nblib.library.kz - /elib/library.kz/jurnal/v_2006_1/

41

1. . // . .: , 1951. . 4,

. 142. . 69-106.

2. ., .

. ., 1958.

3. ., .

. ., 1965.

4. . // . . 1983. . 273, 5.

. 789-793.

5. . // . 1994.

. 30, 9. . 1516-1529.

6. . // . 1977.

. 13, 2. . 294-304.

7. . // . 1990.

. 26, 6. . 943-953.

8. . // . 1986.

. 22, 12. . 2059-2071.

9. . // . 1983. . 274, 4. . 807-810.

i i -

i i

i i .

Summary

Necessary and sufficiently conditions of Riss basis of roots functions in norm terms for other spaces7

517.927.25

. . ,

. 2.02.06 .

. . , . . , . . , . .

( ) -

, -

. .

,

– . -

,

. -

- [1].

-

, -

. - ,

, -

( , .),

.

: , -

, . [2]. -

- .

,

-

, -

[3].

- -

. -

. -

- .

. -

- ,

, ,

, .

-

42

2006. 1

. -

- -

, -

. -

, ,

.

d dt

L q

L

i qi

= Q_i , i = 1,…, 5, (1)

L – , L=K– ; K – -

; – -

; q_i – -

; q_i – -

; Q_i – ( ), -

i- -

i- .

,

, ,

.

-

, i-

. _i

dm i- .

d _i= 1/2( ²+y²+z²)dm = (2) = 1/2 ( _iJ _i T _i)dm =1/2tr( _iJ _i T _i)dm.

-

tr ( ),

J_i i- .

(2) v_i, :

= _i = 1/2 tr( U J_iUT_irq qr) =

= 1/2 tr(U J_i UT_ir)q qr], (3) ,

:

= 1/2 tr( _iJ_{i i}T), (4)

J_i =

J J J m x

J J J m y

J J J m z

m x m y m z m

XX i

XY i

XZ i

i i YX

i

YY i

YZ i

i i ZX

i ZY

i ZZ

i

i i

i i i i i i i

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( ) – (5)

i- , m_i – i- ;

x*_i,y*_i,z*_i – i-

; J⁽ⁱ⁾ , J⁽ⁱ⁾ , J⁽ⁱ⁾_zz – i-

. a₃₁ F

a₃₂

a₂₄

a₂₂ a₄

a₅₁

a₅₂ a₁₁

43 J_i

i- i- -

, .

, J_i, -

. , :

₁= 1/2 t2( ₁J_{1 1}T), (6)

1= U₁₁q₁= HA°₁q₁=

=

0 0 0 0

0 0 0 0

0 0

11 11 11

11

11 11 11

11

C a S

C

S a C

S

q₁

1= 1/2tr

0 0 0 0

0 0 0 0

0 0

1 11 11 1

11 1 11

1 11 11 1

11 1 11

q S a q

S q C

q S a q

C q S

1 1 1

1

* 1 1 1

1

0 0

0 0

0

0 0

0 0 0

m y m

J y m J

J

ZZ YY XX

0 0

0 0 0 0

0 0

0 0

1 11 11 1 11 11

1 11 1

11

1 11 1 11

q C a q S a

q S q C

q C q S

=

= (2J¹_Z+m₁a₁₁²⁾q1^2/2. ,

₁ = (2J¹_Z+m₁a₁₁²⁾q1^2/2, (7) J¹_z J¹ +J¹_yy =J⁵_z,

J⁵_z – 1 -

z₁.

, ,

₂ =(2J¹_Z+m₁a₁₁²)q₁²/2. (8)

3=1/2(2J³_z+m₃a₃²)q₁²/2, a₃= a₃₁ a₃₂. (9)

(9) – -

.

₄=1/2(2J⁴_z+m₄a²₄)q₁²/2.

₅=1/2(2J⁵_z+m₅a₅₃² )q₁²/2.

, -

1, ₂, ₃, _{4 5}:

2

2 2

1 1 11 2 2 22 3 3 3

2 2 2

M z z z

m a

m a m a

K J J J

2 2

2

4 4 4 5 5 53 6 6 6 7 2

1 .

2 2 2

z z z z

m a m a

J m a J J J q

(10) ,

, -

. i-

_i = _i y*, (11)

i – i- ;y* –

i- .

:

1 = –m₁ –g( *₁c₁₁– ₁₁s₁₁)] = ₁(y*₁c₁₁ + ₁s₁₁).

-

2, ₃, _{4 5}.

2=P₂[y^*₂(–S₁₁S₂₂+C₁₁C₂₂)+ ₂₂(S₁₁ C₂₂₊ S₂₂ C₁₁)+a₁₁S₁₁];

3= P₃[(a₃₁C₃₁–S₃₁)(S₁₁C₂₁+C₁₁S₂₁)–

–(a₃₁S₃₁+C₃₁)(S₁₁S₂₁–C₁₁C₂₁)+(a₁₁+a₂₁)S₁₁+a₂₁C₁₁S₂₁];

4= P₄[(a₁₁C₁₁–S₁₁)(S₁₁C₂₂+C₁₁S₂₂)+

=(a₄S₄+C₄)(–S₁₁S₂₂+C₁₁C₂₂)+(a₁₁+a₂₂)S₁₁+a₂₂C₁₁];

5= ₅[a₅₃(S₅₃+C₅₃)[C₄(S₁₁C₂₂+C₁₁S₂₂)+

+S₄(–S₁₁S₂₂+C₁₁C₂₂)]–S₄(S₅₃–C₅₃)(C₁₁C₂₂–S₁₁S₂₂)–

–C₄(S₅₃–C₅₃)(S₁₁C₂₂+C₁₁S₂₂)+a₄[C₄(S₁₁C₂₂+C₁₁S₂₂)+

+S₄(–S₁₁S₂₂+C₁₁C₂₂)+a₂₂(S₁₁C₂₂+C₁₁)+a₁₁S₁₁. ,

:

= ₁(–y*₁S_{11 11}C₁₁) ₁₁+P₂[y^*₂(–C₁₁S₂₂+S₁₁C₂₂)+

22(C₁₁C₂₂+S₂₂S₁₁)+a₁₁C₁₁] ₁₁+P₃[(a₃₁C₃₁–S₃₁) (C₁₁C₂₁–S₁₁S₂₁)–(a₃₁S₃₁+C₃₁)(C₁₁S₂₁+S₁₁C₂₁)+

+(a₁₁+a₂₁)C₁₁–a₂₁S₁₁S₂₁] ₁₁+P₄[(a₄C₄–S₄) (C₁₁C₂₂+C₁₁S₂₂)+(a₄S₄+C₄)(–C₁₁S₂₂–S₁₁C₂₂)+

+(a₁₁+a₂₂)C₁₁+a₂₂S₁₁] ₁₁+ ₅[a₅₃(S₅₃+C₅₃) [C₄(C₁₁C₂₂–S₁₁S₂₂)+S₄(–C₁₁S₂₂+S₁₁C₂₂)]–S₄(S₅₃–C₅₃)

(–S₁₁C₂₂–C₁₁S₂₂)–C₄(S₅₃–C₅₃)(C₁₁C₂₂+S₁₁S₂₂)+

+a₄[C₄(C₁₁C₂₂+ +S₁₁S₂₂)+S₄(–S₁₁S₂₂+S₁₁C₂₂)+

a₂₂(C₁₁C₂₂–S₁₁)+a₁₁C₁₁] ₁₁. (12)

44

2006. 1

(1), .

,

(1) ,

. -

- - .

: , -

, .

-

, . -

( ) ,

- Aq +Cq = 0, (13)

– ; –

. (13)

q(t) = i 1

5

a_i bⁱsin ( _i t + _i), (14)

bⁱ – ; _i – -

; _i – .

a_i, _i– , -

.

- .

0 ,

0 _o

o q

q ,

q_o -

. (14)

.

1. . -

. : F , 2001. 427 .

2. : . .

: 3- . / . . . , . . . .:

, 1988.

3. . . -

. .: , 1985.

,

. , .

i -

i i .

Summary

For theoretical study of dynamics, the definitions of design data are necessary for having settlement mechanical models. The choice of settlement model in each concrete case is defined by the circuit of the mechanism, mechanical properties.

In clause the dynamic model of the mechanism is investigated on the basis of use of the equations Lagrange of the second sort.

621.01

10.02.06 .