: FPM-13,
( ).
: -
. "".
, .
. , m, l. , m, l. a , :
M = - mgl sinα. (1)
:
(2)
da/dt - ; J = ml2 - .
dL/dt = M . :
(3)
(1) :
(4)
, sin a ~ a. :
(5)
σo to = 0, : α=αo cos(ωt); ω=(g/l)1/2 .
, . , , . 1 , 2 , 1 - . 1 , 2 .. , .
. α2 > α1 1 (1) g (.1), :
k - , ε = lo/l, l o - .
.1
, 2 :
(7)
(6) (7), , :
(8)
(9)
α2 α1 - ,
(10)
(11)
. , , (10) (11). :
(12)
(10) (11) :
ml d2(α1 - α2)/dt2 = (- mg - 2kε2l)(α1 - α2). (13)
, "" . ,
. (12), , (α1 + α2) - t = 0 α1o α2o, 2- :
|
|
α1 + α2 = (α1o + α2o) cos(ω+t), (14)
w+ = (g/l)1/2
. 1 2, . (13) :
α1 - α2 = (α1o - α2o) cos(ω-t), (15)
ω- = (g/l + 2ε2k/m)1/2 .
, . (14) (15), :
(16)
(14) (15), :
(17)
, a1o = a1o,
(18)
t = 0, α1o = -α2o, , :
(19)
. - , . , . , α 2o = 0,
(20)
(21)
:
cos A + cos B = 2 αcos[(A + B)/2] cos[(A - B)/2], (22)
cos A - cos B = -2 sin[(A + B)/2] sin[(A - B)/2], (23)
(20) (21) :
(24) (25)
α1 α2 .2
.2
, t = 0 α 2o=0; α 2 , α 1 ,
, 1/2(w- - w+)t = π/2 a1 , α 2 , , . , "+", , , , . ( "-") , . , , .
, . , a1 , a2 ..
. t = 0 1,
, 1 2
, 2. 1 2 :
- (w- - w+)t = π
, , :
|
|
w=2π/t=w--w+ (26)
.
, , , , w1 w2.
( , , ), .
, , "".
, , . , , . " ":
w1 - 1- ,
w2 - 2- .
, w1 .
w2 > w1. , w2. .
, "" .
.3.
.
"" ( ) .
.4.
.
:
- , , ( ).
- , , ,
- <>,
- ,
- <>,
- 10 <>,
- ,
- .
, , .
:
- , ,
- ,
- ,
- 20 .
- , ,
- ,
- ,
- .
.
, w- w+. .
1. , (`10). t, n , w+ = 2π n/t . .
2. 1 w- - .
|
|
3. 1, 2 ( ), , .
w= 2π n/t .
4. 3 w w, w = w- - w+.
5. (18) (19). : m - , k - - ; l 0, l ,ε - . , (.. 1 2).
5. FPM-13, w- w+ .
s1 :
: wx+ - , ,
w1+ - .
s2.
8% . FPM-13, I.
10.
.
- 2
- 0.02%
- 8%
- 8%
.
- 500
- +30
- 3
- 2
- :
030I-0098-0I 0.1
030I-0098-02 0.15
030I-0098-03 0.2
- :
083I-009I-0I 5 /
083I-009I-02 7 /
- 99
- 20
- 1-99999
1. ?
2. ?
3. ?
4. ?
5. ?
6. ?