, , 1687 . ( ) . , .
: () , .
. .
, . , , , . , , - . .
, () ( , ). , , , , , ( ), , .
, , . ., , . , ( ).
, , ( ) ( ) . , ( , 10-12 ).
, , . , . . ( ), , . . ( ). , . , , , .
, () .
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, , , , :
a~F (m=const). (6.1)
, :
~ 1 / (F= const). (6.2)
(6.1) (6.2) , ,
a = kF/m. (6.3)
(6.3) : , (), , ().
k = 1.
a = F /m,
F = m a = md v /dt (6.4)
, () , (6.4) :
F =(d/dt)(m v). (6.5)
p = m v, (6.6)
, ( ) .
(6.6) (6.5),
F =d p /dt (6.7)
: . (6.7) .
(): 1 , 1 1 /2 :
1 =1 /2.
. . , ( ) (. (6.3)) . ( ), , (6.7).
: , , . , , . , . 10 F = m a : Ft ( ) F n ( ).
t=dv/dt n=v 2 /R, v=Rw, :
, , , F
() : () ; , , , , :
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F 12=- F 2I, (7.1)
F 12 , ; F 21 , . (), .
: , , , . , , . , . , . , .
. , .
, . : , , .
, , , . ,
. . , .
() ( ) . , . , , , , .
, , . . (), . ( ) ( ~0,1 ).
. ; .
(. 11), F.
, F F . . (16631705) . (17361806) : F N , :
F =fN,
f , .
. (. 12), F F . , ( )
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F=F
, a0, .
. . . (. 1902)
F = f (N + SP0),
p0 , , ; S ; f .
. , . .
, . ( 10 ), , , . , .
( ..). :
F = f kN/r, (8.1)
r ; fk , dimfk=L. (8.1) , .
.
. (), , . . , , . ,
, ( ). , , , , , , , . . .
, n , 1, m 2,..., n v 1, v 2,..., v n. F '1, F '2,..., F 'n , , a f 1, f 2,..., F n . n :
d/dt(m1v1)= F '1+ F 1,
d/dt(m2v2)= F' 2+ F 2,
d/dt)mn v n)= F 'n+ F n.
,
d/dt (m1 v 1+m2 v 2+... + mn v n) = F '1+ F '2+...+ F ' n + F 1+ F 2+...+ F n.
,
d/dt(m1v1+m2v2 +... + mnvn)= F 1 + F 2+...+ F n,
dp/dt= F 1+ F 2+...+ F n, (9.1)
. , , .
( )
: , . . .
, . , ( ). , . . .
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. , , , .
, (9.1), , .
- . ( ) , . -
mi ri - i- ; n ;
.
, p i =mi v i,
,
p = m v c, (9.2)
. . .
(9.2) (9.1),
mdvc/dt= F 1+ F 2+...+ F n, (9.3)
. . , , , . (9.3) .
(9.2) , , .
, , , . .
. t , v, dt dm
- dm, v +d v. dt
dp = [(m-dm) (v +d v)+dm (v + u)]- m v,
.
d p = md v + u dm
(, dm dv ).
, d p = F dt,
F dt = m d v + u dm,
md v /dt= F - u dm/dt. (10.1)
- u dm/dt
at
F p. u v, , v, .
,
m a = F + F p, (10.2)
. . (18591935).
1881 . . . (18541881). .. (1857 1935) 1903 . ,
. .
(10.1) , . F = 0 , ( ),
dv dm dv/dt=-udm/dt.
. , , = uln m0. ,
v = uln(m0/m). (10.3)
. , : 1) , ; 2) , .
(10.2) (10.3) , . . , v u .
11. , ,
. : , , , . (, ), (, ). , , ( ) , , .
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, .
, .
F, , Fs (Fs = Fcosa), :
A = Fss = Fs cosa. (11.1)
, , (11.1) . , , dr, F ,
. F d r
d = F d r = F cosa ds=Fsds,
F d r; ds = |d r | ; Fs F d r (. 13).
1 2 .
Fs s 1 2. (. 14), . , , , F=const a=const,
s (. (11.1)).
(11.1) , a<p/2 , F s
v (. . 13). a>p/2, . a = p/2 ( ) .
(): 1 , 1 1 (1 = 1 ͕).
, :
N=da/dt. (11.3)
dt F F d r, , ,
N= F d r /dt= Fv
. . , ; N .
(): 1 , 1 1 (1 = 1 /).
.
F, , , . , dA F , 0 v, dT , . .
dA= dT.
F =md v /dt
d r,
F d r =m(d v /dt)dr=dA
, , v,
= v2/2. (12.1)
(12.1) , , . . .
(12.1) , , . , , , , . , .