Документ взят из кэша поисковой машины. Адрес оригинального документа : http://belyakov.imec.msu.ru/papers/SPbGTU2003.pdf Дата изменения: Mon Sep 8 14:32:51 2008 Дата индексирования: Mon Oct 1 19:38:59 2012 Кодировка:

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33

53.082.13


Copyright

©

2003, . .

, . . . . . , , : ( ), .

. .
3- . . . ..-.. . .

Determination of Dynamical Parameters of Massive Bodies by Oscillation Modes
A new measurement method of iner tia moments suggested by V. V. Bogdanov is investigated. Based on this method in the Centr al Aerohydrodynamic Institute a stand for measurement is constructed. In this work a data oper ation algorithm is presented. It is shown that with such stand scheme this algorithm allows to determine not only the gener al inertia moments but all dynamical par ameters of the body: iner tia tensor (without one component), mass and mass center position. Sensitivity analysis of analytical expressions for dynamical body par ameters to input data errors is proceeded

Anton O. Belyakov 1.

15000 , 6 , 2 . , . (1, 2, 3, . . 1) , . , . , . (. 1), . , . , , . 1.

3 2

1 F0 x z a) b) y 1 2 3

. 1 (a) (b) 1.

1. OY 2. OZ 3. OX


1 2 3

1 Y11 Y21 Y31 2 Y12 Y22 Y32
Copyright

3 Y13 Y23 Y33

©

2003


34
2.

. .





n , Ё Ax + C x = 0, x(0) = x0 , x(0) = 0. (2.1)

A -- , C -- , . (1.1)
n

x=
i=1

hi cos(i t),

(2.2)

i -- , hi -- . , f , x0 . , A C . 2 C - Ai hi = 0 , hi . , A . hi , (2.1). hi H . , : H AH = µ, µ1 .. µ = . 0 (2.2) : 2 1 0 , 2 = 0 µn H C H = µ , 0 , µi -- . 2 n A= H
-1 2

(2.3) (2.4)

.. .

µH

-1

.

(2.5)

, A µ = [µ1 , . . . , µn ] . f , x0 : f = C x0 . (2.1) t = 0 x0 =
n i=1

(2.6)

hi , (2.7)

x0 = H [1 · · · 1] . (3.3) (3.2) H : h f = H C H [1 · · · 1] .

(2.3), , µ2 , , : µi = 1 2 i
n

Hk i f k ,
k =1

i = 1 , . . . , n.

(2.8)

, (3.1) (3.4) A C , . , (2.3) C : C= H
-1 n

diag
k =1

Hk i f k , i = 1 , . . . , n H .

, , (3.1) (3.4) (1.1) . , , . .
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35

3.
(1.1) n = 3 . OZ OX . M 0 0 A = 0 Izz Izx , 0 Ixz Ixx

rz , rx -- OZ OX , Lz , Lx -- OZ OX (. . 3 2 2 1). H : H = LY , Y -- , , . 1. , (3.1) (3.4), A . rz rx A12 A13 , . , rz rx A12 = 0 A13 = 0 . . . Y , 1 , 2 , 3 , Lz , Lx f 0 , . OX 90 , . - .

M -- ; Ixx , Izx , Izz -- : 1 - rx L-1 rx L-1 - rz L-1 x x z - L -1 L= L -1 x z 0 L -1 z

. , rz L-1 z 0 . - L -1 z

4.
,
15

i =
j =1

i ( ) j , j

i = 1, . . . , 6, ,

(4.1)

= |f 0 |, Lx , Lz , 1 , 2 , 3 , Y11 , Y12 , Y13 , Y21 , Y22 , Y23 , Y31 , Y32 , Y33 = M , rx , rz , Ixx , Izx , Iz
z

.

, 2 . [2]. . . (3.5). 3. . - , Ixz , . 3 0.1% , , . , 2, . , , , .
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. .



2.

|f 0 | L
x z

1000 2 1.74 13.2 / 16.84 / 28.3 / -4.01 · 10 -1.44 · 10 -2.04 · 10 -6.79 · 10 -1.28 · 10 -6.61 · 10 -5.40 · 10 2.68 · 10 2.08 · 10
-4

, % 0.01 0.1 0.1 0.01 0.01 0.01 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
3.

L

1 2 3

Y11 Y12 Y13 Y21 Y22 Y23 Y31 Y32 Y33

-4



-4 -4 -4 -4 -5 -4

-4



M rx rz Izz Ixx Ix
z

15000 1.7 1.67 44000 · 3000 · 2 200 ·
2 2

, % 0.04 0.04 0.1 0.03 0.09 0.92


( ) . , , 90 . : , . , . , , . .
. .


1. . ., . ., . ., . . , // , 2002. 2. . 37. 2. . . // , 2002. .
20 2002 .

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