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 , . , .
...