W - .
, , , . , δ , 0 , dW , . .
δ = dW.
= m ,
= m .
,
δA = m d = mυdυ = dW ,
.
, m, υ,
W = mυ 2/2. (3.5)
(3.4) , , . . . (3.4) , , . , , , , . , .
Wp - , .
(, , ), , , , , , . , , , - . , , , ; .
, , Wp. ( ) , , :
δA = dWp. (3.6)
δA (3.6)
= - dWp. (3.7)
, Wp (), (3.7) .
(3.7)
Wp = + C,
- , . . . , , , , . - ( ), .
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Fx = - , Fy = - , Fz = - ,
= - grad Wp, (3.8)
grad Wp = + + (3.9)
(, , - ). , (3.9), Wp.
grad Wp . (-) , -:
+ + . (3.10)
Wp . , m, h ,
Wp = mgh, (3.11)
h , Wp = 0. (3.11) , h .
, ( !). , , , ( h '), Wp = - mgh '.
(). , F x F x , . .
F x = - F x = kx.
δA, F x dx,
δA = F x dx = kxdx,
A = = kx 2/2
. ,
Wp = kx 2/2. (3.12)
, , . .
- :
W = W + Wp, (3.13)
. . .
- . .., , . .
(m 1 + m 2 ++ mn ) = + + + + + ++ .
m 1, m 2,..., m n, , ,..., . , ,..., - , , a , ,..., - , . , , ; , , , ,..., . u << c :
m 1 = + + ,
m 1 = + + ,
mn = + + .
, dt , , ,..., . , , = dt, :
|
|
m 1 ,
m 2 ,
mn .
,
- = (3.14)
(3.14)
= = dW,
dW . , , . . dWp (. (3.6).
(3.11) , . ,
d (W + Wp) = δ. (3.15)
1 - 2
,
. . , . , (3.15) ,
d (W + Wp) = 0,
W + Wp = W = const, (3.16)
. . . (3.16) : , , , . . .
, ( ), . : .
, . . . , , .
- , () . ( ) . , .
. , . , , . - , , .
, , , . , . . , , . - .