MEL’NICK V.M.
NATIONAL TECHNICAL
UNIVERSITY OF UKRAINE "IGOR SIKORSKY KYIV POLYTECHNIC INSTITUTE"
ZERO DISPLACEMENT OF THE MOVING PART OF THE FLOAT GYROSCOPE IN THE ACOUSTIC ENVIRONMENT
Differential equations of a movable part of the device will be written down as [1]:
, (1)
where 
; 
; 
- are moments
of inertia of the float; 
- are polar and equatorial moments of inertia
of the rotor; c,b - accordingly
is the coefficient of inflexibility of the spring and the damping coefficient.
We will consider
an individual case. Assume that
, 
, and acoustic
pressure 
. It is easy to find out
the connection between the stable value of the turning angle of the float 
, the angle rate of turn 
of the aircraft about the sensitive axis and hard acoustic radiation. From equation
(1) in this case we obtain -
(2)
Then expression will give:
;
(3)
(4)
where 
is pressure at
a falling wave; 
it is circular frequency of an acoustic wave.
Taking expression (4) into account, correlation (2) will be as following [2-3]:
. (5)
Or so -
. (6)
From this we find the dependence between the stable value of
the turning angle of the float and the angle rate about the sensitive axis:
. (7)
When acoustic vibration is missed (for this
purpose it is necessary in
formula (7) to accept 
and 
),
for small angles 
get the known
formula which establishes a connection between the stable turning angle of the float and the input value 
(by circulation of the fuselage) :
.
(8)
Otherwise, to formula (8) another element is added, so:
(9)
In this case the second
element takes into account the influence of acoustic radiation
on the instrumental errors at the stable value of the input value . In formula (9) the value 
is conformity of the bending motion
of the float end under the action
of hard acoustic radiation.
Thus, ignoring the constituents higher than the second
order of infinitesimality, from expression (5.5) we obtain -
;
;
.
(10)
Or in such form:
, (11)
where 
- accordingly are the constituents of angle rate 
of the first
(
) and second
(
) order of
infinitesimality.
Before inserting expression
(11), let’s expand the function 
and trigonometric functions in rows
in the neighbourhood value, which
satisfies (2) :
;
;
;
;
. (12)
Equations, after the substitution of correlations (12), will look like -
,
(13)
where
; 
. (14)
Literature:
1.
Êàðà÷óí, Â.Â. Íåñòàöèîíàðíîå
âçàèìîäåéñòâèå àêóñòè÷åñêîãî
èçëó÷åíèÿ ðàêåò-íîñèòåëåé ñ
äâóõñòåïåííûì ãèðîñêîïîì [Text] / Â.Â.
Êàðà÷óí, Â.Ã. Ëîçîâèê, Â.Í.
Ìåëüíèê, Å.Ê. Êóíäåðåâè÷ // Space science and technology. -
2001. - Ò. 7, ¹5/6. - Ñ. 21-25.
2. Korobiichuk, I., Karachun, V.
, Mel’nick, V.