SCIENTIFIC ABSTRACT VALEYEV, K.G. - VALEYEVA, F.R.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001858430002-0
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 31, 2001
• Sequence Number: 2
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

ACCESSION NR: AT002916 a
S/3037/63/002/000/0100/0119
AUTHOR: Valeyev. K. G.
TITLE: Linear differential equations with'sinusoldal coefficients and constant
delay argument
SOURCE: Kachestvenny*ye metody* teoril nellneyny*kh kolebanly. Mezhdunarodnytry
simpozium po nelineyny*m kol.ebaniyam, Trudy* Kiev, 1961. Trudy*, v. 2, 103, 100-
119
TOPIC TAGS: linear differential equation, equation with delay argument, equation i
with sinusoidal coefficients, double matrix series, matrix-continued fraction,
series convergence, continued fraction convergence, characteristic exponent
ABSTRACT: Fifteen systems.9f linear differential equations with'sinusoidal co-
efficients are considered...'.For the representation F (A corresponding to the
Laplace transformation of tKe solution Y (t), a system of linear difference equa-
tions Is formed and,:the solution of this system Is obtained in the form of a
double matrix series. The Isomorphism between generalized numbers 47-j (7-9 and the
terms of the series is established. The relations for the generalized numbers give
the corresponding relationsfor the series terms, and so the series of F (M is
OrTsf2imed Into matrix continued fractiqns. These fractions and the series F 000)
ga

ACCESSION NR; AT4002~16
itself converg "he wAole complex pl-ine 0. Convenient formulas are given to
e over t 41
obtain the original Y (t) from the representation F (o0). An equation is derived to
determine the characi6ristic exponents of,the solution Y (0) or the singularities of
the transformation F;lv). .$ystems of linear differential equations with sinusoldal
coefficients and constant delay argument are considered in a similar way, resulting,
i.n a general represantation:of the solutl~n Y (-&) of linear differential equations
with periodic coefficlents and constant dilay argument Is given. The stability of
some illustrative special systems of difforential equations Is investigated.. "in
conclus-ion, I would like to thank Prof. A 1. Lurlye for his h6lp.11 Orig. art. has:
137 formulas.
ASSOCIATION: none
SUBMITTED: 00 DATE ACQ: 20Dec63 ENCL: 00
SUB CODE: MM NO REF SOV: 605 OTHER: 002
07rd 2/2.

6 EWT(d)/FCC(w)/BDS AFFTC IJP(C)
ACCESSION HR.*.' -AP3000950'-
AUTHOR: ey, k. G. (Leningrad)
TITLE: Construct on of solutions of a system of linear diffe~entlal.eqmticns In
'Zthe neighborhood of a regular singular-point
SOURCE: IVUz- HateMatika, no- 3, 1963., 19-22
TOPIC TAGS: differential equation system, regular singular point., Laplace transform
ABSTRACT: Construction of solutions of a system of differential equations in a
:neighborhood of a regular singular point is accomplished by making an expcnential
change of variable and making use of Laplace transform to obtain a solvable system
of difference equations whose solution is theoretically invertible,,-using me of
the standard inversion fox=Llas. "In conclusion I thank Professor A. I px~y
2 for
his attention and help in this work." Orig. art, has: 25 formxlas,
:ASSOCIATION: none
12Apr60 DAM'ACfj: 12Jun63 ENM: 00
SUBMrrM:
SUB CODE: 00 NO REF SOV:' 001 001
Cod 7/1

VALEYEV, K.G. (Leningrad)
-.. -
Stability of solutions of a second-order linear differential
equation with periodic coefficients and a retardation of the
argument, Izv.AN SSSR,Otd.tekh.nauk.Mekh.i mashinostr. no.3:
161-162 FAy-Je 163. (MIRA 16:8)
(Differential equations, Linear)

VALEYEV, K.r,. (Leningrad)
System of linear differential equations with simple harmonic
coefficients. Izv.AN SSSR.Makh. i mashinostr. no-5:203-205 S-0
163. (MIRA 16:32)

AID Nr. 983-14 5 June
CASES OF INTEGRABILITY OF MOTION EQUATIONS (USSR)
Valeyev Prikladnaya matematika I mekhanika, v. 27, no. 2, 1963,
-217. S/040/63/0271002/003/019
A study is made of the integrability of the motion equation
d2r kr r
3 + F, k = const, r
where r is the radius vector of a mass point moving around the fixed origin,
and F is a perturbation force acting upon the unity of mass. Equation (1) is
reduced to the eqpivalent system of motion equations in terms of G(momentum),
Y. g, and s (unit vectors of the orthogonal directed trihqdral) and Fy, F and
F. (projection of the perturbation force F Into axes coinciding with the Arec-
tion of Y, g, s) which is more convenient for integration. Solution of this
gystem is investigated for various particular forms of the perturbation force F.
Card 1/2

AiD i-ir. 983-14 5 Juae
CAEES OF 11MGRABIL ME 0.7 WITION [C=t'd] S/OW/63/027/002/003/019
The case of a plane motion (F 9 a 0; g is the unit vector perpendicular to a
plane of motion) is analyzed first; It is shown, that the system can be inte-
grated when = li~-- 2 + ar- ~- Fs = br"4. and'F = 0 (a and b are constants).
FY P 9
This method for integrating motion equations is proposed for a-more general
case where a and b are not constants but certain functions of G. Integrability
of motion equations when the force* F acts in the direction of the velocity dr/dt
of a moving mass point is analyzed for particular forms of the perturbation
force. LK]
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-L 15569-63 EW-L(d)/FCC(w)/BDS AMC IJP (C)
IR 300q
'T (T 1/0565/0572
ACCESS N I AP P52 S100401631077100
jAUTHOR-1 - Valc~ev, K. G. (Leningrrd)
:7TTLEi Conver.aence'of sorles defininp the bo'vrlnrlpr, or instnbl]Jtv regions for
~rollltlons of A second order iinenr dl~feren+,Inl eauntlen with perlo~ic coefficients
iSOTIMEt Prikladnnym witemntika i makhnnikAt V# 27t noWl, 1.061, 565-572
MPTC TA.CrS:- Instnbillty, inatability region, differentisl eaurtion, smnl.l pnrsm-~I-
eter; nonlinenr differentinl ermation
APSTRAM The author considers tho difrorential envation
d2Y
+ IM (1)) y 0
1where
a,e a-, lma0=0
(1.2)
!He is lritei~nsted in deterrdnin- eypqnslons,
P, PAO
+ lal + +
+lLrb, CA (U)
1. 2....
A3 + tic, + A& + .+P,C, -b clot)
Card

L 15569-6.3
A.CrESST C1,11 !~R: ttP-M-1252
(,.r ninc, +hf., re-1-on or n-th In.-7tnb.11,1+v nnd, in pnrticulpr, obtnining 3stivites of
flepandirg on tho coefficidnts a of (1.2) nnd the
9
cnt,,3 s, as of (I.1). Here Xnl(A) The author 't"es the
fnet t~ntl nn the boiindpry of the n-th region of InsUbility (1.1) ndmits n solution
of rerfo(! "IT-of tbe form
tiff
k
~n Atrinsnn lhf inite system which con be used to
der-nq f~.-i ftinctions in U. 1).
1: The expnnsion of the flinction 'A 0(,At) In powers of derininpr the
ir- of the 7ero-th region of Instnbillty -->O sis 9 -9~ 0) of the solution
~oanei,
of (I.].), IS lipjorized by-,the -series
(p) It7t + 2hi (Tilt)
h, 0.25 +
W~Jch converges for
Pt M hj-1 4 (Y:Fl +
Card - ------

1-556g.-63-.,
1ACCESSTaT ?4R, AP.IrOIZ52
iThere orest mi 3. Pr theorem3 for the function wh1eh ore useful when a(t) Is
n,
0,ontinuous, and one theorom t4 bnndle the cose of dis'* tinuoug a(t). Orig. ert.
con
hns: 93 formulas.
Mr)OCIATTM: none
PTIB?,T TTED: 150et62 -DATE ACQ: 23Jul63 ENCLI 00
61113 CODEt VIV ,NO M7J S OV: 00~ OTFIRt 001 1
Card

~VALEYEV, K.G. (Leningrad)
Adverse effect of combined resonances. Prikl. =t. i =--k-h. 27 no.6:
1134-1142 U-D 163. (AURA 17:1)

(Leningrad) i
"A qualitative analysis of dIfferential equations of flight using a
solar sail"
report presented at the 2nd All-Union Congress on Theoretical and Applied
Mechanics, Moscow, 29 January - 5 February 1964.

L rt9-~9-6' EWT (d.) pg-, T Dk
." . : - LI ELl; dr ,ALSD~ f
ACCESSION HR: A7404114 i -": E kLK snoco/6-4/wo/cooptio/0122
AUTHOR: Va I eyev, K. 0 is (LerijE6grp-d.1; RaIdV:ss 0y, -)(u. V, (L"Ieningrad)
TITLE: Use of difference methods In determining regions of Instablifty of sclu-i---~
tions of systems o f 11near differential equati.ons
SOURCE: Chi s I enny*ye metody* resheni ya -J! f ferent 5 1 a I 'ny-4rkt, 1 1 nregra I nv--'-~
uravnenly Ikv a d r a t u r ny-- y ef c) r-rdi '4u;-ie Ti~r- - ~I:f j 7 f
and
NauK.a, 13"-, i i 22
TOPIC TAGS: differential equation, ordinary differential equAtIon, stability,
difference equation, continued fraction, matrix, determinant
ABSTRACT: The article deals with the stability of ;oluilons of systems of 11inrar
differential equations and thel r correspondi n,; -,y!; of dl rf nren~;n f~qo'tt
Condit ir-)ns ar-L -tudic:~! ~nr flic
er;
i r
e7 s r enn!9,1
~-rlt various rerr'~
i2

L71:aW~
I vt T'A
ACCESSION NR: AT4047i4i
f
fractfori expansions, and operator techniques are air ap" 11 .,4 tia rather pec! F'
examples of I fnear d! fferentla! eau6t;n,,, to test, t4leir sc, j t-)r~ r
W; t h ~ev P 1 ~ ~. -
')e L e 55 Cot, -1HP
as
ASe,OCIATIOU: none
sill BH. I T7 ED: 2 '%3 E
C,ird 2/2'

ACCMION NRs AP4o34278 S/0207/64/000/002/0120/M29
AUTHQRS Val Ke Go (Leningrad)
,TrfLE1 Qualitative investigation of differential equations fbr fli& by solar
.sail
SOME t Zhurnal prikladnoy makhaniki i takhnichookoy f is ikil, no* 21 19640 120-129
:'TOPIC TAGSt optimum inclination angle, solar sails planetary flight, piano wtions
Keplerian motionjtorde section traJectoxy, lopArithmic qdral trajectory, solar salung, solar re-
diation pressure
:ABSrR4GTi A study has been made' to select the optimum solar sail
i setting 9 in planetary flight. The equations of plane motion are written in
1 polar coordinates r and for aolar-sail thrust owponents as follows:
1whare 6 is the *ALI constant., Introduc-ing x And y as dependantimrUbles,
Y= .r
Card 1/3

!Ar,CLWION NRs Ap4o34278
the equations of motion yield
0 _4 - bay + ve
:For a w b - Oethe unperturbed Xaplerian motion is studied for a family of ocnic
i sections with ecomAricity F, 9 For a logarithmic spiral. trajectoryp q w consWit,,
I i
the equations of notion become
xy - 2bzS 0, 1 - z 0 bzY + VA'= 0 (z > 0)
These are solved for the special cases 1) a b - coristant and 2) Crust fom is mXant
!to dip tra jectwy cc 0 a cX, It is shown that for a - b e constantp the resulting
solution in unstable* For thrust vector P. indepwident, In absolute nWdtude
of the force direction,, expressions are derived for the optimum f woo directioa on
circular orbit
p Fj a Ol and a parabolic orbito I* The selection of an
'optimm,.sail setting 0 (with respect to solar rays) leads to the
CA" 2/3,__

AGGMION NHs AP4034278
Wreisions
29 + In 2kf
11M1 k-ar- k..
lu
.the values of which are calculated for 0.. 0.5. and 1,,where y is the angle
.between thrust and solar-ray direction. OrLS, art, hass 4 figures
!and 90 formulas*
:ASSOCIATIONs none
SWO=ED i 12Nov63
SM CODE$ HE$ 8V
ATD PRESS 1 3069
ND REF SM 006
INCLI 00
OMM 003
Cewd 313

V A 12YE V , K.G. ( I onil
so!-,;t fir, cf a jinc-ar ri
expQnential and
mat, i mat. fJz. 4

ACCESSION NR: AP4029378 S/0199/64/005/002/0290/0309
AUTHOR~. Valeyev,-K. G.
TITLE: -Linear differential equations with'a delay li'nearly dependent on the
arguments
SOURCE: Sibirskiy matematicheskiy zhurnal, v. 5, no. 2, 1964, 290-309
TOPIC TAGS: differential equation, linear diffe'rential equation, ordinary
differential equation, stability theory, Laplace transform, analytic ftinction..
delay argument
ABSTRACT: The paper presents'a.sufficiently complete theory of linear diffe'rential
equations with constant coefficients and with delays in the-arguments which are
linear functions of the arguments. The Laplace transform method is used to deter-
mine the analytic properties of the solutions of such equations. Both the solu-
tions and their transforms are given in the form of series. The simplest case,
when the delays are directly proportional to the arguments, is explicitly develop.,;
ed. A great deal of attention is paid specifically to the question of the' stabili-
ty of the solutions. The theory presented in the p 'aper is useful, forexample,
when studying the probigm of control,ling a distant receding object where it is not:
,_poRsibleM Ignore the delays in the transmission of the control signals., In a
-Cdrd

ACCESSION NR: AP4029378
~sense this paper Is a continuation of ear lier work by the same author. ."The
author thanks V. 1. Zubov for his assistance. Orig..art. has: 125 formulas..
ASSOCIATION: none
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ATD PRESS: 3056
SUB CODE: MA NO REF SOV: o04 OTHER: 003
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I

AWALTUS z
n e 7 the Ci-' f a V: 'a Ct i On of
PriklaAn-Va Tiatematika i mek~,,anika,
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!OPT Q - Rat(.- Le 0,
7- 7-
LV
usin6 resullte of V-. G. vadayev (0 nekatorykh aluchayakh integrimlyc=
vu t .-)n
MA si-y
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1/2

L 44354-65
Crl_f;SSiU'TI n., AP501-0629
SUBI&I=, Wat64
IEF 3071 009
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xl~
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ACCESSION N?: V 5(, i-~ 9 La
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S
?rlycia"'lay-a ameruati-KS I ML-rv2nIka, 29, nc- 3, 1~6.
11 Uases C, I, ti-le -Id em 0 L 9F; .4 wl-dr-r, IL [-.~j -j D i-
mDtion a-re i7,tegrable- are equation.9
do kr " r, +- F (h
is givm with initial. conditions
r ~ rc, dr dl ~ rQ*, f
where r is the radius vector if a material point H with unit mass ; F a forco
wippImentary, to M--vtonian. The ~:!enter of ig locato'! a,'- a PC Int
CaBe of planar movemant is stud-i,--4 '-n -,rt-d cl,~ I 9a ii the piano ul aot 1c
C,c,-d

L
AGG&9SION %R i AP9)IJ4?41
po'l ar coo rl 3 ~n~- -n
In this c-oordinaLe system tna ac,
d, -it
rT
with initial conditions
a rvj 7 e
The pr~, i Dn~, f
as
A t rn, -.3 ', o-mpt t-p ~lartns Ali C-~;7-14 -~qt- GS i 3 r."-VI ac i 9
aj~-Pr-X P 9-9~mq, 1,t)t' -. ~. . A. ~, 7 - , t, -. a~-,/ , " I
dur-ad su,-:h taoaL kr
= -;j- (a ; F. = M m con5,.
r rs,~,
7- t 1 11 a f- j n I B fc; artd I 9v sA in It -d' tra 'crt,-irip-q :)f mat J C)n
r1,3 q,
L-~6uc "-~u 1-4
-4 1 1 1

L
i 14,R L-
s[i B pE, 2OMay,6L
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Card 313

_9027g-66
EWT(d)/EWT(I)/g-~ip(m)/.WS(v)-3/L'JA(dY 19 C GW
AC=31ON M AP5021309 W*6/65/09/64/00705
.AMSORt Valeyevp K. G. (Leningrad)
,TITLEs A case of integrability of perturbed motion equations of a satellite
z~
;SOURCEs Prikladnaya. matematika i mekhomikaj v. 29t no# 4# 1965# 751
:TOPIC TAGSt differential equationg satellite orbit
!AZSTRA,CTt
The author considers
+ WO - F,, rV' + 2r*V = F9 (k conet)
an are projections of the perturbing force F in the r and ,p directionsp and
it is assumed that the perturbing force is perpendicular to the velocity and lies in
ithe plane of the trajectory, If the magnitude of F depends only on v and the
distance r from the satellite to the attracting centerg (1) reduces to
'F, = -'F RY
-- ' -T + Y
The author seeks asolution ot-(2)-iu~JeA to
.if V .'i;,
"Which he finds in quadratu;es under the given assumptions@ (I)t (2)'also apply to

L 00 -66 ...
ACCES ON IM: AP5021309
~electron motion in electromagnetic fields. "A. 1. Lurlye n9ted to the author that
certain cases of electron motion in electromagnetic field fV. A.,Bogtwlavskiy. Puti
elektromagnitnykh polyakh. Mosgublit, 929) lead to equations.of the
elektronov v
form (1)t (2)." Orig. art. hast 12 formulas.
ASSOCIATIONs none
OUBMITTEDs 03oct64 ENCLt 00 SUB CODE: ]a
I I g;v
00 REP SOVt 001 WHER: 000
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L 9231-66 Mfl(1-)1M'JF(m)1FS -3AW~(d) aw
(V~
ACC NR: AP6=549 SOURCE CODE2 1111/0040/65/029/006/1100/1104
~AUTHOR.- VaJ=V.JJff-.Q."'(,Leningrad)
12
iORG: none
I
!TITLE: Equations of motidn for an earth satellite with a consideration of
atmospheric resistance r)-) 44
SOURCEt Prikladnaya matematika i mekhanika, v. 29., no. 6p 1965, lioo-llo4
TOPIC TAGSi artificial satellite, aerodynamic drag, satellite orbit
ABSTRACTt The equations of motion describing the orbit of an artificial earth
satellite, including the effects of aerodynamic drag,, are analyzed. The satellite
is described as a p nt particle M(x,y,z), and its trajectory Is given in spherical
! coordinates r, The atmosphoric resistance is_given by the vector
91 M fog
x W),
where P is an empirically determined proportionality constant,, and u 1/r. The
equation of motion for M is given by dr/d1'--gr&dn-p(ir/08-1)Xr
Card 1/2

L 9231-66
AGG NR: AP6000549
where -ff is the potential energy of M
(U r-1, It Com
To make the equations amenable to numerical analysis, the following independent
variable is introduced
dV.-P-ij-rxdrj.nar-IjrXdr1d8jdt*ft*?-qd"$ft(h) th dT
and the resulting set of equations for the satellite motion is written in the form;
8,111 .ali I
M, + U = -'I II PO* I I
h Vu + 00 W Wu--
I OIT Pa
-0 -11-n it - Tq%
OU W Wu
2 an 2+ YK-
As an example, the stability of a circular equatorial orbit is considered, and
the following stability criterion is arrived at
t LI~Wii