-







































:

:

-3.

1.

. . 1 ( ), 1.

. 1

1.

P1, , × q, /
6,0 25,0 0,8

-3.

. , (. 2).

y

P1y P1

90

P1x C

Q M

RAy RBy

RAx RBx x

A B

. 2.

P Px Py.


P1y P1

a

P1x a a

6

. 3.

P1x = P1×sin(a),

P1y = P1×cos(a).

a = arctg(1,5/6) = arctg(0,25) = 14.

P1x = P1×sin(a) = P1×sin(14) = 6×0,24 = 1,44 (),

P1y = P1×cos(a) = P1×cos(14) = 6×0,97 = 5,82 ().

Q = q×3,5 = 0,8×3,5 = 2,8 ().

-3. .

:

(1)

(2)

(3)

3 4 , .

, (.4):


y

P1y P1

90

P1x C

RCx

Q RCy

RAy

RAx x

A

. 4.

:

(4)

(5)

-3.

(6)

, (.5):


y

 

R`Cy

R`Cx

C

M

RBy

RBx x

B

.5.

:

(7)

(8)

(9)

RCx = R`Cx, RCy = R`Cy.

, 4 (1), (2), (6) (9) 4 .

(9)

(1)

-3.

(6)

(2)

:

RCx = -RBx = 12,5 ,

RCy = -RBy = 0,07 .

RBx RBy , RBx RBy .4.

,


-3.



.1.

 


: Q = 2, G = 20, a = 20, b = 30,

c = 10 R =15, r =5.

:

, RAy=RBy=RDy=0


:

*15-q*5=0, , =(q*5)/15

-qx*20+P*60-RBx*80, RBx=(qx*20-P*60)/80

-qx*20-G*(20+30)+RBz*(20+30+30) RBz= (qx*20+G*50)/80

-Raz*80+qz*60+G*30=0 Raz= (qz*60+G*30)/80

Rax*80+ qx*60-P*30=0 Rax=-( qx*60-P*30)/80

qx=Q*cos45; qz=Q*sin45

Ra= RB=

Raz

Rax

Ra

RBz

RBx

RB


.

1.

; . 1. 1, , , 1 , s.

: m1, m2, m3, m4 1, 2, 3, 4; b - ; f .

1. . .


. 1


1.

m1, m2, m3, m4, b, f s,
m 4m 0,2m 4m/3 60 0,10 2

.

:

(1)

T0 T ; - , ; - .

, , ,

, 0=0.

, (1) :

(2)

(.2) 1, 2, 3 4:

= 1 + 2 + 3 + 4. (3)


2

1

w2

VA

V3

3 b V1

A C3 CV

w3

V4

4

. 2.

-10

1, ,

(4)

2, ,

, (5)


J2x 2 :

, (6)

w2 2:

. (7)

(6) (7) (5) 2 :

. (8)

3, :

, (9)

VC3 3 3, J3x 3 :

, (10)

w3 3.

, V.

, (11)

. (12)

(10), (11) (12) (9), :

. (13)

4, ,

, (14)

V4 = VC3 = V1/2:

. (15)

(3) (4), (8), (13), (15):

(3), :

. (16)

, , (. 3).

2

1

N1

 

FTP

3 b

C3

P3 P1

4

P4

. 2.

:

(17)

:


(18)

, 1:

(19)

, 1:

(20)

, (17) (20):

.

, :

. (21)

(2) , (16) (21):

,

/.

-10

-19. .

1.

, . . . .

1. , , .



. 1

1.

G1,

G2,

G3,

R/r

i2x

G G 3G 2

.

. , . , 1 .

: - 1, - 2 - 3 (. 2).


a3


M3Ԡ 2 e2 M3

3 e3 dj3

dj2

ds3

3

G3

1

G2 1

a1

ds3

G1

. 2.

. 1, :

.

2, e2, ,


3, ,

,

- 3, ,

,

e3 3, J3 3 :

.

(. 2). :

, (1)

dj2 dj3 2 3.

, G1 = G2 = G = mg, G3 = 3G = 3mg

:

(2)


, (1), (2), , , :

dj2 = dj3 = ds1/R = ds1/2r;

ds3 = dj2r = ds1/2; (3)

e2 = e3 = a1/2r; a3 = a1/2.

(2) (3) (1), m ds1,

,

3 = a1/2 = 1,87 /2.


3

M3

3 e3 dj3 2-3

ds3

G3

. 3.

1

1-2

1

ds1

G1

. 4.

2-3 3 T2-3 (. 3).

:

,


1-2 1 T1-2 (. 4).

, :

-3. .

1.

. 1

. . 1, 1.

1.

,

w, -1

e, -2

r

40

15

8

2

2


.

.

:

VA = w×OA = 2×40 = 80 /.

. V .

w = VA/r = 80/15 = 5,33 c-1

:

VB = w×V;

V = w×V,

V = r×= 15×1,41 = 21,2 ,

V = .

,

VB = w×V = 5,33×21,2 = 113 /;

V = w×V = 5,33×21,4 = 114,1 /.

BCV, - CCV .


VA

VC

w

O wOA CV A VB

45

C

r

B

. 2

-3

 

.

:

;

/2;

/2.

. e.

:


.

:

/2.

:

,

-2,

/2.

. eK.

:

/2;

/2;

/2.


:

.

:

/2.

-3

:

/2.

. eK.

:

/2.


y

aC aCy

aBy

aB

aAt

eOA eK aACt

x O aAn A

aACn

C

aCx 45

aABn

aBx B aABt

. 3

-3

K-1. .

1.

t = t1(c) , , , , . 1.

1.

t1(c)

x = x(t), y = y(t),

-2t2+3

-5t

0,5

K-1

.

:

x = -2t2 + 3; y = -5t; (1)

t1 = 0,5

(1) . , t .

25x + 2y2 = 75 (2)

.

:

Vx = x = -4t /; Vy = y = -5 /.

. (3)

ax = x = -4 /2; ay = y = 0.

/2.

(3)

t = 0,5 c

x = -2×0,52 + 3 = 2,5 , y = -5×0.5 = -2,5 .

Vx = -4×0,5 =-2 /, Vy = -5 /, V = 5,38 /.

ax = -4 /2, ay = 0, a = 4 /2

/2

K-1

at = 1,487 /2


+ dV/dt , , , .

:

/2.

, t = 0,5 :

.

(2), (. 1) . , . , .



. 1

-2. .

1.

:


, , 1. .

:

1 :

(1).

, :

(2).

(3).

1:

(4).

(2) (3) (1) (4), :

1:

(5).

1:

(6).

1:

, .

(7).

(6) :

3:

, , :


: .. -045 rus

: ..

61 16

: ,

Sr=OM=20 sin t

t1=1/3 c

a=20 c

:

D Sr=OM

t=1/3 c

Sr=20 sin /3 =17.32 c

V=Vr+Ve

Vr=| Vr |

Vr=dSr/dt=20 cos t

t=1/3 c

Vr=10 =31.41 c/

Vr , Vr Sr

Ve=Re

R= Sr2+a2 =26.46

e=|e| e=de/dt=1-t c-1

t=1/3

e= 0.67 c-1

e , D z . e .

Ve=17.73 /

Ve .

V=Vr2+ Ve2 - 2VrVeos

cos = a/R = 0.76

V=21.32 c/

. , ,

W=Wr+We+Wc

W=Wr+Wrn+We +We+Wc

Wr= d2Sr/dt2 =-202 sin t

t=1/3 c

Wr= -170.77 c/2

Wr=170.77 c/2

- , Wr Sr

Wrn=Vr2/=0 (=∞)

We=Re

e= d2e/dt2=-1 c-2

We= -26.46 c/2

e e D, e e .

We=R e2=11.88 c/2

We L

Wc=2e x Vr

Wc=2eVr sin(e Vr)

sin(e Vr)=1

Wc=2eVr=48.09 c/2

Wx= We cos - We cos(90-) - Wr=

Wy= Wc-We sin - We sin(90-) =

W= Wx2+ Wy2=

e, c-1

, /

e,c-2

, /2

Vr

Ve

V

Wr

Wrn

We

We

Wc

Wx

Wy

W
0.67 31.41 17.73 21.32 -1 -170.77 0 -26.46 11.88 48.09

2011 , .