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:

































 

 

 

 


1. . 4




 

m1, m2 m3. m1.

 

; ; ;

 

xc = (m2x + m3x)/(m1 + m2 + m3); yc = (m3y)/(m1 + m2 + m3)

:

 

m1 m2, .

m1xA = m2(l3 xA),

l3 = x2; l22 = x23 + y23; l221 = (x2 - x3)2 + (y2 y3)2.

Ðm3m2 = a..

l21 = l22 + l23 + 2l2l3cosa,

, cosa = -(l22 + l23 l21)/ 2l2l3.

m3xA = d:

d2 = l22 + x2A 2l2xAcosa

( ) d. S = m3C m3

m3S = (m1 + m2)(d S).

S = ((m1 + m2)/m1 + m2 + m3))d.

( ) .

( )

38

û (. .). .

 

 

, , (. .).

 

 

 

2 = f + d/2; Yc1 = b/2; Xc1 = f/2; Yc2 = a/2

:

; ; .

ρ, S h:

m = ρSh; m1 = ρS1h; m2 = ρS2 h; S1 = bf; S2 = ad.

:

rcx = ((bf2/2) + ad (f + d/2))/(bf + ad);

rcy = ((b f/2) + a d /2))/(bf + ad).

39

, , R c a, . (..).

 

 

,

m,

.

, ,

. :

; ;

; .

 

40

m . . = l2 , BC = l1. . m1 m2.

 

 

:

1)

2) :

; ; ; ; ;

.

 

41

. .

` p1= (2t + 3)`i + 3t2`j + 7`k; `p2 = - 2t`i + t`j.

? - ? , ?

 

 

, :

` P = `1+ `2 = 3`i+ (3t2 + t)`j +7`k

, .

Z , Z .

,

.

 

42

m L. F, . ) ? ) ?

.

) v0 , θ0 .

:

F = mV0, FL/2 = Iθ′0, θ′0 = FL/2I,

I = (1/3)m(L/2)2 , .

t ,

θ′0t = FL/2I, t = 2π/θ′0.

,

S = V0t = F/m · 2π /θ′0.

θ′0 = FL/2I,

S = F/m · πmL2/ 3FL = πL/3.

T = m/2·V2o = ½ m·F2/m2 = ½F2/m.

T =½Iθ′2o = ½ I (LF/2I)2 = 3/2 F2/m.

:

T = T + T = 2F2/m.

43

h , , .., . , , K ( ). , . K.

 

.

n ,

K = V2/ V1 = h2/h11/2 = h3/h21/2 = = hn+1/hn.

h2 = k2h1; h3 = k2h2 = k4h1; h4 = k2h3 = k6h1; h5 = k2h4 = k8h1;

hn+1 = k2nh1;

h = h1 +2h2 + 2h3+ 2h4 + = h1 + 2h1(k2 + k4 + k6+) =

= h1(1+2(k2/(1 - k2))) = h(1+k2/(1- k2)).

44

, , , , . , , , , . , , , .. .

 

.

 

, , OO' (. 1). ( F ( , F (. 1). , , (. 1). , , (. 1, ), , . , , O, ( F ).

. 1.

, l . OO'

(1)

 

, , ,

(2)

 

m- , v0 - . a - ,

(3)

 

(4)

 

C ( ) - , , , .

:

 

. l (4) . , , , .

1. L " " ( ) , ,

.

2. (. 2) , c ,

 

,

. , . , .

. 2.

, , , .

 

45

, = 300 , m = 8 . ... η , . , .

 

.

: mu0 = (m + M) u, m , u0 ; , u - ( ). - . :

;

Q , . , .

...

 

 





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