Лебединская. Динамика материальной точки

	, (13.5) (13.4), 2 (
					l .
				μc = tgβ					(13.6)
					S
	+				l S ,
	:
	α0 αn . '. (13.2) , 2 .
	: D,
	F, -4 - α0 , -
				E, -4 -
				- αn .			.	13.2	,
					l = OE′ − OF′.		OE′	OF′
	αn	α0		L
				-
			L	. %, EOE′
				, OE′ = Lcosαn , -
	F'		F	FOF′ – OF′ = Lcosα0 . ,
	'	E	l		l = L(cosαo − cosαn ) .
				0 , * *
	D			cosα =1− α2 / 2		( .
				),		l
	'. 13.2				l = L / 2(α02 − αn2 ) .				(13.7)
	,S, , , -4
	. 8 * ,
	4A. 8 n			S = 4nA.
	* #0,
	DF, An,			DE, 2
	. . 13.2 , #0 ≈ α0L, An ≈ αnL (
	*), ,
	L(α0 + αn)/2. ,

S = 2nL(α0 + αn ) .

(13.8)

, (13.7) (13.8) (13.6),

2 (

μc =	α0 −αn tgβ .	(13.9)
	4n

#

* * - ,

, * . %

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- . /

.

, - , -4

( ( , ),

4 ( . 13.3).

1 2 ( μk

- (

F ) M - F

&	Q	Qn
R
F
	k		F
'. 13.3

μ	=	M	.	(13.10)
		F

, ( *

(. -

, -4

* Q ,

F , -4

*. !-4 Q , -

* Qn ,

F , (

), -4

F . ! -

4 ( , -

. ,

4 . ! Qn F - ,

- 4.

0 ( ,

. - F ,

- k,

-				,
R. + ,
	F R = F k ,				(13.11)
		F R
	k =		.		(13.12)
		F
!	(13.12) (13.10), * ,			μk = k	(
F R = M ).	+ ,
, , .

74

/ F / F , * 4 (13.12),

(13.9). , (13.9) (13.12), 2 (

μk = k = tgβ α0 − αn R .	(13.13)
4n

2 (

, 2 ( . 2 ,

4 * . ", *

* , *

, n αn

α0.

' R: – 10,2 ; - – 10,3 ;

– 10 .

( ! * ! '* # %

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-4 **2: 1±3 ± , , 4 ± ±(, 5 ± :

, 6±8 ± , * .

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* : 1 ±

2 ( 4- ; 2 ±

2 ( 4- ,

. , :

75

1)4

* ,

;

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, 2 4

* (

,

4- * ;

3), *

4 * ±(.

91

# & !422 3 #!&).

1.& 4 :*(* )

γ 1±5º, 2 β , * 4 : -

, β = 90° − γ .

2./ α0 8±11°.

3./ , n ,

αn . / . & ( -

*, (180 ° = π ).

4.2 ( μc 4- (13.9),

n αn .

5. . ** .

2 ( .

6.( ,

*-, -4 - . %

* . 1±6.

7.! 2 ( .

8.' ( 1

5

γ

β

α0

αn

n1

n2

n3

<n>

μc

(

1

2

9. .

92

# & !422 3 #

1.& 4 :* γ

30±55º ( - ), 2 β , * 4 -

β = 90° − γ .

76

2./ α0 = 5±10° ( -

) : , *γ α0 .

3./ n

αn . , . & ( -

*, * (180° = π ).

- : n, - * αn .

4., (13.13) 2 ( k 4-

αn n.

5. . ** β .

6.2 ( (.

7.4( ,

*-. , . 1±6. !

2 ( .

8.' (

5

γ

β

α0

αn

n1

n2

n3

<n>

kc

(

1

2

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1.1 4- - ?

2.9 ?

3.9 2 ( ?

4.9 ? 9

?

5.9 , n ?

6.9 ( 2 (,

n ?

7.8 *2 -4 .

8./ 2 ( ?

9., .

# (#

1.! . . 1 . +. 1, ± .: ,1989. !. 56±79.

2.+ +. . 1 . ± .: . ., 2001. !. 14±27.

77

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00 9

+ : 6

7 :

9 &) # ! ,: 1) (

* (; 2)

( * 4 (*

); 3) . +# !#, # & . !: , ,

, (.

! ! , ! #- . & , ! #3

4

( . 14.1). ,

* * ( , (

* , - 4&& ( .14.1). / , 4-4 -

,

M = Iε ,

(14.1)

M ± -4 **

, I ± ( 4-

r dm.

r . dm

, ε ± .

( 4

(+.10) (+. 11):

n
I = miri	2	,
i=1
I = dmr 2 ,		(14.2)
v

mi – 27 ,

4

,dm – 2 , V –i

'. 14.1 7 . , -

* , – * .

(14.2) , (

4. /, 4

. * - ,

! ! ,* ! * #- . ! 4 – 2 ,

( * ) *

.

9 , , -

, 4- * m , *

L ( . 14.2). ! -

%, -4 ( , &&,

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( . 14.2 ). , 4 ² – ²

( - F1 F2 . ,

4, F1 F2

- , 4

, . 9

,

f1 f2 . + ,

. 0 , 4

.

- , .

0 4 * ( ² –

² 2 - ( .14.2 ), , -

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, , - .

01

01

m

f1

F

1

L

g

F2

g

L

F1

F2

m

f2

02

02

'. 14.2

6 , , – . +

, , 2² ², *

. 1,

, 2 4

. + , (

* ) * ,

- 4.

+ . + -

, 4-

, * 4 ( ( ( , (

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- "& ,* ! * #3. % 2

79

(	.				, (
- X, Y, Z ( . 14.3),
(* .
% * * (,					, *
		′		′	( * * &
	Z	1	2		* * & ( . 2 Z),
	B′	. F′	C′		- ( !% ,*. +
B		C			,
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2	1				.
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4		* *
* , * , 4
* .
, , (
. % , 4-4
- , - 4,
4- - (.						/ -
4 - ( ,
2 4-4 *							- ,
(-4 .

( ! * ! '* # %

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( I0 (14.2).			,
I0 =	1	m(a2 + b2 ) ,	(14.3)
12

m – , a b – ,

4 ( ). 0 ( , * 4

( , (

, * 4 ( ,

3 (+. 12).

80

* * ( -

, 4 - ) (

- . 4 – *

.

( . 14.4)

– 2; – 3,

* 4- ; – 6, -4

(

). %

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4- - ,

- 8 4- 9.

'. 14.4

1 ( . 1.3), *

(

	T = 2π		I		,	(14.4)
			D
	T – *

4, I – ( 2 , D –

, ( ).

81

0 , ,

, (

I = DT 2 .	(14.5)
4π2

4 * (

- - ( , ,

-4 , -

- - ,

, (14.4),

D =	4π2I	0	.	(14.6)
	T 2

, 2 ( -*

* 4.

+!# ! , ! ! ,

1., –

( ).

2.' (14.3) (

* * ( ( -

) I0.

3.8 3 ,

,

( . 2. % -

9.

4./ .

t, n (15–20)

* . / * . ,

- , ,

-, T = t /n .

5.8 * ( I0

4, (14.6) .

6.' (

5 m a b I0 n

t <t > <T0 > <D >

1

2

3

7., ,

4 ( *). 6

- , -4 * .

8./ *

, . 4. , -

82