,, (CIP) /. :, ISBN V21 CIP (2002) : :127 : : ( 029) : / : : 787 mm1 092 mm 1/ 16

Transcription

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2 ,, (CIP) /. :, ISBN V21 CIP (2002) : :127 : : ( 029) : / : : 787 mm1 092 mm 1/ 16 : : 332 : : : 17.00

3 , ( ),,,,,,,, ; ;,,,

4

5 /

6

7 ,,, ( 1 1 ) 9,, 1487, 1673,, ? 200,, 7, 8, 16,,,,, ( 1279 ),,,,,, 1

8 3. 18,, , km, ( 1 2 ),,, 1852, ( 1 3), 1900,, ,,,, 19,, 19,,,,,,, W (12 ) ( 1 4) 1 4,,,,, 1908, 2

9 ,,, , 800 m, ( 1 5) 1 5,,,, 1.,20,, 1911,, 20,,,, 2., 16 km/ h 755 km/ h, ( 1 6 ) 1 6?,,,,, 3

10 ,,,,,,,, 3/ 4,,,,, 1.,,, , H e178, () 15 F80 F86, 2., 900 km/ h,,,,,,,,,,,,,,,, 1947, X1 1953, F100, 19,, 3.,,, 2.5, 300 C,,,,,,,, SR71, 93%,, 3.3,,,, F22A, 5, Y F22 ATF Y F23 37 ( S37) 1.44 JSF X32A X35A, X32A X35A,,, 4

11 21, :,,, ;,,, ; ;, 1. 2,,,,,,,,,,,,,,,, 1952,, ( ), , , 60, , 5F ,, 9 15, 4 5F, ,, 1959, 5F 767, , 6, , 1956,, 1 1,,,,, 1, 6 6 5

12 1990, ,, , 302, 56,,,,, , 5, 1969,, 5,, , 7, , , 6 :,,, 6, , 7 ( ), , , K8, 1992,, ,, , 5 000,, ,, ,, 6 5 7M 8/, 7 9, (1 ):,,,, F16 ( ), ( ) / 29, 27, 2000,

13 4000 (2 ):,, ( ) 27, 17, F111 F15E F16E, 2E, Saab35 ( 1 8) 1 7 F (3 ):, ( 300 m ),,,,,, A10 () 25 ( ), A (4 ):,,,,,, km, 510 t FB111, 22, 6 ; km, 10 t, B1, B2, 26, ( 3 5 t, km) B57 5, (5 ):,,,,,,,,,,,,,, ( )22, 124, KC10 C17, 8 7 H 7

14 (6 ):,,, 575 K8 (7 ):,,, SR7125P, RF 4C25P 6 (8 ): 5,,,,,, (9 ):,,,,,,,,, E2 E3 126,,, (10) :,,,,,, EA6B, E F111A ( 1 11 ) 1 11 EA6B (11) :, F117A / ( 1 12 ),, ; V,,, B2,,, A H F117A 8

15 (12) :,,,,,, ( 1 13 ) 1 13 (13) :,,,,,,, ( 1 14 ) 1 14 (14) :, /,,, ( 1 15 ) 2.,, ( > 100 t) ( 4090 t) ( < 30 t) ( < 150 kg), 9

16 1 15 (, ) ( ) ( ),, (1 ) : (), 7.62 mm 12.7 mm,, 20 mm, 23 mm, 30 mm (2 ):,, 20 30,,, 10

17 (3 ) :,, ; ( ) ; ( ) () ( ), (, ) ( ) (4 ) :,, ( 1 17 ) ( ) ; 2 ( ) ; 3 ;4 ; 5 ; 6 ; 7 1. (1 ):,,,,,,,,,,,,,, m,,,, 3( P L3), 9 ( PL9 ),, (2 ):,,,,, ( ), (),,,,,,, AGM69A/ B, AGM86B/ C, A GM129A, ; AS11, AS20, AGM53A, AGM65, AGM114, 11

18 () AT9, A T12 (3 ):,,,, ;, 5, 80, 2000, (4 ): ( ), ( ),, ;, ;,, () 2. (1 ) :,,,, (2 ) :, (3 ) :,,, 3. ( 1) :,, (2 ) :,,, 12

19 ,,, k m, ( 2 1 )

20 , : 1.,, 78 k m, 1517 k m, 11 k m : (1 ),,, 100 m, 0.65 C,,,,,,, 3/ 4 (2 ), (3 ),,,,, 2.,, 30 k m, : (1 ), C, (2 ), (3 ),,,,,,, (4 )1/ 4,, 1 km, 3., km 1/ km, 200 km400 C, 5.,, km,,,,, () p ON, 14

21 p O N = kg/ m 2 = Pa ( O N ) t ON t ON, K ) = 15 C = ( ) K = 288 K (, p ( kg/ m 2 ) ; T ( K) ; V, ( m 3 / kg) ; R, R = m/ K pv = R T (2 1) V, g, ( 2 1) p g = R T = p gr T, ON O N = p ON gr TO N = kgs 2 / m 4 ON = O N g = kg/ m 3 (2 2), p,, T, ;, p + p,+, T + T, v v ( 2 2( a) ),,, u, u - u ( 2 2( b) )

22 F2, F1 = = F, (2 3 ), (+ ) ( u - u) F( u - u) - u Fu = pf - ( p + p) F (+ ) ( u - u) F = u F uu = p (2 3) (+ ) ( u - u) = u + u - (+ )u = u u = + u + u2 = p u = p + (2 4),,,, p T,, p 0,0, a a = lim u = p0,0 d p d (),,, a = p K = C d p d = CKK - 1 p = RT g = K p (2 5) a = K p = Kg R T 20 T (2 6), ap,,,, ;,, 16

23 ,,,,,, (2 5 ), K, K = 1.4, p,, a ON = m/ s a,, Ma : Ma = v a Ma, : Ma < < Ma < < Ma < 5.0 Ma > ,,, R Y R Y, 1. ( ) ( ), ( 2 3 ),, ( 2 4) Ma 1,,, ( 2 5 ): 17

24 (1 ) :,, ( ) A ( ) B b (2 ) : f,,, f max bf max/ b,, 0.4%, 0.004, f A x f b x f/ b, x f, (3 ) : c, cmax/ b,, 12%, 0.12 Axc b x c/ b, xc,,, :,,, 2 6 : (1 ) :, l (2 ) : S 18

25 (3 ) : S l S l = bcp l,, = l bcp = l2 S (4 ) : b b,, 0 1 (5 ) : ( 2 7) 8 > 0, < 0 2 7,, ( ),, 2 8, 19

26 ,,,,,,,,, S1, S2 S3, ; 2 ; 3 ; 4 ; 5 ; 6 S1, S2, S3 m1, m2, m3, m1 = m2 = m3 = (2 7) m = M t, = M V, V = LS, v = L t M ; ; V ; t ; S ; v ; L m1 = M1 t = 1 V1 t = ( S1 L1 ) = 1 S1 ( v1 t) t t = 1 S1 v1 (2 8) (2 8 ) ( 2 7) 20

27 1 S1 v1 = 2 S2 v2 = 3 S3 v3 =,,, (2 S1 v1 = S2 v2 = S3 v3 = (2 9) 9 ), ( 2 9) :, ;,,,,,,, 2 8,,,, ;, 2, 9,,,,,,,,,,,,, 2 9,,,,,,,,, 2 8,,,,,,,, 21

28 ,, A, S1, v1 C, S3, v3, v2 B, S2 A, C :, ;,,, ( ) + = ( ) p, 1 2 v2 () p v2 = S1, S2, S3, p v2 1 = p v2 2 = p v2 3 = = ( 2 10) 1 2 v2, v p,,, v, p ;, ;,,,,,,, 1. ( 2 10)

29 ,,,, ( ) ; ( ),,,,,,,, 2.,, ( 2 11), 00 00, 2 11 :,, 00 ;, 00 (, ), (, ), 2 12, p - p < 0 ;, p - p > 0 23

30 3.,, ( p), R, Y,, l Y, d S = ld x, ( 2 13 ), dy = p ; p cos(+ ) d S 2 13, d S d x cos (+ ) d x cos d x dy = p cos(+ ) ld x p ld x, Y = dy = b 0 p ld x + 0 b p ld x = b 0 ( p - p) ld x Cp = p - p 1 2 v2 ( p, ; v, ), q = 1 2 v2 x = 24 x b, Y = b ( p - p) ld x = 0

31 lb 1 ( qcp + p) - ( qcp + p) d x = S 0 q 1 0 q 1 2 v2 ; Cy S ; Cp, Cp Cy (2 Cy 1 ( Cp - Cp ) d x, 0 ( Cp - Cp ) d x Y = Cy qs ( 2 11) 11), S q Ma Ma,, Cy = 1 ( Cp - Cp ) d x 0 : b x, Cp = ( 2 p - p q, 14 ),, Cy 2 15 : (1 ), Cy 25

32 ( ) C y = Cy = ; (2 ), Cy, Cy ; (3 ), Cy ( 2 =, Cy, 16) 2 16,,,, ; Cy,,,Cy 26

33 , Cy, Cy,,,,,,, Cy 2 15, = 0 Cy 0, = 0,, Cy = 0 0, 0 Cy Ma,, = 2 Cy Ma 2 17 Cy Ma, Ma Ma 1. (1 ) Ma :,,,,, ( ) v K RT = K - 1,, Ma Ma ( Ma ),,,,, :, v, Ma Ma Ma, Ma 27

34 v, Ma Ma, Ma > Ma,,,,, ( ),,, u = p +, p,, u,, ( 2 18 ), 2 18 (2 ) : Ma 2 19 : Ma Ma Ma,, Ma;, Ma, ;, Ma, Ma > 1,, Ma Ma Ma Ma,,,, ;,,,, Ma (3 ) :, : Ma < Ma, ; MaMa < Ma, Ma,, ; 28

35 2 19 (a) M = 0.75; ( b ) M = 0.81; ( c) M = 0.85; ( d) M = 0.89; ( e) M = 0.98; ( f ) M =

36 MM, ( ),, ( 2 20 ) Ma Ma (1 ) : Ma 2 17 A Ma Cy Ma, Ma Cy Ma Ma Ma d = - Ma2, Ma ( Ma < 0.4 ),,,, Cp Cp = d v v p v2 = p+ 1 2 v2 p - p 1 2 v2 = 1 2 v2 - Cp = 1 - v, v v = S v S, Cp = 1 - S S 1 2 v v2, Ma, Cp S S 30

37 ,, S Ma S Ma, Cp Ma Ma > 0.4, Ma,, ( ), ( ) (),,,,,, ;, Cp, Ma,, Ma, Ma (2 ) :, Ma 2 17 A D, Ma > Ma, MaCy ) ; ( AB ) ; ( BC AB,,,, Ma,,, Cy Ma BC Ma Ma,, Cy Ma CD Ma Cy Ma (3 ) : Cy Ma, Ma, Ma, Ma,, Cy C y Ma C y Ma 31

38 ,, X, X = Cx qs ( 2 12), Cx, Cx Ma,,,,,,,,,,, ;, 99 % (), ,,,,, 1 2 m,. 2 22, P1 Q1, P2 Q2 p n = 0, n P1 Q1,,,, 32,,

39 ,,,, a, a, ( 2 23 ) 2 23 a ; 1 ; 2 ; 3 1.,,, : F; F, F = F,,, F F F,,,,,, a,,,, 2., ( 2 24 ), 2 24( a),, 33

40 ,,,,,,,,,, 2 24( a) 1/ 5, 2 24 ( b ),, 1/ 20 1/ 25, 2 24( c) ; 2 ; 3,, 2 24,,, 2 25, 34

41 , ( ),, ; ( ),,, 2 25 (),,,,,,,, ( ),,,,,, vy, ( 2 26 )vy, 2 26, Y ( 2 27),, X, 2 27,, X = Y sin 35

42 sin X = Y sin Y= Cy 1 2 v2 S,,,, Cy = Cy ( ), 2 27 = = Cy ( ) ( 1 + ),,, X = C 2 y 1 2 v2 S Cx = C 2 y,,,,,,, Ma (, ) Ma, ( ) ; Ma 1,, 1., Ma Ma,,, ( 2 28),,,,,,,,, ( )

43 2 28,,, Ma,,,, ,,,, ( 2 30 ), R,, Ma 1.,,, 70 % 80% 37

44 , ,, ( 2 31 (a) ),, ( 2 31( b ) ) ( 2 32 ),,, Ma, 2 31, ( (c) ),

45 , X X = X + X + X + X+ X X = X+ X+ X+ X+ X = ( Cx + Cx + Cx + Cx + Cx ) qs , :,, ;,,, ;,,,,, 2 33 C x,,,, : () Cx0 ; AC 2 y, Cx Cx = Cx0 + AC 2 y ( 2 13) 39

46 Cx0 ; A, 3. Ma Ma, (1 ) :, Cx0 Ma, Ma Ma Ma Ma, Ma ; Ma,,, (2 ) :, Ma Ma Ma,, Ma ( Ma ),,,, (3 ) :,,,, ( ) Cp Ma, Ma Cx = Cx0 + AC 2 y Ma 2 Ma C x0 Ma ,,, 40

47 1.,, 2% 3%,,,,, 2. Y = Y,,,,,, kq 2 kq = q q = v2 v 2 (),, kq ( ) 1., 2., , ,,, = - ; ; 2 35( a),,, = - = ( 1 - ) = (1 - )+, z 2 35 ( b), Y = 1 Cy 2 v2 S = C 1 y 2 v2 S, Cy, C y 3. 41

48 , Y Y- + Y 1 Cy- 2 v2 S + 1 Cy 2 v2 S = C y- + C y kq C y- + C y (1 - ) kq S S 1 2 S v2 = S 1 S 2 v2 S + C y z kq C y 1 2 v2 S + C 1 z y z 2 v2 S = ( C y+ C z y z ) 1 2 v2 S S S 1 2 v2 S = C y = C y - + C y ( 1 - ) kq S ; S C y z = C y k q S, S 2 35 Cy- = C y- (- 0 ) = Cy0 + C y - Y = ( Cy0 + C y+ C y z z ) 1 2 v2 S ( 2 14), Cy0 Cy = Cy0 + C y+ C y z z z = 0 Cy0, C y C y z Ma Ma, Cy = f ( ) Cx = g( ), Cy = f ( g - 1 ( Cx ) ) = f ( Cx ), Cx, Cy,,

49 , Cx Cy, CR = C 2 x + C 2 y R ( R = X 2 + Y 2 = CR 1 2 v2 S) ;,, tan= Cx Cy = X Y 2 36,,, K = Cy,, 1. Cx = Y X = cot, (,,, 2 Y + Psin= G Pcos= G ; P, X 37) 2 37, Y = G P = v, G, Cy = Y 1 2 v2 S Ma, Cx, X = G 1 2 v2 S 43

50 P = X = 1 Cx 2 v2 S v 2. Ma Ma, Kmax ( Ma) ,,, dv d t, G, Y X, P,, 1. ( ) OX d Y d Z d O,, OX d ; O OY d ; OX d Y d OZ d, OX d Z d, 2 38 O m r, v = d r d t OX g Y g Z g O,, 44

51 3. ( ) OX YZ O, OX, OY OX,, OZ OX Y, 4. OX s Ys Z s O ; OX s v ; OYs OX s ; OZ s OX s Y s, 5. ( ) OX t Y t Z t O ; OX t ( ) ; OY t OX t, ; OZ t OXt Y t 6. OX b Yb Zb ( ) O ; OX b, ; OY b OX b, ; OZb OX b Yb, , Io = [ x0 y0 z0 ] T ; Ii = [ x i yi zi ] T 3, 1,2, y y, y 45

52 1 I1 = 2. 2 x1 y1 z1 = Y y = cos y 0 - sin y sin y 0 cos y x0 y0 z0 cos y 0 - sin y sin y 0 cos y = Y y I0 z z, I2 = x2 y2 z2 = Z z = cos z - sin z sin z 0 cos z cos z - sin z sin z 0 cos z x0 y0 z0 = Z z I z 2 41 x 3. 3 x x, I3 = x3 y3 z3 = cos x 0 - sin x sin x cos x x0 y0 z0 = X x I 0

53 X x = cos x 0 - sin x sin x cos x y ; z ; x, : (1 ) 12 3,,,,, X x Z z Z z X x, x, y, z, 1,2,3: I1 = Y y I0 I2 = Z z Y y I0 (2 ), I3 = X x Z z Y y I0 X - 1 x = X T x Y - 1 y Z - 1 z = Y T y = Z T z, OX t OX t,, ( 2,, OXt OX 42) (), OY t OX t, OY t, ( 2 43) OX t OX t, 47

54 ,, (OX s ) c OX d ( ) c XsOYs 1.,,, OX g Y g Z g OY g c, OX Y g Z, OZ, OX Y Z ( 2 44 ) 2 44 : I = ZY c I g 2. 2 T = ZY c 45, OX c, c : Is = X c ZY c I g T = XZY c c 3. Y, Z, X ( ),, ( 2 46 ) 48

55 2 45 It = XZYI g T = XZY ,, X, Y, Z

56 2 47, X c, ;, Ys ;, Zb It = ZYX c I It T = ZYX c It = XZYI g XZYI g = ZYX c I = ZYX c ZY c I g XZY= ZYX c ZY c,, OX g Y g Z g c c c - c c OX YZ c OXs Y s Zs c OX t Y t Z t c - OX b Y b Z b,,, ;, 50

57 2. 3, : (1 ),, ; (2 ) ; (3 ),,,, : 1. (), ma = F, m, F, a ; ; a = d dt = t +, t, a,, m d vx dt + y v z - z v y = X m d vy dt + z v x - x v z = Y ( 2 15) m d v z d t + x v y - y v x = Z, X, Y, Z F ( 2 15),,,,,,, OX YZ = x i + y j + z k v = vx i + vy j + vz k 51 ( 2 16)

58 , i, j, k,, i, j, k, 2 48 a = d = d vx dt dt i + vx di d t + d vy dt j + vy d i d t = i d j dt d k d t = j = k d j d t + d vz d t k + vz d k d t ( 2 17) ( 2 18) 2 48 (2 18) (2 17) ( 2 16 ), a = d = d vx d t d t i + d vy dt j + d vz d t k + vx [ ( x i + y j + z k ) i] + vy [ ( x i + y j + z k) j] + vz [ ( x i + y j + z k) k] ( 2 19), ( ) ii = 0, j i = - k, k i = j 2 vx ( x i i + y j i + z k i) 48,,,,, a = d = d vx d t d t i + d vy dt j + d vz d t k + vx ( z j - y k ) vx ( z j - y k) + vy ( x k - z i) + vz ( y i - x j ) = d vx dt + vz y - vyz i + d vy d t + vx z - vz x j + d vz d t + vy x - vx y k ( 2 20) 52

59 ,, m d vx d t + y v z - z v y = X m d vy d t + z v x - x v z = Y m d vz d t, ( 2 + x v y - y v x = Z 15 ) 2 49,, (2 vx = v, vy = 0, vz = 0 15), ax ay az = d v d t = v z = - v y ( 2 21), ( 2 44 ) x = c sin= d c d t sin y = c cos= d c d t cos z = = d d t 53 ( 2 22)

60 (2 22) (2 15) m d v dt = X mv d dt = Y m - vcos d c = Z d t,, 2 G:, OY g Y: OYb Q: OX b Z: OZb 49 (, Z) ( 2 23) P: OX t (, OX t ),, m d v dt mv d dt = = Pcos(- )cos- Qcos+ Zsin- Gsin P[ sin(- ) cos c + cos (- ) sin sin c ] - Qsin sin c + Ycos c - Gcos- Zcos sin c - mvcos d c = P[ sin (- ) sin c - cos(- ) sin cos c ] + dt Qsin cos c + Y sin c + Zcos cos c ( 2 24) c,, 2. ( ), d H d t, H, d H d t = M, M = H + H,, t d H x d t + y H z - z H y = Mx d H y d t + z H x - x H z = My ( 2 25) d H z dt + x H y - y H x = Mz Mx, My, Mz M ; H x, H y, H z H 54

61 H x H y Hz = I x x - I x y y = I y y - Ix y x = I z z ( 2 26) I x, I y, Iz I x y (2 26) (2 25) I x I y I z d x - ( Iy - Iz ) y z - I x y d t d y - ( Iz - I x ) z x - I x y d t d y - z x dt = Mx d x + y z = My dt d z - ( I x - Iy ) x y - I x y ( 2 x - 2 y ) = Mz d t ( 2 27) (, ), I x y 0, ( 2 27 ) Ix Iy Iz d x - ( I y - Iz ) y z = Mx dt d y - ( Iz - I x ) z x = My d t d z - ( Ix - Iy ) x y = Mz dt ( 2 28) ( 2 24 ) (2 27 ) ( 2 28),,, , ( ),,,,, 1., ( Cy C y = C y 2. = Cy ), 55

62 ( ),,, Cx0 = Cx0+ 1 S ( Cx0S+ Cx0 S+ ) ( 2 29) ( ),,,, Cx = AC 2 y ( 2 30), A, 2 50 Cx0 A Ma, Cx = Cx0 + AC 2 y ( 2 31) 2 50 Cx0 A Cy, (2 31 ) Ma Cy Cx () 2 50 C x0 A Ma, :,, (2 P = Q = Cx G = Y = Cy 1 2 v2 S ( 2 32) 1 2 v2 S ( 2 33) 32),,,, P (2 33) (2 32) P = G Cy Cx = G K 56

63 P = G K ( 2 34), K = Cy Cx,,,, : (1 ) Ma, (2 ), Cy =, C = 2G Sa 2 G = Cy 2 G SMa 2 a 2 = 1 2 v2 S Cy = 2 G S v 2 2G Sa 2 1 Ma 2 = C Ma 2 ( 2 35) (3 ), Cy Cx, K = Cy Cx Cx0 A, Cx = Cx0 + AC 2 y Cx, K (4 ) Ma K,, P = G K (5 ) v(ma), P, H = 8 km : H = m, S = 23 m 2, G = N := kg/ m 3, a = 308 m/ s = km/ h C = 2G a 2 S = = 0.113, ( ) 57

64 ,, 1. G ( kg/ s ) ; C P = G ( C - v) ( 2 36) g,, ( C - v),,,, 2 52 AB,,,, 2 Map 52 BC,,,,,,, ( C - v),, 2 52 CD ,,, ( m ),,, ( m ),,,,, ,,, Map H = 0 Map = 1.9 H = m Map = 2.4, Ma p,,, 58

65 ,,,, Ma p m,, Map G ; G G = 1 2 ( G+ G),, 2 55,, 2 55 vmax, vmax, P = P, Y = G 2 vmax = 2 P CxS ( 2 37) 55,,, m, vmin, Y = G,, Cy v = 2G CyS ( 2 38), v, 59

66 ,,, Cy Cy Cy = Cymax vmi n = 2G S Cy ( 2 39) 2 55,,, vm in, 2 56,,, ;, 2 56, vm in 1.,, qmax qmax = 1 2 v2 max kg/ m 2 Maq = vmax a = 1 a 2 qmax ( 2 40) 60

67 (2 40 ),, Maq, qmax ( AB ) 2.,,,, Ma,,, Ma 2,, Ma, 2 56 CD Ma, Ma,, Mamax 2 56 DE,, ,, ( )

68 ( : P cos= Q + Gsin Y + P sin= Gcos, 41) max Q = P, sin= 0, cos= 1 sin= P = Q + Gsin Y = Gcos P - P G = arcsin P G = P G ( 2 41) ( 2 42) ( 2 43),P,,, P,, (2 max = arcsin Pmax G ( 2 44) 44) max, max,,, v vymax,, vy ( m/ s ),, vy = vsin= v P G P ( 2 ( 2 45) 45) vy, 58, vymax, v, v v P P

69 Hmax 2 55, H = 0 Pmax,,Pmax, vymax P P,, vymax = 0,, ( ) Hmax, 2 59 a a,,,,,, vymax = 5 m/ s, Hmax, vymax = 0.5 m/ s, 2 59 b b , ( ),,,,,,, 0.7 vmax 0.97 vmax, vmax 0.7 vmax, d v d t G g d v d t Y = G = P - Q = P ( 2 46) P 63

70 ,,, Y = G ;,,, Y = G (2 46) dt =, v1 v2 v1 v2 t = v 2 G g ( P - Q) d v ( 2 47) v 1 d L = vd t = v L = v 2 v 1 Gd v g ( P - Q) Gd v g ( P - Q) GVd v g ( P - Q) v1 v2 t L ( 2 48) ( 2 49) ( 2 50),,,, H,, ( v1, H1 ), E1 ( v2, H2 ), E2, ( P - Q),, Y, G E1 = E2, : v1 E1 = H1 + v2 1 2 g G ( 2 51) E2 = H2 + v2 2 2 g G ( 2 52) H = H2 - H1 = 1 2 g ( v2 1 - v 2 2 ) ( 2 53), v2, v1max v2 mi n ( 2 53 ), H ma x = 1 2 g ( v2 1 max - v 2 2 min ) ( 2 54),,, vmin,,

71 , ( H = m), v1 max ( km/ h ), Hmax, ( H = m ) ( H = m), 2 60,,, ;,,,,,,,,, 360,,,,,,

72 , ( ), R Pcos- Q = 0 Gv 2 gr = ( Psin+ Y ) sin ( Psin+ Y ) cos= G, Pcos P, Psin 0, (2 P = Q ( 2 55) 55) Y sin= G g v 2 R = G g v ( 2 56) Y cos= G,2 (2 56) 3 R = G g v 2 Ysin = 1 g Y G = 1 cos ny = Y G = 1 cos ny (2 sin= 1 - cos 2 = 1-57) T = 2R v R = v 2 g n 2 y - 1 v 2 ny sin 1 n 2 y = n 2 y - 1 = 2 v 2 v g n 2 y - 1 = 2v g n 2 y - 1 ny ( 2 57) ( 2 58) ( 2 59) ( 2 60) ( 2 61) (2 60) (2 61),, ny,, R T, ny, R T ; (2 58), ny,,, Cy,,, ( Ycos= G),, 66 (2 58) P = Y K = G 1 cosk P = ny G K ( 2 62),,

73 ,, nymax, nymax, 2 62, , ny G G, 2 62 AB Cy, BC DE, CD ny = 1, ;, ABCDE, ,, 1.,,, 2 63,,,,, (L) 2., 67

74 T 3. Q,,,, Q = Q - ( Q + Q + Q + ) ( 2 63) Q = Q - ( Q + Q ) ( 2 64) Ce,, kg/ ( kgh), n H v Ce nh v Ce 5. q, P, q = P Ce ( kg/ h ) ( 2 65) (2 34) 68

75 q = GCe K T = Q q = K GCe Q = Q P Ce ( 2 66) 6. q, v, 7. L = Q q = q v q = GCe K v = Kv Q = GCe Qv P Ce ( 2 67) ( 2 68),,, - dg = dq = qd t ( 2 69) d t = - dg q = - K dg ( 2 70) GCe G1, G2, ( G2 = G1 - Q), T = - G 2, G 1 K dg GCe = G 1 K d G ( 2 71) GCe L = G 1 G 2 G 2 KV d G ( 2 72) GCe, K, Ce G,,, G = 1 2 ( G1 + G2 ) = G0 - Q 2 ( 2 73),,,,, Cy P Ce G,,, Ma v, G = Y = 1 2 v2 SCy Cy, Cx P = Q = 1 2 v2 SCx P, Ce, (2 66 ) ( 2 68),,, 69

76 ,, P P,, Ce,,,,,,,,,, ;,,,,, Ma,,,,, ;,,,,,,, ;,,,, ,,,, c d c ( x y ) d t, : 70 : m d v d t = Pcos (- ) - Q - Gsin (1 ) ( - ), ( + ), 2 65( a) ; (2 ), 2 65( b) ; (3 ) ; (4 ) ; (5 ) ; (6 ), 2 66 mv d ( 2 74) = Psin(- d t ) + Y - Gcos, d, d t

77 : m dv dt = Pcos (- )cos- Qcos+ Zsin P[ sin(- ) cos c + cos (- ) sin sin c ] + Ycos c = Qsin sin c + Zcos sin c + G - mv d c = P[ sin(- ) sin c - cos (- ) sin cos c ] + d t Qsin cos c + Ysin c + Zcos cos c ( 2 75) 2 65,, = 0,, ( 2 m d v d t 75 ) : = Pcos (- ) - Q Psin (- )cos c + Ycos c = G + Zsin c - mv d c = Psin (- ) sin c + Ysin c + Zcos c d t ( 2 76)

78 : (1 ), 2 67( a) ; (2 ), 2 67( b) ; (3 ) ; (4 ) ; (5 ) ,, ;,,,,,,,,, 2 68( a),,, 2 68( b ),,,, 2 68 (c), 2 68, 72

79 , Y G, P Q,,, (),, ( ),, (), (),,, OX, OZ, OY,, OX, OZ, OY, 2 69,,,,, 2 69, 2 69, O,, 2 69 ( b), f, M,,,, 2 69 (c),,,, 2 70, 2 70 (a),,,,,, v, f, M1, 2 70 ( b),, 73

80 OX 2 70, 2 71,,, Y, Y G, Y, Y G R R,, v3, Y1 Y2, M,,,, 2 72 ( ),, v2,, Y G R R, 2 71 v3,, va vc, va v c,, M 74

81 ,,,,,,,,,,,, 2 72,,,,,,,,,,,,,, (1 ) : ( ),, ( ),, ( ) f O M1 (M2 ), OZ (), 2 73, () (2 ) :,,,, f O M,, 2 OY, 74,, (3 ) :, ( ),,,, ( ), 75

82 ,, M, OX,, ; v 1 ; O ; v 1,,,,, ; 2 ; 3 ; M 76

83 ,,,,,,, 2 76,,, Z 2 76 R ; Z ; r,,,,,, 77

84 ,, : 1.,,,,,,,,,,, 2.,, R530,, AMI ,,, 78

85 ,,,,,,,,,,,,,,,, 3 1 X1, 3 1( a) ;, X1, 3 4( b ) P Y1 P, P, 3 1,,,,,,,,,,,,,, ;,,, ( ) 79

86 ,,,,,,, ;,,,,,, : (1 ) : (2 ) :, (3 ) :,,

87 ,,, ( 3 3 ( e) ),,,,, - - -,, : ( 3 3 ( a ) ) ; ( 3 3 ( b) ) ; ( 3 3 ( c) ) ; ( 3 3 ( d ) ), ( ),,, ( 3 4 ),, ( ) ( ) (), : ,, (, ) ( 81

88 3 5)( 3 6 ) ,, 1.,,, ( ) R - 73 R550 2.,, : (1 ) :, ( ) (2 ) :,,,,,, 82

89 (3 ) :,,,,,,,,, AIM120, 1.,, m, 20 km,,,,, AIM - 9L, ()R - 73, R550,, kg km km mm mm mm kg AIM - 9L R k m,,,,,,,, AIM - 7M, ( ) R - 27,,, +,, AIM MICA,

90 3 2 kg km km mm mm mm kg AIM MICA + / km,, AIM - 54C R - 77, kg km km mm mm mm kg AIM - 54C R ,,, 1.,,,, ;,,,,,,,,,, 2. 84

91 ,,,,,,,,,,,,,, 3.,,,,, 4., 5., ; 3. 2,,,,, 1. ( A X Y Z) A, A X, A A Y A Z X A Y 2. ( OX YZ) O m,, 3. ( OXh Y h Z h ) O m, OX h, OYh OX h,, OZh OX h Y h,, OY c, OZ 4. ( OXv Y v Zv ) O m, OX v, OYv 85

92 OX v,, OZv X v OY v,, OX c 5. ( OXt Y t Z t ) O m, OXt, OYt O X t,, OZt O t X Y t,, OY, OZ, OX ;, OY, OZ, 3. 3,,,, : :, ( ), X Y ( ) Z, X Ox v Oy v Ozv ( v), Y Z : q( q = 1 2 v2, )S, X = Cx qs Y = Cy qs Z = Cz qs (3 1), Cx, Cy, Cz, S,, ;,,, (), (),,, 86

93 ,,,,, Y W 0,,,, Y W ( B) ;, Y B( W ) Y W,,, Y W = Y W 0 + Y W ( B) + Y B( W ) (3 2) ( + ), Y B ; Y T Y = Y W + Y B + Y T (3 3),,,, Cv = CyW + CyB S B S + CyT kq S T S (3 4),, SB/ S S T/ S ( ) : kq, z, Cy = Cy0 + C a y+ C y z z (3 5) Cy0, x1 Oz1, Cy0 = 0, C y, ; C z y Cy = C a y+ C z y z (3 6),,, Cx 0 W ;,, Cx 1 W, CxW = Cx 0 W + Cx 1 W (3 7),,, 90,,, : C z = - C y (3 8) 87

94 , , ( ) ( ), mc ( ) ; ue ; Sa ; pa ; p H (3 P = mc ue + Sa ( pa - p H ) (3 9) 9 ) : P,, ( 3 9), ( ) ; pa p H, P0 = mc ue + Sa ( pa - p0 ) 3 7,, (3 9)P0 = m0 uc + Sa ( Pa - P0 ),, p0 P = P0 + Sa ( p0 - p H ) ( 3 10),, 3 Ma 7 P,, Oxt, 3 8 (a) ; O xt, 3 8 ( b ) ;, 3 8 ( c), P, P,, M P P P x t, P y t, Pz t, RP,, x tp, yt P, zt P, P M P M P MP = RP P ( 3 11) 88

95 3 8 P MP x t 0 - ztp y tp Px t Pz t y t P - Py t z t P MP y t = MP z t ztp 0 - x tp - yt P x tp 0 Py t = Pz t Px t z t P Py t x t P - Pz t x t P - Px t y t P ( 3 12) ,,,, G1, Fe,,, 3 9, G1 G = G1 + Fe ( 3 13),,,, 3, m, 9 M Re, e, e, Fe G, Fe = mre 2 e cos e ( 3 14) : Fe G1, G1 GG1 = mg ( 3 15), m,,, m 89

96 t, m0 ; mc,, mc ), mc, Re, Re dm = - mc ( 3 16) dt m( t) = m0 - t mc d t ( 3 17) 0, ( ; g g = g0 = 6371 km; R 2 e ( Re + H) 2 ( 3 18) g0, g m/ s 2 ; H (3 18), g H H = 50 km, ( 3 18 ), g = 9.66 m/ s 2, g0, 1. 5%,,, g,, g = 9.81 m/ s 2, ,, Mx t, My t, Mz t (, t ), ( ) ( ) Mx Ox t x (, 3 10, My O y1 y (, 3 10, Mz Oz1, z (, 3 10,, Mx My Mz = mx qsl = my qs L = mz q SL ( 3 19) mx, my, mz, 90 ; S ( ), S ;, SB ; L,,

97 ba ;, l,, L B,, 3 10 ( ),,,,, Ma H, z Ozt z 2, Mz = f ( Ma, H,, z, z,, z ),, x x,, 2, z,, z, Mz = Mz 0 + M a z+ M z z z + M z z z + M a z+ M z z z ( 3 20),, z, z = z L V ; mz = mz0 + m a z+ m z z z + m z z z + m 2+ m z z z ( 3 21), z, = L V, z = z L V ; mz0 = z = z = z = 0, O x1 z1, mz0 Ma m z, m z z, m z z, m z z, m z z, z, z,, z Oyt, Oyt 91

98 ,, my Oxt y t m y, m y y, m y y = m y+ m y y y + m y y y + m y+ m y y y ( 3 22) y = y l/ V ;=l/ V ; y = y l/ V, my0, m y, m y y, y y,, y ( ) Mx Ox t, ( ) O xt, Oyt, ;,, ( ) ( ),,, y, x, x, y,,, l mx = Mx qsl ( 3 23),, mx mx = mx0 + m x+ m x x x + m y x y + m x x x + m y y y ( 3 24) mx0 ; m x, m x x, m y y, m x x, m y y, x, y, x, y, ( ),,, ( ),,,,, () ( ),, mh ; qt ( ); St ; bt Mh = mh qt St bt ( 3 25), x Ox,, Z, 92

99 My 3. 4,,,, ;,,,,, ;, ,,,,, m, v, H ( O ), F; M m dv d t = F ( 3 26) d H dt = M ( 3 27), ( ) :, ;,,,, ; (),,,, ;,, ;,,,,,,,,,,,,,,,, 93

100 , : () ( ) ( ) ( ),,,,, m( t) m, P ; m( t) = dv dt = F + P ( 3 28) d H dt M; = M + MP ( 3 29) MP (, M P = 0) ( ), 6,, ( 3 28 ) ( 3 29 ),,, :, ( 3 28 ),,,,,, v,, : ( ) ( ),, d dt = t + d () ; d t 94 () t, ( 3 28 ) m d d t = m + = F + P ( 3 30) t

101 ih, j h, kh O x h y h z h ; x h, y h, z h O x h y h zh O x h y h zh = vx h i h + vy h j h + vz h k h ; vx h, vy h, vz h = x ih h + y h j h + z h k h ( 3 31) v t = d vx h d t i h vx h vy h = vz h + d vy h d t v 0 0 j h + d vz h d t k h v t = d v ih ( 3 32) d t v = ih j h k h x h y h z h = vi h v y h v z h ih j h k h x y h h z h v 0 0 = c + = ( z h j h - y h k h ) ( 3 33), c,ay Oz h x h y h z h = ZY c (3 34) (3 33), 0 c = c sin c cos (3 32) ( 3 35 )( 3 30 ), ( 3 34) = j h - v c cos k h ( 3 35) m d v d t = Fx h m v d d t = Fy h + Px h + Py h - m vcos d c d t = Fz h + Pz h ( 3 36) Fx h, Fy h, Fz h (R, G ) O xh y h z h ; Px h, Py h, Pz h P O x h y h z h R G P R X Y Z, Rx v Ry v = Rz v - X Y Z 95

102 R x h R y h Rz h = X T c Rx v Ry v = Rz v - X Ycos c - Zsin c Ysin c + Zcos c ( 3 37), G A y, Ox h y h zh Gx h Gy h Gz h Gx Gy Gz =, = XY c P O x t Ox h y h zh Rxh Ryh Rz h = X T rc Y T Z T P x t Gx Gy Gz 0 - m g = 0, Px t P y t = Pz t Py t = Pz t P mgsin - mgcos 0 Pcos cos P( sin cos c + cos sin sin c ) P( sin sin c - cos sin cos c ) ( 3 38) ( 3 39) (3 37) ( 3 38 )(3 39) ( 3 36), m d v d t = Pcos cos- X - m gsin m v d = P( sin d t cos c + cos sin sin c ) + Ycos c - Zsin c - m gcos - m vcos d c = P( sin dt sin c - cos sin cos c ) + Ysin c + Zcos c d v ( O xh d t ), ; v d ( x h Oy h ) ( Oyh d t ; 96 - mvcos d c ( Ozh d t ( 3 40) ), ), - :, c ; c 2.

103 ( 3 29 ),, (), ( 3 29 ) d H d t = H + H = M + MP ( 3 41) t it, jt, kt O x t y t z t ; x t, y t, z t ; H H x t, H y t, H z t H, J H = d H x t t dt it + d H y t d t H = J H H x t H y t = H z t j t + d H z t d t Jx t x t - Jx t y t - Jx t z t - J y t x t J y t y t - Jy t z t - Jz t x t - Jz t y t J z t z t J x t x t, J y t y t, Jz t z t ; k t ( 3 42) x t J x t y t, J x t z t,, Jz t y t y t ( 3 43) z t,,,, Jx t, J y t, Jz t, ( 3 43 ) H x t H y t = Hz t (3 44) (3 42), H = Jx t Jy t Jz t H d x t = J x t t d t i t + Jy t it j t k t x t y t z t H x t H y t H z t = d y t d t x t y t = z t J x t x t J y t y t ( 3 44) J z t z t d z t j t + Jz t d t k t ( 3 45) it j t k t x t Jx t x t y t J y t y t z t J z t ( J x t - J y t ) z t + y it t + ( J x t - Jz t ) x t z t j t + ( J y t - J x t ) y t x t k t ( 3 46) (3 45), ( 3 46 )( 3 41 ), d x t J x t + ( Jz dt t - J y t ) d y J t y t + ( Jx d t t - Jz t ) d z t Jz t + ( Jy dt t - Jx t ) z t y t = Mx t x t z t = My t y t x t = Mz t z t = 97 ( 3 47)

104 J x t, Jy t, Jz t ( ), ; x t, y t, z t ; d x t d t, d y t, d z t dt d t ; Mx t, My t, Mz t ( ), ( 3 47 )t 1. ( ),,,, A x y z, O xh d x d t d y d t d z dt vx h = vy h = vz h vx vy vz v 0 0, ( 3 48) ( 3 49) vx vx h 98 vy vz = Y T c Z T vy h ( 3 50) vz h (3 49) (3 50), ( 3 48 ), d x dt = vcos cos c d y d t = vsin d z d t = - vcos sin c ( 3 51)

105 2.,,,, x t, y t, z t, =++,Ay O x t x t y t z t sin+ XZY cos cos+ sin - cos sin+ cos = 0 0 = + Xr 0 0 +, Oz, 0 0 = 0 sin 1 sin cos cos 0 cos- cos sin0 0 sin cos 0 cos cos - sin cos 1 - tan costan sin,, (3 d d t = y sin+ t z cos t d d t = 1 cos ( y cos- t z sin ) t x t d d t = x - tan ( y t t cos- z t sin ) 53) t y t ( 3 52) z t ( 3 53),,,,, dm dt = - mc ( 3 54) d m,,, d t mc, (3,, mc mc, mc,, 54), m( t) = m0 - t mc ( t) d t ( 3 55) 0 99

106 , m0, 8 (,,,, c,,, c ), 3 11,, 8, A x y z,,,,,,,,,, c c, 8 5, 3 5, 8 3,,,, c,,, c, , 3, ( 3 12 ),

107 cos= cos 1 cos 2 + cos 1 cos 2 + cos 1 cos 2 ( 3 56) i, j, k A x y z, A < l 0 1, l 0 2 >, (3 56) < l 0 1, l 0 2 > = < l 0 1, i > < l 0 2, i > + < l 0 1, j > < l 0 2, j > + < l 0 1, k > < l 0 2, k > ( 3 57) Ox h Ozt l 0 1 l 0 2, A x y z, < l 0 1, l 0 2 >, Ox h y h z h O x t y t z t O A, O xh O x v, (3 57), sin= cos [cos sin (- c ) - sin sin cos(- c ) ] - sin cos sin ( 3 58) Oyt O x h l 0 1 l 0 2,,, ( 3 57 ), sin= {cos [ sin cos cos(- c ) - sin sin(- c ) ] - sin cos sin }/ cos( 3 59), O xt y t z t, Ozv A y l 0 1, l 0 2 (3 57), sin c = ( cos sin sin- sin sin cos cos+ cos sin cos )/ cos ( 3 60) (3 58) (3 60) 3,, (= 0) (= 0), =-,, = c,,, c = -, ( 3 40 ) ( 3 47 ) ( 3 51 ) ( 3 53 ) (3 54) (3 58) (3 60), 16,, 16 : v( t), ( t), c ( t), x ( t), y ( t), z ( t), x( t), y( t), z( t), v ( t), ( t), ( t), m( t), ( t), ( t), c ( t) 16,,,,,,,,,,, 1.,,, R P G,,, R P N, N N = P + R N N t N n, 3 13, 101

108 ,, 3 13 Nt = Pt + Rt Nn = Pn + Rn Rn = Y + Z, Rn,, ( ),,,,,, ( ),, ,, ; ;, +,,, 3 15, 3 16, 102

109 (),,, 3 16 ( a) ;,,, 3 16 ( b ) ;,,,, 3 16( c),, 3 17,, ( ) ,,, ( ),,, () 3 17,,,,,,,,, z, Y, y,, Z,, z, y,,,,,,, XPn Pt,,,, z ;,,,, 103

110 , 3 18,, 3,,,,,, Ozt Oy t,, Oxt, ;, Ozt O x t,, c, 3, O yt,,, P 18, 4 : 2., 4, 4, 4,,,, (, c ), Nn,,, 3 13,,,,,, *,, =- *, z, z = k(- * ) = k, k,,,,,,, x * i, x i, i = xi - x * i ( i = 1, 2, 3, 4 ), i, 1, 2, 3, 4,, i,,, : z = f1 ( 1 ), y = f2 ( 2 ), x = f3 ( ), P = f 4 ( 4 ) ( 3 61), : 104

111 z = f1 ( 1 ), x = f2 ( 2 ), y = f 3 ( ), P = f 4 ( 4 ) ( 3 62) (3 61) ( 3 62 ),, : (3 (3 1 (, i,, i, ) = 0 2 (, i,, i, ) = 0 3 (, i,, i, ) = 0 4 (, i,, i, ) = 0 ( 3 63) 63) 63) : 1 = 0, 2 = 0, 3 = 0, 4 = 0 ( 3 64) 1 = 0, 2 = 0,, ( ) 3 = 0, 4 = 0, ( ),,,,,, 4 : i = x i - x * i = 0 ( i = 1, 2, 3, 4),,, 1 = 0, 2 = 0, 3 = 0, 4 = 0 ( 3 65) 1 =- * = 0 2 = c - c * = 0 3 = = 0 4 = v - v * = 0,, 1 = - * = 0 1 = y - y * = 0 ( y * ) 2 = - * = 0 3 = = 0 4 = v - v * = 0 ( 3 66) ( 3 67) (3 66), ( 3 67 ), *, c*, *, v* ;, v,, v (3 40), ( 3 47 ), (3 51), ( 3 53 ), ( 3 54), (3 58 ), ( 3 59 ), (3 60) (3 64), 105

112 m dv dt = Pcos cos- X - mgsin mv d = P( sin dt cos c + cos sin sin c ) + Ycos c P(sin sin c - cos sin cos c ) + Ysin c + Zcos c - Zsin c - mgcos- mvcos d c dt = Jx Jy Jz d x dt + ( Jz d y dt + ( Jx d z dt + ( Jy - Jy ) z y - Jz ) x z - Jx ) y x = Mx = My = Mz d x dt = vcos cos c d y dt = vsin d z dt = - vcos sin c d dt = y sin+ z cos ( 3 68) d dt = ( ycos- z sin )/ cos d dt = x - tan ( y cos- z sin ) dm dt = - mc sin= cos [cos sin(- c ) + sin sin cos(- c ) ] - sin cos sin sin= {cos [sin cos cos(- c ) - sin sin(- c ) ] - sin cos cos }/ cos sin c = (cos sin sin- sin sin cos cos+ cos sin cos )/ cos 1 = 0 2 = 0 3 = 0 4 = 0 (3 68),, 20, 20 : v( t), ( t), c ( t), x ( t), y ( t), z ( t), x( t), y( t), z( t), ( t), ( t), ( t), m( t), ( t), ( t), c ( t), z ( t), y ( t), x ( t), P ( t), ( 3 68 ),,

113 , 20,,,,,,,,,,,,,, ( 3 68 ),,,,, c, x, y,, c, z,, Oxt y t, O xt y t,,, c, x, y, A x,,, c, z,,, ( O xt y t ) Ozt,, v,,,, z, x, y,,,, c, x, y,, c, z,,, c, x, y,, c, z, Ozt O x t Oy t (3 68) :,,,,,,,,,,,,,,,, 10, : v,,,, x, y, z, m, z, P 10,,,,, (3 68 ),, 107

114 ,,,,, c,, c, x, y,, : (1 ),, c,, c, x, y x, y cos cos cos c1 sin sin c, Zsin c, x y, y sin,, x, y X (2 ),, cos c1 (3 ) ;, m d v = Pcos- X - mgsin d t m v d = Psin+ Y - m gcos d t Jz d z = Mz dt d x dt = vcos d y d t = vsin ( 3 69) (3 d d t = z d m d t = - mc = - 1 = 0 4 = 0 69), 10, 10 : v( t), ( t), z ( t), x( t), y( t), ( t), m( t), ( t), z ( t), P ( t), (3 69), 108

115 - m vcos d c = ( Psin+ Y ) sin dt c - ( Pcos sin- Z)cos c Jx Jy d x + ( J z - J y ) z y dt d y + ( J x - Jz ) x z dt d z d t = - vcos sin c = Mx = My d d t = ( y cos- z sin )/ cos d d t = x - tan ( y cos- z sin ) sin= cos [cos sin (- c ) + sin sin cos (- c ) ] - sin cos sin sin c = (cos sin sin- sin sin cos cos+ cos sin sin )/ cos 2 = 0 3 = 0 (3 ( 3 70) 70) 10, c ( t), x ( t), y ( t), z( t),( t), ( t), ( t), c ( t), y ( t), x ( t) 10, x v,,, z, y,, z (3 70), v, y m, ( 3, ( 3 69 ), 70 ),,,,,,,,,, ( ),,,, (),,,,,,, v, c (A x, c = 0 ) ; P,, (),,,, c, Ozt, Ozt, O xt Oy t,, z = 0, x = 0, y = 0, 109

116 : P X Y G (3 69),, v,,,,, v, ( ) ( ),,,,,,, z, Ozt,, Oyt, O xt ; ( ), O xt, Oyt,,, (3 1., = 0, y, 0, c = 0, x 0, 68) m d v dt = Pcos cos- X mg = Psin+ Y - mv d c dt = - Pcos sin+ Z d y J y d t = My d z Jz d t = Mz d x d t = vcos c d z d t = - vsin c d dt = z d d t = y/ cos d m d t = - mc = - c = 2 = 0 4 = 0 ( 3 71) 14, : v( t), c ( t), y ( t), z ( t), x( t), z( t), ( t),( t), m 110

117 ( t), ( t), ( t), z ( t), y ( t), P ( t)14, 2., 0( y ) 0 y 0 ( ) z, m d v dt = P - X mg = P cos c + Y cos c - mv d c d t = P sin c + Ysin c J x Jz d x = Mx d t d z d t = Mz d x d t = vcos c d z d t = - vsin c d d t = z cos d d t = - z sin d d t = x d m d t = - mc = arcsin c = 2 = 0 4 = 0 sin(- c ) sin ( 3 72) 15, : v( t), c ( t), x ( t), z ( t), x( t), z ( t), ( t),( t), ( t), m( t), ( t), c ( t), z ( t), x ( t), P ( t)15, ,, :,, ;,, : (1 ), 111

118 J x = Jy = Jz = 0 (2 ),, (3 ),,,, Mz My = Mz ( v, y,, z, z,, z ) = My ( v, y,, y, y, x,, y ),, x, y, z,, z, y M z M y,,, z, y M z M y, Mz My = Mz ( v, y,, z ) = 0 = My ( v, y,, y ) = 0,,, z B y B = - = -, : z y,,, ( ),,, z, Ozt, ( 3 19 ),,, :,, (,, z, y ), m z m z z m y m y y 3 19,, ( ), (), Y Z X, Y Z X 112

119 ,,,,,,, (3 68) () m d dt = Pcos B cos B - X - mgsin m d dt = P(sin B cos c + cos B sin B sin c ) + Y B cos c - ZB sin c - mgcos- mvcos d c dt = P(sin B sin c - cos B sin B cos c ) + Y B sin c + ZB cos c dx dt = vcos cos c dy dt = vsin d z dt = - cos sin c dm dt = - mc ( 3 73) B = - m z z z B m z B = - m y y y B 1 = 0 2 = 0 3 = 0 4 = 0 m y, B, B ; B, B ; Y B, ZB B, B (3 73) 13, v( t), ( t), c ( t), x( t), y( t), z( t), m( t), B ( t), B ( t), c ( t), t B ( t), yb ( t), P ( t) 13, 3 73,, mc,, (3 73 ) 7, 4 = 0, 2, 2 ( m, P ), (3 73), :,, (3 73),,, 113

120 ,, ( 3 (3 69 ), m d v d t = Pcos B - X - mgsin mv d dt = Psin B + Y B d x d t = vcos d y d t = vsin d m dt = - mc 1 = 0 4 = 0 - mgcos ( 3 74) 74) 7, v( t), ( t), x( t), y( t), m( t), B ( t), P ( t)7,, z ( t), ( 3 74 ), ( 3 71 ) (3 72),, m d v d t = P - X mg = P B + Y B - m v d c d t = - P B + Z B d x d t = vcos c d z dt = - vsin c d m dt = - mc = c + B B = 2 = 0 4 = 0 ( 3 75), v( t), c ( t), x( t), z( t), m( t), ( t), B ( t), B ( t), ( t), P ( t) 10 zb ( t), yb ( t),,, 114

121 ,, (3 73), ( 3 74 ), (3 75),, (, ), ( ), (),,,,,,,,,,,,, ,,,,,?,,,, N ( ), a a= N + G m g, ( ) a g = N G + g g N G, n, n = N G,, N, N,, 115

122 , ( ), n, n= N + G G n= a g,,,, g,, 3 20 ( ),, 1 ( ), 2,, g ;,,,,, 3 20 ;, n O x h y h z h nx h = Nx h G = 1 G ( Pcos cos- X) ny h = Ny h G = 1 [ P( sin G cos c + cos sin sin c ) + Ycos c - Zsin c ] ( 3 76) nz h = N z h G n O x v y v zv = 1 [ P( sin G sin c - cos sin cos c ) + Ysin c + Zcos c ] nx v nx h ny v = Xv ny h nz v nz h nx v = 1 G ( Pcos cos- X) ny v = 1 G ( Psin+ Y ) ( 3 77) nz v = 1 G ( - Pcos sin+ Z) (3 77) (3 76) c = 0 116

123 nx h n x v ; ny h, nz nz h v,,,, ;,,,,,, n Ox t y t z t nx t nx v ny t nz t = ZY ny v = nz v nx v cos cos+ ny v sin- nz v cos sin - nx v sin cos+ ny v cos+ nz v sin sin ( 3 78) Oxt ny t, nz t nx v sin+ nz v cos n x t ;, nx h, ny h, nz h (3 1 d v g dt = - nx h v g - d d t = - ny h - sin - cos v g cosd c d t = nz h ( 3 79) 79),,, ( v,, c ), (3 nx h ny h = 1 g = v g nz h = - d v d t + sin d dt + cos v g cosd c dt ( 3 80) 80) v, c,, (3 80) :, nz h = 0;, ny h = 1; 117

124 , ny h = cos=, nz h = 0;, nx h = sin=, ny h = cos=, nz h = 0;, ny h = 1, nz h = 0;, nx h = 0, ny h = 1, nz h = 0, (3 (3 79) 81) : d v dt = g( nx h d d t = g v ( ny h d c d t = g vcos nz h - sin ) - cos ) ( 3 81) nx h = sin, ; nx h > sin, ; nx h < sin, Ox h y h, ny h > cos, d > 0, d t ; ny h 3 21 < cos, ; ny h = cos, 3 21 n yh Ox h z h, nz h > 0, d c < 0, dt ; nz h 3 22 < 0, d c > 0, ; nz d t h = 0,,, K 118

125 s, 3 22 Oxh z h nz h K = d d s y h K, (3 y h = d s d = 81) v d / d t v y h = ( 3 82) g ( ny h - cos ) : v, ny h,,, ; ny h, v,,, xh Oz h (3,, z h z h = - d s = - d c 81) v d c/ d t z h = v2 cos ( 3 83) g nz h,,,,,,,,,, 1., nr (3, 80),,,, ; ; 119

126 ,,, () 2.,,,?,,, ( ),, ( ), ( ),, ( ) z, y,, m z z, m y y, m Y = Y + Y z z ( 3 84) Z = Z + Z y y z, m y, m y y,, m z+ m z z z = 0 m y+ m y y y = 0 ( 3 85) (3 85) (3 84 ), ( ), ( 3 76 ),,, c, n y h B = 1 G ny h B nz h B = n y h B = n y h B P Y - n z h B = 1 G - P Z - ( 3 m z Y m z z z m y Z m y y y ( 3 86) ( 3 87) 86 ),,,,,,,,,,, ( 812 ), Ma,,,, 120

127 , nl 3. (3 85) (3 84),,, ( ) (3 ny h B nz h B n y z B h = 1 G - m z z m a z n z y B h = 1 G - y m y m y = n z y h B z = n z y h B y P Y Z - + Y z P Z y ( 3 88) ( 3 89) 88), ( ) z, y, z, y, zmax (1 ) :,, ( cb ) zmax < m a z m z z ( cb ) ( 3 90) (2 ) : ( ) (), 20,, z zmax < 20/ 1 - m z (1 - ) ( 3 91) m z (3 91) (3 90) (3 ) : zmax, np zmax, zmax ( ),,,,,,,,,,,,,,,,,,n np nr + n 121

128 , nr, np nl nl > np > nr 3. 5,,, ( ) ( ) :, , O XF OXM, 3 23 ( ),, OX H OXM,,,,,,,,,, 3 23,,,, AIM - 98, ()K - 13,,,,,,,, , OXF OXM ) H,,, 3 C, ( 24,,,,,,, ( ) H,, AIM - 7F, 122

129 ,,,,,,, OXF OXM, () OX H, H,, ,,,,,,, OXF O X F 123

130 , 3 24,,,, AIM - 9L/ M, / /,,,,,,, / /,, 20 70, B - 1,, (),, 1993 ( Jane s Defense Weekly) Su - 35 s to haveover the shoulderability, /,, , ; ( ),, ( ),,,, (),,,,,,,,,, 124

131 ,, (1 ) (, ) ( ) ( ) ; (2 ) ( ) () ; (3 ) ( ) ( ); (4 ) ( ) (, ),, : ; ; ;,,,,,,, ,,, T, M 3 26 M T( ) ( ) A x,,,, ;, 125

132 , r, q 3 r r = 0 26 : q, ( ), q, T,,,, T, ;, c, T, ( ),,, T r q 3 26 T vcos, r ; vcos T, r d r dt = vt cos T - vcos vsin, q ; vt sin T, q 3 (3 d q d t = 1 ( vsin- vt sin r T ) 26,, d r dt = vt cos T - vcos r d q = vsin- vt sin d t T q =+ q = T + T 1 = 0 ( 3 92) 92), 1 = 0 ( ) :,, := 0, 1 == 0; : q= q0 =, 1 = d q d t = 0; : = K q, 1 =- K q = 0 : v( t), vt ( t), T ( t) T ( t), 5 : r ( t), q( t), T ( t) ( T ( t) ), ( t), ( t),, r( t), q( t) 126

133 , ) ( )( ),, ( ), ( ),,,,,, C 3 27 M T, 3 27 : RT ; RM ; T,, C qt, qm 3 27, d RM d t = vcos ( qm - ) - vc cos( qm - c ) RM d qm dt = - vsin( qm - ) + vc sin ( qm - C ) d RT d t = v T cos ( qt - T ) - vc cos( qt - C ) RT dqt d t 1 = 0 = - vt sin ( qt - T ) + vc sin( qt - C ) :, : qm = qt ; : qm - qt = Cq ( RT - RM ) ( 3 93), v( t), vt ( t), vc ( t), T ( t), C ( t), 5 : RM ( t), RT ( t), qm ( t), qt ( t), ( t),, :,, 127

134 ,, 1 = = 0, ( 3 v, vt d r d t = v T cos T - v r dq dt = - v T sin T q= T + T T, (3 93 ) 3 : r, q T r0, q0 T0,,, :, A x, T = 0, q = T ( 3 28 ), (3 93) : (3 (3 d r = vt cos q - v d t r d q d t = - vt sinq ( 3 94) 94) r = f( q) 94) d r r = v T cos q - v - vt sin q d q 3 92 ) ( 3 93) 28 p = v/ vt,, p d r r = - cos q + p d q sin q r = r0 tan p t an p q 2 sin q0 ( 3 95) q0 2 sin q c = r0 sin q0 tan p ( r0, q0 ) 128 q0 2 ( 3 96)

135 tan p q 2 r = c sinq ( p - 1 ) q sin = c 2 q 2cos ( p + 1 ) 2 ( 3 97),,,,,,,,,,,,,,,,,, ( ),,,,,,,1 < p2, ,,, q0 1 = d q d t = 0 1 = q - q0 = 0, d r dt (3 = vt cos T - vcos r d q = vsin- vt sin d t T q =+ q = T + T 1 = dq dt = 0 ( 3 98) 98 ) vsin= vt sin T ( 3 99),,, T , r,,,,, 129

136 = arcsin v T v sin (3 100) T, q,,, (3 100 ) :, ( T ), p (p > 1 ),,, ( ),, (3 (3 d v d t 99) d v dt 101 ) sin- vcosd d t = d vt an (3 sin+ vcosd d t = d vt dt sin d t sin T T + v T cos T d dt = - d d t, d T d t = - d T d t - v T cos T = v d ; ant dt = n = an g = nt d T d t vt cos T cos + 1 g d T d t (3 101) d T = nt g dt d v sin d t cos - d vt dt sin T cos (3 102) 102 ),, d v/ d t, d v T/ d t,, p,, : (3 99) t = -, T = - T v > vt, ( 3 99) p cos= T cos T v = cos T v T T cos v v T T T > = an ant n< nt :,,, ( 130 < 1

137 3 30 ), 3 30,,,,,,,,,,,,, ( vsin= vt sin T ),, vr ,,,, K K, (3 : q =+ t, (3 1 = d dt - K d q = 0 (3 103) d t 103 ), 1 = (- 0 ) - K( q - q0 ) = 0 (3 104) d q d t = d d t + d dt 103 ), d dt = ( 1 - K) d q d t d d t = 1 - K d K d t 131 (3 105) (3 106)

138 (3 105) : K = 1, d = 0, = 0 =,, d t = 0 ; K, dq 0, q = q0 dt,, K 1 < K <, 26, 3, 31 K,, d r dt = vt cos T - vcos r d q = vsin- vt sin d t T q =+ q = T + T d dt = K d q d t v, vt, T ( r0, q0, 0 0 ), ( ) ( K = 2,, ), ( ) = 0, q = 0,= 0, = 0 = (3 107) (3 107 ), 3 vsin- v T sin T = 0 (3 108) 3 =, ( K = 5, p = 2, 0 = 0, T = 0 ),,,, = arcsin v T v sin T (3 109) t = t 0 32,, K = 5, 0 = 0, T = 0, p = 2, q0 = 0q0 = 180, ( 3 109), 132

139 , ( ), q0,, 0, q, (q0 ), r0, qk, qk r0 rk = 0, (3 105 ) (3 k = arcsin 1 sin( qk - p Tk ) (3 110) k = 0 + (1 - K) ( qk - q0 ) 110 ), 0 = 0 ( ) T 0, qk = q0-1 K - 1 arcsin, qk r0 sin qk 1 qk - q0 1 K - 1 arcsin sin qk p, qk - q0 max qmax, K = 5, p = 2, ( ) qmax = 7.5, q0 = 97.5, qk = 90, qmax q0 = 33.7, qk = 30, qmax p K,, 33, p K 2. q, q 3, q (3, : 107 ), r q + r q= vsin+ v cos- vt sin T - vtt cos T = ( 1 - K) q T = q - T 1 p r = - vcos+ vt cos T (3 111) 33 ( 0 = 0 ) r q = - ( K vcos+ 2 r) ( q - q * ) (3 112) q * = vsin- v T sin T + vt T cos T kvcos+ 2 r 133 (3 113)

140 (1 ),, ( 3 113) (3 (3 112 ) q = - 1 r q * = ) : ( Kv cos+ 2 r) > 0, q q q> 0, q < 0, q ; q < 0, q> 0, q, q 3 34, q, q, q ( K vcos+ 2 r) < 0, q q, q, q 3 ( K vcos+ 2 r) q (3 114) 35 q q,,, q, (3 K > 2 r vcos (3 115) 3 : K, (3 115 ), q ;, 115 ), q,,,, (2 ), : (3 113 ) : q *, v T, vt T v, q * ( Kcos+ 2 r)0, q * (3 112 ), ( K vcos+ 2 r) > 0, q < q *, q > 0, q ; q > q *, q < 0, q, ( K vcos+ 2 r) > 0, q, ( K vcos+ 2 r) < 0, q * 3 q q *,,, qk 34 ( K vcos+ 2 r) > 0 q 35 ( K vcos+ 2 r) < 0 q ( K vcos+ 2 r) > 0, q ( ), rk = 0,, q q *, qk = q * k = vsin- v T sin T + vt T cos T (3 116) K vcos+ 2 r t = t k, 134

141 (3 nk = vk k g = K vk q k = 1 g g ( vsin- v T sin T + vtt cos T ) cos- 2 r (3 117) t = t k K v 117 ), r( ),,,,,,, r, r = v + vt, r = v - v T r r,,,, ( 3 : ( K vcos+ 2 r) < 0, q, q, qk 117 ) K,,,,, K < ( 2 r / vcos ), K, K, K,, 1. K q q q, q K ( 3 K > 2 r vcos (3 118) 118 ),, r, K, K,, ; 2. K (3 118 ) K, n = ( K v q/ g), q,,, K 3. K K, q, K, K, : K > (2 r / vcos ), q,, ;, 135

142 K, 0, q0, p,,,, q,,, :,,, 1.,, K1, K2 n = K1 q (3 119) n = K2 r q (3 120) n= K1 q n = ( K v/ g) q( = K q), (3 (3 K = K1 g v 117 ),, nk = 1 g ( vsin- v T sin T + v TT cos T ) cos- 2 r K1 g t = t k (3 121) 121 ) : n = K1 q, n= K2 r q,,, K = K2 g r v (3 117 ), n = K2 r q (3 nk = 1 g ( vsin- v T sin T + v TT cos T ) 2 cos- K2 g t = t k (3 122) 122) : n = K2 r q,,, 2. (3 ( ), r = - vcos (- q) + vt cos( T - q) r q = - vsin(- q) + vt sin( T - q) 123 ),, r q+ 2 r q = - vsin(- q) + vt sin( T - q) + (3 123)

143 vt T cos ( T - q) - v cos(- q) (3 124),, n = A q (3 125) n = v g + cos (3 126), n ( ) ( ) (3 126 )( 3 125), (3 127 )( 3 124), q + r r A gcos (- q) r = g v ( A q - cos ) (3 127) - 2 q = 1 r [ - vsin (- q) + vt sin ( T - q) + vtt cos( T - q) + gcos (- q) ] (3 128) N = A gcos (- q)/ r,, ( 3 128) q+ r r ( N - 2) q= 1 r [ - vsin(- q) + v T sin( T - q) + vtt cos( T - q) + gcos (- q) ] (3 129),, ( ),,,, y n= A q+ y (3 130) = g v ( A q+ y - cos ) (3 131) (3 131 )( 3 124), vt = 0, T = 0, r q+ 2 r q+ A gcos (- q) q= - vsin (- q) + gcos (- q) - gcos (- q) y : q + r r ( N - 2) q = 1 r [ - vsin (- q) + gcos (- q) - gcos (- q) y] (3 132) t; T r = r0 - r t, T = T0 r 137

144 (3 (3 132 ) 133 ), q= q0 1 - q + 1 T - t ( N - 2 ) q = 1 r [ - vsin (- q) + t T N - 2 gcos cos(- q) - gcos (- q) y] (3 133) + n= A q+ y = A q0 1 - : t = T, n, 1 ( N - 2 ) r [ - vsin(- q) - gcos (- q) y + gcos (- q) ] t T N t T N - 2 A ( N - 2) r [ - vsin (- q) - gcos (- q) y + gcos (- q) ] t T A ( N - 2 ) r [ - vsin(- q) - gcos (- q) y + gcos cos(- q) ] + y = 0 y = -, N - 2 (3 134) + y (3 135) N 2 g v tan (- q) + N cos (3 136) 2 N n = A q - 2 g v tan (- q) + N cos (3 137) 2, , ,,, O 1, 2, 3, 1, 2, 3, 1, O11,

145 (SA2 ), ( - ),,,,,, ( )SA ( ),, 3 37 O, T, M R, R, C, = CR (3 138) qm = qt + 37 qm = qt + CR (3 139) qt ; qm qm = qt + CR + C R (R = 0),, qm = 0, qt + C R = 0 (3 C = - qt R = - qt R (3 140) R 140 ), : ( SA2 2030k m),, (3 140 ) 139

146 (3 (3 140 ), 140 ), = qt R R,, (3 140),,, ,,,,,,,, (),,,,,,,,,,,,, -,, ( ),,,,,, ,,,,, (1 ),,,,, ;,,,, 140

147 ,, np nr + n1 + n2 + n3, np ; nr ;n1 ;n2 ;n3 () (2 ),, -, -,, (3 ),,, (4 ),, (5 ),,,,,,,,,, : ( ) ( ),, :, ;,, R , AIM - 54C + +,,,,,, 3. 7,,, 141

148 ,,,,,,,,,,,,,,,,,,,, , AIM - 9B, ( )K - 13,, A B, CD, AC, BD 142

149 , 3 39 () R - 73,,, ;, ,,, 2.,,,, 3., 4.,, 1.,, 2.,,,,, 3.,, 143

150 4.,,,,, ,,, 2.,, ,, ;, ;,,,,,,,,,, 3 41,,,,,,, 144

151 (),, ( ), 19 60, ( ) ( ), (), :,,,,,,,,,,,,,,,,,,,,,,, 145

152 ,, : ( ),,,,,,,,,, (, ), (, ),,,, ,,,,,,, :,,, ;,,,,,,,,,,, 20% 50%, 15 % 30 %, 146

153 ,,,,,,, 34, ( ),,, : ;, : (1 ),, 0, ; (2 ) P,, ; (3 ),, ; (4 ) ; (5 ), ; (6 ),,,,,,,, j = a+ J + g d dt = J + g a, a = m m u e m, ue ; d dt = a+ J + g J, J = CH( y) G( v, a) v, C, H( y) ( ), y, G( v, a), v, a ; 147

154 g, g, : h: : () : ( kg/ m 3 ) =g; ( kgs 2 / m 4 ) H( y) :, H( y) = ; O N O N Cx 0 Cx 0 : : i:, i = Cx 0 Cx 0 C:, C = id2 q 103, d (cm), q ( kg) F( v, a) :, F( v, a) = v 2 Cx 0 v a G( v, a) :, G( v, a) v = F( v, a) a J,, H( y) = H( y), G( v) = G( v, a) O N d = a + J + g (4 1) d t d = J + g (4 2) dt a = m u e (4 3) m J = C H( y) G( v, a) v (4 4) J = C H( y) G( v) v (4 5) O N, v = v O N,,,,,,,,, ( KMS), ( SI) 148

155 , O O H O, O 01 (, ), ( 4 1 ) 4 1 C, OC,, a, = a + (4 6) M,, u w g,, a, a u v a w J v, - J u v - J w v 4 1 d d t d u d t d w d t 4 1 a J g a u v - J u v 0 a w v - J w v g (4 1 ) 149

156 (4 5 ) d u d t = a u v - J u v d w d t = a w v - J w v + g d u dt = a u v - C qk q d w d t = a w v - C qk q H( y) G( v) u H( y) G( v) w + g, qk/ q q, C, C= id qk ( ) qk, qk/ q,, * d u d t = a u v - C q K q * d w dt = a w v - C q K q * d dt = u * d d t = w H( y) G( v) u H( y) G( v) w + g *, (4 7), u, v, w,,, y6,, y = H + sin 01 - (4 8) = u + w = u 0 + w 0 (4 9), 0, 0 (4 8) (4 1 ), lg, v v1 v01 (), 0 : t = 0, u = v1, w = 0,= 0,= 0 (4 7 ) t = 0 ; t = tg,,, (4 2 ), (4 7 ) a = 0 q = qk 150

157 * d u = - C H( y) G( v) u dt * d w d t = - C H ( y) G( v) w + g d dt = u * d d t = w y = H + sin 01 - v = u 0 + w 0 ( 4 10), 1 K, 4 2, K, 1, 1 k ( 4 10) 1, 1 t = tk ( ), u = uk (), w = 0, 1 = 0, 1 = 0 4 2, t = 0, u= v01, w = 0,= 0 = 0,, t (4 7 ) d u d = d t d u d d t = 1 u d u d t 151

158 (4 * d u d = a v - C q K q * d w d = a v dt d = 1 u * d d = w u H( y) G( v) w u - C qk q H( y) G( v) w u + g u d d P d = P = w u = d d w d w u u d = 11), d P d = g u 2 d - W d u d u 2 ( 4 11) P, * d u d = a v - C q K q * d P d = g u 2 * dt d = 1 u * d d = P H( y) G( v) (4 8 ) ( 4 9) : = 0, u= v1, P = 0, t = 0, = 0, 152 * d u = - CH( y) G( v) d * d P d = g u 2 dt d = 1 u * d d = P y = H + sin 01 - v = u 0 + P u 0 ( 4 12) ( 4 13)

159 = 0, u = v01, P = 0, t = 0, = 0, ( 4 2) O, O, C, OC,, O, Ov01 a, Mn, M,( ), n (4 2 ), n, n d d t d v d t v d dt J - J - gsin(+ ) 0 - gcos (+ ) g d v = - C H( y) G( v) v - gsin(+ d t ) d d t = - gcos(+ ) v, 153

160 * d v = - C H( y) G( v) v - gsin (+ d t ) * d dt = - gcos (+ ) v d dt = vcos * d d t = vsin y = cos+ sin t = 0, v = v01, = a, = 0, = 0 ( 4 14),,, H, 4 y = H + cos+ sin 4 4 4, d t = d vcos * d v d = - C H( y) G( v) 1 cos - gsin(+ ) vcos * d d = - gcos (+ ) v 2 cos dt d = 1 vcos * d d = tan ( 4 17) 154

161 , y = cos+ sin, y = H + cos+ sin = 0, v = v01, = a, t = 0, = 0 Ox y, H O, x 1 (), y, 4 5 M x y u w, ( 4 2), * d u dt * d w d t = - CH( H - y) G( v) u = - C H( H - y) G( v) w + g d x d t = u = vcos * d y dt = w = vsin ( 4 v = u 2 + w 2 5 ), 1 x, ( 4 18) 4 5 t = 0, u = v1, w = 0, x = 0, y = 0 ( 4 6 ) t = 0, u = v1 cos, w = v1 sin, x = 0, y = 0 ; 155

162 v1 4 6 ( ), O x y,, y, P = w u d u d y = d u d t = - C H( H - y) G( v)/ P d td y d P d y = d P d d t d d td y = g u 2 P d t d y = 1 u P d x d y = 1 P y * d u = - C H( H - y) G( v)/ P d y * d P d y = g/ u2 P * d x d y = 1/ P dt d y = 1/ u P ( 4 19) v = u 1 + P 2, y = 0, u = v1, P = 0, x = 0, t = 0, 156

163 y = 0, u= v1 cos, P = tan, x = 0, t = 0 ; (,= 0 ) ; v1 t ( y, x, w u v y x ) : t = 0, * d u dt * d w d t * d y dt = w = - CH( H - y) G( v) u d x d t = u x : x = 0, * = - C H( H - y) G( V) w + g v= u 2 + w 2 ON u = u0 w = w0 y = y0 = 0 x = x0 = 0 = v1 cos = v1 sin d u = - H( H - y) G( v) u d x * d P d x = g u 2 * d y d x = P d t d x = 1 u v= u 1 + P 2 O N u= u0 = v1 cos P = P0 y = y0 = 0 t = t0 = 0 = tan ( 4 20) ( 4 21),,, 157

164 :,, ;,,, vk, 4 7 ( b), Ok 4 7 ( a) ; ( b ),, a = 0,,, (4 14) d v = - C H( y) G( v) v - gsin(+ d t ),+ > 0 sin(+ ) > 0 C, H( y), G( v), v g, CH( y) G( v) v > 0, gsin (+ ) > 0 dv dt < ( a) K S, 4 7 ( b ) ks S,+= 0, sin (+ ) = 0, d v dt s = - C H( y) G( v) v < 0,+< 0, gsin(+ ) = - gsin +, dv, dt, CH( y) G( v) v > gsin + 7 (a)t

165 , vm in CH( y) G( v) v = gsin + dv dt = 0, +, gsin(+ ), d v > 0,, 4 d t CH( y) G( v) v < gsin + 7( b ) t m G( v)v, H( y),, d v = 0, dv = 0, C H( y) G( v) v d t dt M, 4 7 ( b) m, sin (+ ) + 90, sin (+ ) ; H( y), G( v) v, CH( y) G( v) v > gsin +, d v < 0,, 4 dt 4 7( b) mc 7( b ), ( 4 8) (4 9 ), :, kstmc, v01 vk ;,,,, st mc, v1, , x = xs = X 2, X,, (4 10 ), v0 = m/ s, 0 = 45 ( C = 0.3 ) ( C= 1.0)( C = 6.0 ) ( C = 0.1 ) 159

166 , d > a, c > 0 a d ( 4 11 )( 4 21 ) 2 P d P = - g u 2 P d y 2 Pd P = - 2 g d y u 2, a s 0 2 Pd P P a s d d y = - 2 g y y a u 2 a P 2 a y d y = 2 g y a u 2 a P a 0 y a d y 2 PdP = - 2 g 0 u 2 d P 2 d y d y = 2 g y d u 2 d 4 11, ua > ud, 160

167 P0 < Pc, y dy d y < y a u 2 a P 2 a y y d < P 2 d Pa < Pd u 2 d a < d o < c ( 4 22) 2. xs > X 2 (4 21) d x = d y P, xs - xa = y y a d y P a y d d y d y xd - xs = = y P d y y d P d xa = 0, xd = X y Pd > Pa d y d y > y P a y y d P d xs - xa > xd - xs xs > X 2 ( 4 23) : xs = (0.50.7) Xxs = 0.5 X ; xs 0.55 X ; xs( ) X 3. ts < T 2 (4 21), d t = d y u P = - d y w ts - ta = - y y a d y w a td y d y d y - ts = = y w d y d d y wd 161

168 wd < wa ts - ta < td - ts ts < ta + td 2 ta = 0, td = T, ts < T 2 : ts (0.40.5) T ;, ts 0.45 T ; ts = T/ 2 C, H, v01, 01 (4 10) u, w,, t,, C, H, v01 01 ( a ) C, H, v01, 01, : (1 ) C, H v1 ; (2 ) C, H, v1 4. 3,,,,,,,,,,,,,, 4.3.1,, v01, D,,,, : (1 ) ; (2 ) ; (3 ),,, ; (4 ) 162

169 4. 2,,,, (4 13) * d u = - CH( y) G( v) = - CH( y) G( v, a) d * d P = g/ u2 d dt d = 1/ u * d d = p y = H + sin ( a + ) - = u 0 + w 0 = u 0 + Pu := 0, t = 0,= 0, w = 0, u = v01, P = w/ u = 0 ( 4 24) D, m; (, = 30, D = m, m, H ( y) = 0.093) ; ;, ;, (4 24) : (1 ) H y, H( y)h( H) (2 ) ON y, G( v, a) G( v, aon ) H( y) G( v, a)h( H) G( v) (3 ) u v, 4 12 ( b), u sin( = 2 + ) v sin 2 - (+ ) U = vcos / (+ ), 01 = +, cos cos (+ ), uvg( v)g( u),, 4 13 ( a),+ > 0, u > v, G( u) > G( v) y > H, H( y) < H( H) H( y) G( v) < H( H) G( u) cos (+, H( H) G( u) ) < 1, cos,, > +, 4 13 ( b), u < v, y < H,, H ( H) G( u) cos(+ ) > 1, cos 163

170 4 12 ( a) ; ( b ) 4 13 ( a) ; ( b ) 164

171 H( y) G( v)h( H) G( u) cos (+ ) cos (4 ) D,,, D D 4 14 D = cos(+ ) cos, D < m,< 30, ( 4 d u = - C H( H) G(U) d D d P d D = cos g cos(+ ) u 2 d d D = cos cos(+ ) P d t d D = cos 1 cos(+ ) u 24 ) : D = 0, u = v0 1, P = 0,= 0, t = D ( 4 25) H( H),, H ( H), C, CH ; D,, D, cos (+ ) 1,, cos cos (+, P,, t ), cos d u = - G( U) d CH D d P d CH D = d d CH D = g C H u 2 P C H dt d CH D = 1 CH u : CH D = 0, u = v01 (4, P = 0,= 0, t = 0 1. (4 26) ( 4 26) 24), 165

172 d u d CH D = - G( u), d CH D = - CH D = 0, u = v01 u, v 01 d u CH D = - u u v 01 G( u) d u G( u) + d u G( u) =d u u G( u) G( u) = Cx 0 ( u/ ao N ) u d u G( u) v 01 d u G( u) Cx 0, G( u)cx 0 ( M),, u d u G( u) d u,g( u) v 01 = D( u), D( u) u, = D( v0 1 ) v01 CH D = D( u) - D( v0 1 ) D( u) = CH D + D( v0 1 ) ( 4 27) D( u)d( v01 ),,, (4 27) u= f ( CH D, v0 1 ), CH D v01 u u v01 = f ( CH D, v0 1 ) v01 = gu ( CH D, v01 ) ( 4 28) u= v01 gu ( CH D, v01 ) ( 4 29) u = v01, u < v01, 2. (4 26) d P d CH D =, gu 1, gu, g C H u 2, (4 29), CH D = 0, P = 0, P 0 C H D d P g =CH 0 d CH D v 2 01 g 2 u ( CH D, v0 1 ) C H D g d CH D P = CH v gu = P = g d v g 2 u

173 C H D 1 d CH D = gp ( CH D, v01 ) ( 4 30) CH D P, ( P = w u ), gu 1, u, gp 1 0 g 2 u P = g D v 2 gp ( CH D, v01 ) ( 4 31) 0 1 D = 1, w = gt, t = v01, gp = gp ( CH D, v01 ), 3. (4 26) d d CH D = P C H, gp (4, (4 31) P, CH D = 0,= 0, = 1,= gt2 2 = g 2 0 C H D gd d= 0 C H D CH v gp d CH D g = C 2 H v01 2 CH DgP d CH D D 2 v 2 01, = C H D D v01 g 0 = t C 2 H v ( CH D) 2 2 = gd2 2 v ( CH D) 2 CH D g P d CH D = g( CH D, v01 ) ( 4 32) 0 = g D2 2 v g( CH D, v01 ) ( 4 33) 32), gp 1, g1, g = 1g, 4. (4 26) dt d CH D = 1, u, CH D = 0, t = 0, CH u gu = 1, t 0 C H D dt = 0 t = CH D CH v01 d CH D CH v01 gu = D v01 167

174 1 C H D CH D 0 d CH D = gt ( CH D, v01 ) ( 4 34) v01 g u t = D gt ( CH D, v0 1 ) ( 4 35) (4 34) gt = 1 gu 1, gt 1, 5., CH D, v ( a) ; ( b ) tan=, tan sin = D sin 2 - (+ ) sin = D = sin cos cos- sin sin D cos (+ ) cos, sin< < D, D + sin D cos= g D cosg( 2 v 2 CH D, v0 1 ) ( 4 36) 0 1 v C, 4 15( b), 168 u sin 2 + (- ) = w sin (+ )

175 P = w u tan= sin(+ = ) cos (- ) Pcos- sin cos- Psin, P, : P cos 1, tan, sin, Psin< < 1 = Pcos- = gd cos (2 2 v 2 gp - g) ( 4 37) 01 2 gp - g= g( CH D, v01 ) ( 4 38) = gd cosg( 2 v 2 CH D, v01 ) 01 g, g 1,, : vu= v01 gu ( CH D, v01 ) P = gd v 2 gp ( CH D, v0 1 ) 01 = gd2 2 v 2 01 t = D v01 g( CH D, v0 1 ) gt ( CH D, v01 ) ( 4 39) = cos gd 2 v 2 01 = cos g D 2 v 2 01 g( CH D, v01 ) g( CH D, v01 ) gu, gp, g, gt, g, g g, CH D v01,, ( ), g g g, CH D v01, g v0 1, CH D, 169