

(91)

++

=

SCSCCSCSSSCCSSCCSCCCSSSCCSCSS

stC

: =2

(02)

=

++

10000

10000

CSSC

SSCCSCCSCSSCCCSS

.

21 :31-1 . 42

.

- 3 s . s t : 41-1 s . t 2 1

. t 3 2 -

. 01-1 -

. s t -

.

53

. - -

.

: 6-1 :51-1 ) -

(. -

.

. s t :61-1 .

.

63

-2 .

. .

. .

.

.

.

1-2

. = sttt Css 12 [] (4-2-1) = tsss Ctt 12 [] (5-2-1)

. .

. !( )

.

73

.

. ( ) . .

.

.

.

( ) .

( ) : ( ) = = = Q K Q K Q Q K Qtt t t t] [ ] [ ) ( (1)

Q ( ) K , .

. :

= = = = Q Q Q K Q Q K Qt tt t t t t] [ : ] [ ) ( (2)

.

83

. .(51-1 )

. .

. (2) . ( )

.

: ( 2) = ststst ssssss 123123] [ ] [ (3)

] [ ] [ (4)()()()

123123

CttCt

sssssststs

tts

tst

ttst

ttst

tttt

==

K

) Q K (

- 6

93

:

( 5)

+++++++++

=

211112221122231132

311113321123331133

312213322223332233

132333

122232

112131

cccccccccccccccccc

ccccccccc

.

.

(4)

. t () (4)

. . :

()= sttstst CCt (6) 000 ()()() ++ ststtstst CttCtCtt (7) ++ sttstst CttItCt 00 ()()()(8)

(6) (4) .

. 3 ( 2) 6 ( 3) 9

. .

04

.

. .

. .

t (4) : 71-1 ( 4) s .

.

s s t : 81-1 K t

. :

(), CCKets stK ==] [

81-1 : 91-1 :

() stCCKIK =+] [ ( 9)

.

14

st t s . us s u

ut =st+ us t u :

(4)

) (

=+

=+=+=+

==

=

CCC

CCCCCCCCCCCC

CdCCtdCCCC

su

tuss

tst

ttu

su

tuss

stu

tsts

t

susu

tss

su

tsts

stu

ts

su

ts

su

ts

tsu

ususs

u

tsts

tts

()

=+ () uttsttusut CC (01)

.

.

2-2

E t ( 5-1) 3

: . ,00 = tEEtT] [ (1)

:

42

)2( [ ]TEFFE 00, = )3( [ ]TFssF 00, =

: )4( FsEFtEts ++=

Fss

EFFTF

stEETE

sFss

EFFs

FtEEs

Etss CCCC ++=++=

( ) FssEFFTtEETFs

sEF

FTtE

ET

CCC

CC

++=

++= )()()(

)(),(

112

112

)5( FssEFFTtEETTtss CCC ++= )()()( 121

)1( )2( )3( )5( :

+

+

=

+

+

=

00

001

0

0000

00

0

0

00

00100

0010

0

00

001

SC

CCCS

S

CSSC

CS

SC

CSSC

tss

tss

)6(

=

=

CCSCSC

S

rqp

tss

00

01

p q r roll pitch yaw .

)6( :

34

(7)

=

rqp

SCCCCSTSTC

001

.

. 3-2

:

2 12112(1) =++ dtdKKscKK sstsstsst) ( ) ( ) ( ) ( (8)

sst Kt> (0),(0) .

.

4-2 3

4 . .

r q p : (4-1-2) 4-1

44

( 1)

+++++++++

=

=

332333132313

322232122212

312131112111

132333

122232

112131

()()()

qcrcpcrcpcqcqcrcpcrcpcqcqcrcpcrcpcqc

ccccccccc

st CtCttts

sts

: (01-1)

421 =+st PrtC} { (2) : 4P

244 ==== PPdtdrtCrtdtdCrtCrtC ststststsst} { } { } { (3) : (02-4-1)

2 4123 PPpPqPr) ( (4) = 1

(1) (01-1) : 1P jP

=+==++

" 1423321414233213331222 PPccPPPPcccrcpcqcp

() (5)21

=+ PPpPqPr 1432 :

() (6)21

=+ PPpPqPr 2341() (7)

21

=++ PPpPqPr 3214

:

] [ ( 8)PAP

PP

PPPP

pqrqprrpqrqp

PPPP

Tst

sst

sst

s

21

201

00

00

21

4

3

2

1

4

3

2

1

=

=

++++++

=

54

. . P

.

.

. s t : 02 -1 3 t 1

. . .

:12 -1 . ]s/R 0 0[

. 0 , 4/ ,0 .

(12-1) :22 -1 .

. ( 12-1) :32 -1

/2)100.0( knilumiS /2 /2)10.0(

. (12-1) :42 -1

. s/R 0 1

64

. tst [ = 1 2 3 ]T :25 -1

. ) 5-2

(

.

.

.

. .

.

.

.

74

. sr(t) t s r

: . sr(+tt): : s

+ ss rttrt ()() (1)

:

) ( (2)

+++

=+=()()()()()()

()()

33

22

11

rttrtrttrtrttrt

sss rrttrts

. s s r s s r :

: ... -1 -2

.

:

) ( ) ( ) ( ) ( ) ( (3)

===

=

=

3

2

1

rrr

rDrrtdrd

tdsss Drd

s

s

ss

##

rt() + rtt ()

r

s2

s3

srt() -7 s1

84

. s ( ) sD-

. D

. ( )

t :

) ( ) ( ) ( (4)

==

=

3

2

1

rrr

rCPrCtdst Drd

tss

s

t

st

: :62-1

rss Drrrs

s =+ 1[] s

. r 1sr r - r r : )

.( r

1 ( 5) :

: .

r) ( ) ( (6)tdrd

tdDrDrd

ts ts

meroeht siloiroC 1

94

. .

, sssttt DrDrDrDr == ) ( ) ( ) ( ) () ( ) () ( ) ( ) (

) () (

=+ ) ( ) (=+

=+==

Drr

CDrCr

CDrDCr

DrDrDCr

stt

st

r

sst

tsss

tss

tss

tss

tss

tt

t

sts

=+ tsst DrDrr (7) .

a :62 -1 :

= ts DaDa . 12-1

. 22-1

1 12-1 :72-1 - : .

. -.

( ) :82-1 .

. .

05

: 92-1 .

: 03-1 . ( ) ( )

.

:13-1 ,,,, ===== ttttttsststtsttsttst DrDrDrDrDrDrDrCDrDrCDr ) ( ) ( ) ( ) ( ) (

" r " : . t s

=+ vvr BtBsstB (8)

. . (9)

) (

) () ( ) (

) (

) (

t tst Bs BtB

t t tst st BsB B

sBs st Bs

s ro tstB

sst st Bs st st stB B B

r v D v Dr D r D v Dv v D

r D

r v r r D

+ = + + =+ + =

+ + = +

15

(01)

N

N....

.

2()()atepirtneClccA

ststB

laitnagnaTccA

trosstB

siloiroCccA

stBsccAnithgiSfOstanidroC

Bs

ccAnithgiSfOttanidroCBt

avDrr

a

+++

=

vBs=0 s s . aBs=0

aBs=0 .

: (11)

. 2 1 z (,,)

: 3

(21)(3)(2)(1)

zzyniSxsoC

===

. ( )

.

etanidrooC raloP 1 etanidrooC yrdnilyC 2 etanidrooC naitraceD 3

25

( )

rB . ( )

rB

.

rB . .

.

" "

.

rB

-8

z

35

: ( 8) =+ rz (31)

(41)

=

z0 DCz

0,

=

00

C

(61)

=

z0 Cr

.

=+ DCCD DrDrr

Drr

DrDrrC

CDCC

CDC

CC

DC

=+=+

()()()

(71)

=

+

=

zzzBD v

C

00

0 0

- .

.

(81)

+

=

==

zSCCS

zSCCS

BD vCvDC

BDCD

00100

. .

+ = =v v D v D aC DBD CD BD BD BD

45

: (01)

: (91)

====

zCC DvDDrDrDr

CCC

CCBD

C

22 ()(())()0

: ( 02)

=

=

02

000

0 2()2

z CDBCv

C

: ( 12)

=

==

0

000

0 (())

z CDC DrDr

CCCD

C

=

=

z

CD rrC

CDC

CDCDC

00000000

0000000

(())()

: ( 22)

=

00

2

.

(32)

+

===z

D aDvDrC

DBDC

BDC

2

2

2

.

55

r ( 31) : 23 -1 . ( 81)

( 32) 23-1 : 33 -1 .

1 :43 -1 ( 11) .

. r] [ xyz] [ .

lacirehpS 1

rB

x

y

z

er

e

e

65

.

.

.

:

=

rS

rr

BD vS

+++

=

rSrSrCrrrSC

rrrSBD a

S

222 2

222

.

. " "

.

03- 1 . ( ) .

. ( )

. .

. .

75

. ( ) . .

.

53-1 .

. ( ) ( :63 -1 v . v

. vv () v . R

v

. R = Rv . ( (

. ( = 12581 tonkmh) 4 : 73-1

=2 . =01 ( . (

. : 83-1

1mks =1 =2zdaR

85

( . ( (. z) .

. : 93- 1 . s

()()()

()()()

DvwDvwvDw

DvwDvwvDw

sss

ss

=+

=+

63- 1 : 04-1 , aa BxBy)

. ( . (r) (

. . (

.

A ,, : 14-1 .