KARACHUN
V.V.
NATIONAL TECHNICAL
UNIVERSITY OF UKRAINE "IGOR SIKORSKY KYIV POLYTECHNIC INSTITUTE"
DIFFERENTIAL EQUATIONS OF THE TRIAXIAL GYROSTABILIZER MOTION
Linearized differential equations of the
platform can be written
as follows [1].
;
;
;
;
;
, (1)
where 
– moments
of inertia GSP together with the gimbal relatively to the axes 
respectively; 
– coefficients
of moments of the viscous friction forces;
- the projections of the angle rate of the platform of the stabilization axis; 
– moments
of inertia of the gyroscope moving parts relatively
to the axes of precession; 
–the precession angles of the gyroscope; 
– the projections of the external moments on the stabilization axis; 
– kinetic momentum of the gyroscope rotors; 
– coefficients
of viscous friction of the gimbal sensitive elements;
– projections of external
moments on the precession axis; 
– functions characterizing the dependance between the moments of the stabilizing engines and the corresponding precession angles; 
– "false" angle rate, on which reacts
a float sensor element of GSP, conditioned by the influence of
acoustic radiation on the gyroscope gimbal;
;
;
, (2)
where 
– moments of friction on the axes of gyroscope precession; 
– moments of the gyroscopes unbalance; 
– additional
angle acceleration of a moving part of float sensitive elements caused by diffraction phenomena in the gyroscope gimbal [2]:
;
;
, (3)
where 
– floats
radii of i-gyroscope; L – length of floats; 
– moments of inertia of the
moving parts of
the floats relatively
to the input gyroscope axis; 
– masses of the float ends; 
– bending of the butt ends under the influence
of acoustic radiation; 
, 
–movement of the elements of the
float lateral surface in the
former plane (
– tangential
components, 
– radial components); 
; 
; 
; 
; 
; 
;
; (4)
; 
;
;
,
– central
angle in the former plane; 
, [m-1] – wave number;
– pressure
in the falling sound wave, dB; 
(fig. 1), where 
[3];
; 
; 
; 
; 
; 
Fig. 1. Chart of the sound waves passing through the
butt end
of the float gimbal 1 - falling wave; 2 - reflected wave; 3 - passed wave
– cylindrical
stiffness of
the butt end;
.
Let’s assume that the aircraft
fuselage causes determined perturbation, that is periodic with a constant frequency and amplitude and given
non-random time functions (fig. 1) –
;
;
, (5)
where 
– quantity values of the moments; 
– constant components.
It is clear that consideration of the constant components of the moments will not
bring the significant changes in the
final results. Therefore, we assume
that 
.
The solution of the of
equations system (6.1) we will search by the method of successive approximations.
References
|
1. |
Karachun, V.V.
Vibration of Porous. Plates under the Action of Acoustic [Òåêñò] / V.V.
Karachun // SOVIET APPLIED MECHANICS. – 1987. –
Vol. 22, ¹3. – Ð.
236-238. |
2. Mel'nik, V.N. Stress-strain state of a gyroscope
suspension under acoustic loading [Òåêñò]/ V.N. Mel’nik // 2007; Strength of Materials.
ISSN: 00392316. Volume: 39. Issue:
1. Pages: 24-36. Year:
2007-01-01. EID: 2-s2.0-34147198666. Scopus ID:
34147198666. DOI: 10.1007/s11223-007-0004-6.
3. Mel'nik, V.N. Influence of acoustic
radiation on the sensors of
a gyrostabilized platform
[Òåêñò]/ V.N. Mel’nik, V.V. Karachun//
2004; Prikladnaya Mekhanika.
ISSN: 00328243. Volume: 40. Issue:
10. Pages: 122-130. Year:
2004-12-01. EID: 2-s2.0-14844342416. Scopus ID:
14844342416.