nblib.library.kz - /elib/library.kz/jurnal/v_2006_6/

22

2006. 6

. .

. -

,

, ,

- [1]

2 2 2

1 3

2 2 sin

U r . (1)

(1) -

- :

2 2 2 2

2

2 2

2 2 2 2

cos 3 sin ,

cos 0,

cos sin 3 sin cos , d

dt d dt d dt

(2)

–

; – .

(2)

2 2 2

2 2 2 2 2 2

1 1

cos 2 3 sin

F h

2 2 2 2 2 2

1

cos 3 sin

1

F h ,

2 2

2

cos

2

F & h . (3) (2)

2 3

0

, 0

0

, . (4)

(4) ,

0

x

1

, x

2

, x

3

, x

4

, x

5

0

x

1

, x

2

, x

3

, x

4

, x

5

. (5)

(5), (3):

2 2 2

1 2 0 1 4

2 2 2

0 1 3 5

0 1

2 2 2

0 1 0 1 3 1

cos 2

3 sin .

F x x x

x x x

x

x x x h

(6)

2 2

2 0 1

cos

3 5 2

F x x x h . (7)

. . , [2]:

2 2

1 1

0

2 2

0

2 2

0

V F F F F F F .(8)

(8) (6) (7),

:

2 2 2

2 2 2

2 0 1 4 0 1 5 3

2 2 2

0 1 0 1 3

0 1

2 2 2 2 2

0 0 0 1 5 3

0

4 2

2 4 4 2

0 0 1 5 3 0

cos

2 3 sin

2 cos

cos .

V x x x x x x

x x x

x

x x x

x x x

-

1 2 3 4 5

0,

x x x x x

2

x

i

:

(9)

2 2

0 0 1 1

0 1

2 2 2 2 2

0 0 1 1

2 2 2 2

2 2 2 ...,

x x

x

x x

2 2 2

0 1 4 0 4

2 2 4 2

3 3 3 3

...,

cos 1 ..., cos 1 2 ...,

x x x

x x x x

23

V

₁

– .

V

₂

2

2 2

0

3

3 . (10)

,

₁

> 0 (10),

2

2 2

0

3 , 0

3 q q . (11)

(11)

₁

4 2 2

1 0

2 2 2 2 2

0 0

4 3

9 9 0.

q

2

3 ,

₁

> 0

q 1.

V -

(11) .

, F

₁

F

₂

0

V & _{, , -}

- , , , , & & & .

1. .

. : , 2001. 128 .

2. . -

. .: , 1971. 312 .

i -

i -

i -

. -

.

Summary

The stability circular movement of tested body in the sphere of gravity as a ball figure of central and the exterior body of the second method of Lyapunov is researched in this article. The conditions of existence and the stability of circular movement of testing body not in the central body of gravity is found.

531.1

10.12.06 .

2 2 2

0 1 5 3

2 2 2 2 2 2

0 0 5 0 5 0 1

2 2 2 2 2

0 1 5 1 0 3

cos

2 2

4 ...,

x x x

x x x

x x x x

2 2 2

0 1 0 0 1 1

2 2 2 2

0 1 3 0 3

2 ,

3 sin 3 ...,

x x x

x x x

2 2

0 1 5 3

2 2 2 2

0 0 1 1 0 3

2

0 5 0 1 5

cos 2

2 ...,

x x x

x x x

x x x

4 2 4

0 1 5 3

4 2 3 2 2 2 2 4

0 0 1 0 1 0 5

4 2 2 4 2 3

0 3 0 5 0 1 5

cos

4 6 2

2 8 ...,

x x x

x x x

x x x x

(9),

2 2 2 2 2 2

1 2 0

3

3 0 4

,

V x x x

2 2 2 2

2 0 1

3 2 2 2

0 1 5 0 0 5

3 4

2 2 1 .

V x

x x x

2 2 2

1

3 4

0

0,

2 2 2 3

0 0

2 3 2 4

0 0 0

3 3 4 2

0, 2

2 2 2 2 2

0 1 2

2 2 2 2 2

0 3 0 4

2 2 2 3

0 0 5 0 1 5

3 4

3

1 2 2 ...,

V x x

x x

x x x

V V

₁

V

₂

:

2

,

2 2 2

3

0

3 0 ,