, - . , . . , () , .
(. (133.10)), I = j d S S, L.
(138.4)
(138.4) , .
139.
, , , .
:
1. (. 137) ( Q), ( B), = Q + B. Q (. (137.3)), B (137.2),
, , .
2. (. (138.4)):
, ( ), .
3. D (. (89.3)):
(139.1)
r, (139.1)
4. (. (120.3)):
, :
, , ( ):
e 0 m 0 , e m , g .
, , , ( ), . . , , .
(E= const B= const )
|
|
.. , . , .
( ):
, . , , .
, . , , . . (. 90, 134):
( , , ).
. , . , , , . . .
, , , , . (. 138), , . , ( ) = 3×108 /. , . . (18571894), , . , .
, .
, , , . . . : , , , D, .
|
|
, . Ta, , , , , , , . , , , , .
, , , , , .
4
18
140.
, . , , . . , . , , . . . , . . (18421919), . . , - . . (18661912). . . (18791944) .
( ), (, ). , (). : 1) , , , ; 2) (, ) . s
(140.1)
, , w 0 () , j t= 0, (w 0 t + j) t. . +1 1, s + .
, , , , 2 p, . .
(140.2)
, ,
(140.3)
. . , , . (140.2) (140.3),
|
|
(): 1 , 1 .
s:
(140.4)
(140.5)
. . . (140.4) (140.5) w 0 w . (140.4) (140.1) p/ 2, (140.5) (140.1) p. , , s= 0, d s/ d t ; s , d2 s/ d t 2 (. 198).
(140.5)
(140.6)
( s = A cos (w 0 t + j)). (140.1).
, . , , j, , , (. 199). w 0, , +, s=A cos (w 0 t + j). , , j, , w 0 .
, . . ,
(140.7)
. (140.1) :
(140.8)
(140.8)
. Re (140.8)
, s , .
141.
, . t , (140.1), s=x:
(141.1)
(140.4) (140.5), v
(141.2)
F=ma, , (141.1) (1412)
, ( ).
, ,
(141.3)
(141.4)
, F,
(141.5)
(141.6)
(141.3) (141.5), :
(141.7)
, , .
|
|
(141.4) (141.6) , 2w0, . . , . . 200 x, T . ásin2añ = ácos2añ = 1/2, (141.3), (141.5) (14l.7) , á T ñ = áñ = ½ E.
142. . ,
, , (140.6);
(142.1)
. , , ( , ; . 146).
1. , F = kx, k .
(142.1) (140.1) , = s (w0 t + j)
(142.2)
(142.3)
(142.3) , (. (21.3)), . . . , (141.5) (142.2),
2. , , , (. 201).
a, (18.3) M
(142.4)
J , , l , Ft= mg sina mga. ( , Ft a ; sin a a , .. ). (142.4)
(142.5)
(142.1), (140.1) :
(142.6)
(142.6) , w0 (. (142.5))
(142.7)
L=J/ (ml) .
' , L, (. 201). (16.1),
. . ' . ' : ,
, .
3. , , , . , .
(142.8)
l .
, , , , (142.8) (1417),
(142.9)
(142.7) (142.9), , L l , . , , .
143.
, (, ) . , L, R.
|
|
, (R 0). , Q. t= 0 (. 202, ) , Q 2 (. (95.4)). , , I. , ( .
R 0, , ,
. t= ¼ T, , , ( , ) (. 202, ). ; , , , ( ) , . , , , , (. 202, ). (. 202, ) t= (. 202, ). . , , .. () Q , U I, . , , .
(. 202 ), . (Q 2 / (2 C)) , (LQ 2 / 2) , . L , , .
, , L, R,
IR , Uc=Q/C , ... , ( ... ). ,
(143.1)
(143.1) L Q :
(143.2)
... , (. 140). R= 0, . (143.2) .
(142.1) (140.1) , Q
(143.3)
Q m w0, , . .
(143.4)
(143.5)
(143.5) . . (. (140.4))
(143.6)
I m = w0 Q m .
(143.7)
U m= Q m/ C .
(143.3) (143.6) , I Q p/2, .., , ( (. (143.7)) , .
144. .
, , , .
(. 140). (. 203). Tax A1 2 w0, (j 2 j 1) . ,
(144.1)
(144.1) j
(144.2)
, , , , . (j 2 j 1) .
(144.2) (j 2 j 1):
1) j 2 j 1 = 2 mp (= 0, 1, 2,...), A=A 1 +A 2, . . ;
2) j 2 j 1 = (2 m +1) p (= 0, 1, 2,...), A= | A 1 A 2|, . . .
, . . , , .
, w w +D w, D w << w. , :
, D w /2<< w,
(144.3)
(144.3) w, , :
(144.4)
( ), . . :
(144.3) . 204, (144.3), (144.4) .
( (. 158)) . , . .
s = f (t) , , , w0:
(144.5)
(144.5) , . * , w0, 2w0, 3w0,..., ( ), , . . .
* . (17681830) .
145.
w, . , ,
(145.1)
a , . (145.1) t.
cos wt / sin wt , , :
(145.2)
, .
a. , :
1) a = mp (m =0, 1, 2,...).
(145.3)
(. 205, ), (. 205, ). w , (145.3), j= arctg . ;
2) a = (2 m+ 1) (m =0, 1, 2,...).
(145.4)
, , (. 206). , =, (145.4) . , .
, . , , , . * , . . 207 ( ) ( ; j).
* . (18221880) .
, . . , .
146. ( ) .
, - . , .
. , , , . , , ( ), , , , . , , , .
(146.1)
s , , d=const , w 0 , . . d = 0 ( ) .
(146.1)
(146.2)
u=u(t). (146.2) (146.1)
(146.3)
(146.3) . , :
(146.4)
( ()>0, ). (142.1) ü+w 2 =0, = 0cos(wt+j)(. (140.1)). , (146.1) ()
(146.5)
(146.6)
, 0 . (146.5) . 208 , (146.6) . t=1/d, , .
, , , . , ( ) (. 208). (146.4)
A(t) (t + ) , , ,
,
(146.7)
; N e , . .
Q,
(146.8)
( (), T 0).
(146.8) , N e, .
, , ( ) ( ).
1. . (. 142) , F= kx, , . .
r ;
(146.9)
w 0= (. (142.2)) ,
(146.10)
(146.1) :
(146.1) (146.5) ,
(. (146.4)).
, (146.8) (146.10), Q= /r.
2. . ( R¹ 0) (. (143.2))
(143.4)
(146.11)
(143.2) (146.1)
(146.1) (146.5) ,
(146.12)
, (146.4),
(146.13)
w 0 (. (143.4)). R= 0 (146.13) (143.4).
(146.7), (. (146.8))
(146.14)
, d d=w 0 , . . . , t ¥. . .
. . , , .
, , (. 147), . , ( ).
. . , , , . , .
, , . .
147. ( )
, . - X (t), :
, X (t)
(147.1)
(147.1) (146.9)
(142.2) (146.10),
(147.2)
, X (t) ...
(147.3)
(143.2) (147.3)
(143.4) (146.11),
(147.4)
, ..., .
(147.2) (147.4)
(147.5)
(x 0 F 0 /m, U m/ L).
(147.5) (146.5) (146.1) . (. 140). (147.5) 0 :
(147.6)
s (147.6),
(147.7)
, t . , h=w. , (147.7) s 0
:
(147.8)
(147.9)
, (147.6)
, (147.5),
(147.10)
j (147.8) (147.9).
, (147.5)
(147.11)
(147.5)
(147.12)
(. (146.5)) (147.11). (147.12) ( ) , , (147.8). . 209. , w ; , (147.8) (147.9), w.
(147.10), (147.8) (147.9) , , (. (143.4)) (. (146.11)):
(147.13)
Q=Q mcos(wta) t, :
(147.14)
(147.15)
(147.14)
j = a p /2 (. (147.3)). (147.13)
(147.16)
(147.16) , (j> 0), wL> 1/(w ), (j< 0), wL< 1/(w ).
(147.15) (147.16) . 149 .
148. ( ).
w. , () , (Q) .
(147.8) , () . w , , () , (147.8), , , . w , , w :
w =0, , . ,
(148.1)
( ) , , ( ). w w 0 . (148.1) (147.8),
(148.2)
. 210 d. (148.1) (148.2) , d, . w 0, (. (147.8)) , , , . , U m / (L ). w ¥, . .
(148.2) , () ()
Q (. (146.8)), . , Q : Q, .
. 211 (). ()
w =w 0 , . . d, . (142.2), (146.10) (143.4), (146.11), ,