1. .
2. , .
3. .
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8. : ) , ) , ) ?
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10. : ) , ) ?
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12. .
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17. .
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20. : ) , ) , ) .
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23. : ) , ) ?
24. , , ?
25. ?
26. : ) , ) ?
27. ?
28. ( ) - ?
29. ?
30. ?
31. .
32. .
33. ?
34. ? ?
35. .
36. .
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38. .
39. ?
40. ?
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, . : , , , , , . : , , .
( , , ). , ( ), ( ).
10 ( , ), . , , . , . 1.4 . 4 1 .. 0 9 1- ( 1- ) .
, ; , 46, 4 . 6.
; , , . , .
, , , . ( , ..), , . .
1
, (. 1.01.9).
. 1.0 | . 1.1 |
. 1.2 | . 1.3 |
, = 25 .
. 1.4 | . 1.5 |
. 1.6 | . 1.7 |
. 1.8 | . 1.9 |
= 60 , . C1. . 1 , q. , .
1
- | q = 10 / | ||||||||
F1 = 10 | F2= 20 | F3 = 30 | F4 = 40 | ||||||
a1 | - | a2 | - | a3 | - | a4 | q | ||
H | K | KL | |||||||
D | E | LC | |||||||
K | E | KL | |||||||
K | H | LC | |||||||
D | E | KL | |||||||
H | D | LC | |||||||
E | K | KL | |||||||
D | H | LC | |||||||
H | D | KL | |||||||
E | K | LC |
|
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, . = 0,5 .
. 1 , , , , . ( ), , . , , , m0() = m0() + m0().
1. ABCD (. 1) D ( ). . 1. , P. F, M q (. 1).
. 1
: F = 30 , P = 25 , M = 40 ., q = 10 /, a = 60, g = 45, b = 30, l = 0,5 . = 0,5 .
: D, .
. : , , ( = ) , , ( , D ). Q = q2 l = = 102 0,5 = 10 , ( L) .
. = F cosa = F sin a:
åFkx = 0, XA + RD sin b F cos a T sin g + Q = 0;
åFky = 0, YA + RD cos b F sin a + T cos g = 0;
åmA( k) = 0, M + RD cos b 2 l + F cos a 3 l F sin a 2 l +
+ T sin g 2 l Q l = 0.
, : XA = 4,89 ; YA = 22,5 ; RD = 35,57 .
. D:
åmD( k) = 0, M +F cos a 3 l T cos g 2 l + T sing 2 l Q l YA 2 l =
= 40 + 30× 0,5 ×3× 0,5 25× 0,707×2 × 0,5 +
+ 25× 0,707 ×2 × 0,5 10×0,5 (22,5)2 × 0,5 = 0.
, .
: XA = 4,89 ;
YA = 22,5 ;
RD = 35,57 .
YA , , . 1.
2
= 3 = 3 l, = 2 l , () ' (2.02.9).
. 2.0 | . 2.1 |
, , = 5 ×. , . C2; ,
|
|
. 2.2 | . 2.3 |
. 2.4 | . 2.5 |
. 2.6 | . 2.7 |
xy, , xz, , yz. (D, E, H) . , , . l = 0,8 .
. 2.8 | . 2.9 |
2
F1 = 4 | F2 = 6 | F3 = 8 | F4 = 10 | |||||
y a1 x | z a2 x | z y a3 | y a4 x | |||||
- | a1, | - | a2, | - | a3, | - | a4, | |
D | E | |||||||
H | D | |||||||
E | D | |||||||
E | H | |||||||
E | H | |||||||
D | H | |||||||
H | D | |||||||
E | H | |||||||
D | E | |||||||
E | D |
. 2 , , () , , . , , m() = mx() + mx() ..
2. (. 2) , () , , yz. ( yz), ( x) ( ).
. C2
: P = 5 H; M = 3 H; F1 = 6 H; F2 = 7,5 H; a = 30; AB = 1 ; BC = 2 ; E = ; K = .
: , .
. , F1, F2 , . () ( , ), , , .
:
åFkX = 0, XA + XB F2 = 0;
åFkY = 0, YA + YB F1 cos a + S sin 30 = 0;
åFkZ = 0, ZA + S cos 30 + F1 sin a P = 0;
åmX() = 0, S sin 30× AB + F1 cos a ×AB YA ×AB = 0;
åmY() = 0, S cos 30×BC F1 sina + XA×AB
F2 + M = 0;
åmZ() = 0, S sin 30 ×BC F1 cos a = 0.
Y , Y Z, = F1 cos a, = F1 sin a (. ). .
, , .
: XA = 7,8 H; YA = 2,6 H; ZA = 2,5 H; YB = 0 H; XB = 0,3 H; S = 5,2 H.
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, , .2.
(, Y'), .
1
xy x = f1(t), y = f2(t), x y , t (. 1, 1). (, , , t = 0). , t = 1 .
1
x = f1(t) | ||
4 cos (πt/6) | y = f2(t) 00 29 ( ) 2 . 1 | |
2 4cos (πt/6) | ||
2 cos (πt/6) 3 | ||
4 2t | = f2(t) 30 69 ( ) 3 . 1 | |
2 t | ||
2 t | ||
t 4 | ||
8sin (πt/6) 2 | y = f2(t) 70 99 ( ) 4 . 1 | |
2 sin (πt/6) | ||
2 4sin (πt/6) |
1
y = f2 (t) | |||
00 29 | 30 69 | 70 99 | |
12 sin (πt/6) | 2 t² + 2 | 4 cos (πt/6) 2 | |
4 6 cos (πt/3) | 8 sin(πt/4) | 14 16cos (πt/6) | |
3 sin² (πt/6) | (2 + t)² | 4 cos (πt/3) | |
9 sin (πt/6) 4 | 2 t³ | 10 cos (πt/6) | |
4 cos (πt/3) 2 | 2 + 2 cos(πt/4) | 4 cos (πt/6) | |
10 sin (πt/6) | 2 3t² | 8 12 cos (πt/3) | |
2 6 sin² (πt/6) | 2 2 sin(πt/4) | 2 cos (πt/6) | |
2 sin (πt/6) 2 | (t + 1)³ | 2 8 cos (πt/3) | |
8 cos (πt/3) + 5 | 2 t³ | 8 cos (πt/6) 4 | |
3 8sin ( πt/6) | 4 cos(πt/4) | 8 cos (πt/3) |
. 1 , ( ), , .
t = 1. ( ) :
cos 2α = 1 2sin2 α = 2cos2 α 1;
sin 2α = 2sin α × cos α.
1
: xy:
x = 2 cos + 3; y = 3 sin 1,
x, y , t .
: ; t = 1 , . .
t. , :
cos ; sin . . (. 1). , t = 1 : xt=1c = 1,59 ; yt=1c = 1,12 (. 1). : | |
. 1 |
Vx = ; Vy = ; V = ,
t = 1
Vx = 1,11 /c; Vy = 1,67 /c;
V = 2,0 /c.
:
; ;
; ; ; .
t = 1
a x = 0,87 /c2; a t = 0,6 /c2;
a y = 1,30 /c2; a n = 1,67 /c2;
a = 1,57 /c2; r = 2,38 .
(. . 1).
: V = 2,0 /; = 1,57 /2; t= 0,6 /2; n = 1,68 /2;
r = 2,38 .
2
j = j(t), . 2. j (. 2.02.9).
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. 2.0 | . 2.1 |
2.7, 2.8, 2.9 1 ( ). . 2.0, 2.2, 2.4, 2.5 , . 2.1, 2.3, 2.6 .
. 2.2 | . 2.3 |
. 2.4 | . 2.5 |
. 2.6 | . 2.7 |
. 2.8 | . 2.9 |
s = OM = s(t) (. 2). , s = .
2
j = j (t), | R, | s = s(t), | |
4 (t2 t) | 1,2 | R (4t2 2t3) | |
3t2 8t | 1,6 | R (2t2 t3) | |
6t3 12t2 | 1,0 | R (2t2 1) | |
t2 2t3 | 1,6 | R (2t4 3t2) | |
10t2 5t3 | 0,8 | R (3t t2) | |
2(t2 t) | 2,0 | R (t3 2t) | |
5t 4t2 | 1,2 | R (t3 2t2) | |
15t 3t3 | 0,8 | R (t 2t2) | |
2t3 4t | 1,0 | R (3t2 2t) | |
6t2 3t3 | 2,0 | R (t 2t2) |
t = 1.
. 2 , .
, t = 1 c , ( , ). , R, .
2. (. 2) j = j(t). φ . 2 . s = M = s(t); s .
: R = 0,5 ; φ = 2t2; s = = pR (φ , s , t ).
: Va a a t = 1 .
. 2
. , .
.
s = = pR . (1)
, A t = 1. (1) t = 1 , . . . 2 , .
:
, (2)
r = R . t = 1 c, , R = 0,5 ,
; /2; /2. (3)
V , s, , . . . 2.
. () φ = 2t2. ω ε :
ω = = 4t; ε = = 4.
t = 1
ω = 4 -1; ε = 4 -2. (4)
, ω ε φ (. . 2).
V :
KB = h = 2R R×cos 30 = 0,57 .
t = 1, (4),
V = ω × h = 4 × 0,57 = 2,28 /;
a = ε × h = 4 × 0,57 = 2,28 /2; (5)
a = ω2 × h = 42 × 0,57 = 9,12 /2.
. 2 ω : ( ), ( , ).
= 2 | V | |ω | sin α,
α , , . 2, α = 30.
(3) (4) t = 1
= 2 | V | | ω | sin 30 = 2 π/4 4 1/2 = 3,14 /2. (6)
, , 900 (. . 2).
. . = + , (. . 2), t = 1
V= = = 2,4 /.
.
= . (7)
xyz (. 2) , (7) , - . , , , yz.
(3), (5), (6), t = 1
x = + = 5,42 /2;
y = s 60 + s 30 = 0,74 /2;
z = - s 60 s 30 + = 7,27 /2.
= = 9,1 /2.
: V = 2,4 /; = 9,1 /2.
3
1, 2, 3, 4 , . . 3.3 3.8 3 . . 3.33.8 D .
: l 1 = 0,2 ; l 2 = 1,0 ; l 3 = 1,2 ; l 4 = 0,8 . R = 0,3 .
j1, j2, j3, j4 (. 3.03.9). . 3, 1 w1 VC .
. 3.0 | . 3.1 | |
. 3.2 | . 3.3 | |
V ω, . 3.
, φ1. ,
. 3.4 | . 3.5 | |
. 3.6 | . 3.7 | |
. 3.8 | . 3.9 | |
3
, | ||||||||
φ1 | φ 2 | φ 3 | φ 4 | ω1, -1 | VC, / | V | ω | |
, , , , , , , , , , | 2 3 2 4 2 3 2 4 2 3 2 4 2 3 2 4 2 3 2 4 |
w1 , VC .
. 3 , ( ) .
3. (. 3) 1, 2, 3, , .
: j1 = 90º; j2 =150º; j3 = 240º; j4 = 150º; l 1 = 1,0 ; l 2 = 0,9 ; l 3 = 1,0 ; = 2; VC = 4 /.
: VA, V w1, w2.
(. 3).
V. . V, - . VC = 4 /c , . , , , ; , ^ . , , ( ) , . , ( ). , ,
VC s 30 = V; V = VC s 30 = 4 = 3,5 /c.
. 3
VA. A . , , . , ^ . VB
.
= 2, ,
= 2V = 2×3,5 = 7 /c.
, , . , , () ; 1, , . . . ,
VB = ω11; V = ω11,
.
1 1. 1 , 30º 60º,
;
BP1 = A1 sin 30º = 1,2×0,5 = 0,6 .
/c.
w1:
.
w2:
.
: VA = 14,0 /c; V = 3,5 /c; w1 = 11,7 c-1; w2 = 7,8 c-1.
1
D, m, V0, , (. 1.01.9).
. 1.0 | . 1.1 |
. 1.2 | . 1.3 |
. 1.4 | . 1.5 |
. 1.6 | . 1.7 |
. 1.8 | . 1.9 |
, , , , . , , , . , , , Fx . 1. m, V0, Q, (l = ) t f .
1
m, | V0, / | Q, H | f | l, | τ, c | Fx, H | ||
2,4 | 0,2 | 1,5 | 4 sin (4t) | V1 | ||||
0,4 | 2,5 | 5 cos (4t) | x1 | |||||
0,3 | 6t | V1 | ||||||
1,8 | 0,3 | 2 cos (2t) | x1 | |||||
0,2 | 5 sin (2t) | V1 | ||||||
4,5 | 0,3 | 3t | x1 | |||||
0,1 | 2,5 | 6 cos (4t) | V1 | |||||
1,6 | 0,4 | 3 sin (4t) | x1 | |||||
4,8 | 0,2 | 4 cos (2t) | V1 | |||||
0,3 | 4 sin (2t) | x1 |
, = (t) .
. 1