SCIENTIFIC ABSTRACT KOSTYAYEV, P.S. - KOSTYGOV, V.A.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000825310008-4
• Release Decision: RIFPUB
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: January 4, 2017
• Sequence Number: 8
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

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P.S., inch .... - .........

~5impli�1ed method for ~at~ ~o/q~[b[~lat e~utio~
uaed in ~.c~d conc~, l~, d~. ~ ao. 1:27 ~a

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~o.S~T~___AYEV,_P. avel__Sargeyevioh; 4~INA, L.I., red.; ATHOSHCHENIiO,
L.Ye., tekhn, red.

[Start of an engineer's career]Nachalo puti inzhenora, l*~o-
skva, Izd-vo "Znanie," 1962. 31 p. (Novoe v zhizni, nauke~
tekbnike. X Seriia: Molodezbn~nia, no.19) (MI.RA 15:10)
(Railroads--Construction) (Bridges, Concrete)

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KOSTYAYE~s P, S., kand. t~kh~, nauk

Unheated mortars for seal_i~g precast elements. Transp. stroi.
13 no.3:51-52 Mr ~63. (MIRA

(M~rtar)
(Precast cencrete censtruction--Celd w~ather condition~)

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KOSTYAYEV, P.S., inzh.

Examination of "cold" concrete ~n~ Stl~ctures being used. Transp.
stroi. 12 no.3:49-51 M~ ~62. (~.~RA 16:11)

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KOST~AYEV~ Pavel Sergeyevichs kand. tekhn.nauk; MEL'NIKOVA, Zh.M.,
red.; RAKITIN, I.T., tekhn.red.

[Co~d concrete] Khoiodr~i beton. Moskva, Izd-vo "Znanie,
1964. 32 p. (Novoe v zhizni, nauke, tekhnike. IV Seriia:
Tekhnike, no.4) (MIRA 17:3)

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O~JFRIYEV, Timofey Grigor'yevich, dots.; S~/~EA', Boris Nikolayevich,
dots.; IV~J~'KO, Timo�ey Yakovlevich, inzh.; GEiIOL'SKAYA, Lyudmila
8ergeyovna, dots.; SAJ~YC~VA, Nina Petrovna, dots.;~K_~OS~'~AYEV~_~_.
Sergey Petrovic~h,_ inzh. [deceased]; YEGOi(OV,L. P. ,dots., retsenzent;
Z~/L~O-~. R. sdots. ,ret~enzent; BYAI2N ITSKIY ,V.A., inzh. ,retsenzent;
CHF2bKASHIN ,N.A. ,inzh.,retsenzent; DYNEH,I .I., inzh. ,retsenzent; PAUL',
VeP.,inzh.,red.; NEKLEPAYEVA, Z.A.,inzh.,red.; ~DVEDEVA, :.~.A.,
tekhn, red.

[Buildings in ~ailroad transportation] Zdaniia na zheleznodorozh-
nora transports. ~o.~,kva, Transzheldorizdat, 1(~62. 40~' ~:. (~IRA 15:6)
(Railroads--Buildings and structures)

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USSR/Soil Science - Cultivation, Imp~vement, Erosion.

Abe Jour

Author
I~st
Title

Orig Pub

Ref Zhur Biol., No 22, 1958, 100108

nukin, V.N.~.._K~o_st~a~,~ V~
:

: Tillage of Bog~, Soils Without the Usc of a Moldboard.

: ~ocha~n kishloki Tochikiston. 1957, No 9, 45-47
(tadS.); S. ~. Tad~ikistana, 195% No 9, 46-~

Abstract : N~ abst~'act.

J

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Nutrietn requirements of ramie plants on d~rk Sierozems of the
Giesar Valley. Dokl.Aa Tadzh, SSR 2 no. 5:23-29 '59.

1. Tadzh~ksk~y uauchno-~ssledovatel'skiy ~nst~tu~ sadovodstva
~mea~ I.~. ~chur~na. Pre~s~avleao akadem~kom AN Tadzh~kskoy
$SRP.N. Ovch~nn~kovym.
(~issar Falley--Razie)

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KOSTYAYEV~ V. M,, CANO AeR SOil nEFFECTIVENESS OF MI-
NERAL FERTILIZERS UNDER CROP8 IN THE SIEROZEU~OF TADZHI-
KISTAN." STALINABADI 1960. [ACAo $GI T^$SE, {NST OF HOR-
TICULTUREt |U J, V. MICHURIN), (KL, 2-61, 215),

-221-

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Using the leaf-diagnosis method to determine the supply of nitrogen,
phosphorus, and calcium in the ramie plant. Doklo AN Tadzh. ~R
3 nq.~:45-47 t60. (MI~ 16:2)

!o Tadzhikskiy nauchno-issledovatel,skiy institut sadovedatva im.
L.y. Michurina. Predstavleno chlenom-korrespondentom AN Tadzhiksk�y
SSR VoF. Petrovym.
(Ramie) (Plants~Nutrition)

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BUP~5.~Y!CH~ ~,.P.~ k~p! Lan 2,~go rang~ KOSTYAYEV. V.V., k,pltan-ley~.enant

Frc~ the prae~.iee ot' carrying-out radio devlaLion work on
Su~:~rine~ Mot. s~r. l7 no,5.63-6~ My '6A. (MIt~ 18:6)
/

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YEGOROVA~ L.I.; KOSTYAYEVAj S.I.

Use of some diuretic substances (diamcx, chlorurit, hypo-
tkiazide) in cardiovascular pathology. Terap. arkh. 35 no.2:
30-37'63. (MIRA 16:10)

1. Iz Tsentral'noy klinicheskoy bol'nitsy (glavnyy vrech
A.I.Khrimlyan) IV Gl~vnogo upravleniya pri ~tinisterstve
zdravookhrancniya SSSR.
(CARDIOVASCULAR SYST~--DISF~SES)
(DIURETICS AND DIU~ESIS)

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~;~.',~ (lesi6~n of valve Joints for depth
,~' ._. :~

(Oil ~.lell pu~aps)

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4, Co.-.-,1 :"dna~ and I';intn~ - Periodicals

?. Serious omissions in the periodical "U':ol'." Z:, ekon. i'~..:t. ,'~.~. f, !952.

9. k~onth!y List of R~sian Accessions, Library of Con?ess, ~,[~rch 1953. Unclaszi�ied.

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S/1~?/61/000/00~/005/021
/~, /~.~ ~ E161/E~35
:\UT~iOR: K?s tx_c_l~ev. G.,~,
TITLE: Contribution to the problem off the opLimum shape of
bodies in unstabilized motion

PERIODICAL: imvestiya vysshikh uchebnykh zavedcniy.
Aviats~onnaya tekhnika, no./l, .1.961,

T2X-T: The author- considers a body, taken as a particle,
movin~ in a tra3ectory defined by Cartesian coordinates (x,y).
The "P = mE" type equations of mokion are written down ill
~2ngential and normal form. Along the line of flight, P is the
d2 ~ferenee between the thrust and the weight component plus the
frontal resistance %o motion, the latter term being expressed as
the aggregate of all the elemental resistances summed over the body.
Nora~al to the line of flight, P is the difference between the
lift force, expressed as an integral taken over the body, and the
weight component. The cross-sectional shape of the body is
specified by two Cartesian coordinates (~, r). With this
introduction the problem now considered is the determination of the
shape of the bod~, r = r( ~ ), and the parameters defining the
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Contribution to /he problem ...

S/1~7/61/000/00~/005/021
E161/E~35

motion, e.g. si, ced, coorciinates, so that the velocity un at tho
end of the motion should assume a stationary vnlue. A va~'iational
method is used, employing Lagran~;e multipliers. This leads to a
complex equation in which the coufficients of most ter~s can b0
made zero, Lhus leading to 3us~ sufficient equ~%tions to determine
the unkno~cns. A particular case - when sot;lc of the functions
introduced assume special forms - leads to simplified condi'tions.
Finally, equations are derived for the shape of the body ~,'hen the
work done during the motion is a mirlimum, and also %ebon the speed
of the body is constant. There is 1 Figure.

~\SSGCIATION: Kazanskiy aviatsionnyy insti~u%
Ka�edra aerodinamiki (Kazan' Aviation Institute
Department of Aerodynamics)

$UB~ITTED: ~larch 11, 1961

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the f~Lo~ paet_aiTaul&r ca~&dee of profiLe~. Tru~ EAI
(Atrtotll)

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1 ~-~4" 1957- 10' 115-t-t
Translation from: Referativny7 zh,irn:~l, Mckhanika. 1957, Nr 10, p 51 (USSR)

AUTHOR: Kostychev G. l

TITLE:
'I'o thc Calculation of l-tyd,,-c.�iy.~t.,~ic C:-:'~Cadc.; (K ra:~chetu
� id rodi namic he,_.~ kikh
i~ERIODICAL: Tr. Kazan.-;k. ~'?'.'ia!,~. in-t-t, i~-,(-~, Vol
ABSTRACT: The Author de*.ermine~ expre.::lcns for the coe!'fi, cients of a
function which tran:;form~ cenform~,l]\, thc t~xterior surfacl~, of a
cascade COmposed of arbitr,:~ i!5. 3hap~d Prcl'ile~ upon the peri-
pheries of conccnt.,-ic circle~ !y:ng c,~ an infinite Riemann -~urface
by-meana of the coeffic!ent.a cf th,z no~ma! W.:'amctric represen-
tation of the profile. The re-",':~ion:.:hir~:; can bc exl~ressed with
any' desired degree of ~-ccu.'-~c~..,

I. S. Sirnono;-

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SOV/1 g4-57-8-8761
Translation from: Referativnyy zhurnal, Mekhanika, 1957, Nr 8, p 25 (USSR)

AUTHOR: .K�stychev, G.I.

TITLE: Contribution to the Problem of the Flow A.bout at Airfoil
ob obtekanii krylovogo profilya)

PERIODICAL: Tr. Kazansk. aviats, in-la, 1956, Vol 31, pp 37-49
ABSTRACT:

(K zadache

The author gives a calculation method for the plane-parallel
flow of an ideal incompressible fluid about an airfoil of arbitrary
form. The airfoil contour is represented in the form of a
trigonometric series; all basic hydrodynamic quantities are
expressed in terms of the coefficients of that series.

Ya. M. Serebriyskiy

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ShGpe of bodies having minimum wave resistance. Izv. vys. ucheb.
zav.; ay. tekh. no.2:9-15 '58. (MIRA 11:6)

1. Eazanski� aviatalonn27 in.s~,itut, Eafeclra aerodinamiki.
(Airfoils)

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TITLE: On the Solution of a Variational Problem in Supersonic
Flows (K Resheniyu odnoy variatsionnoy zadachi
sverkhzvukovykh techeniy)
2 RIODIOAL.Izvestzya Vysshikh dchebnykh Zavedeniy, Aviatsionnaya
Tekhnika, 1958, Nr 3, pp 3-7 (USSR)
The author has already dealt (Ref.1) with the problem
of the optimal shape of the nose of a body of
revolution (or a wing) giving a minimnmwave drag in
a supersonic stream. There are, however, cases when
axisymmetrical bodies are subjected to a disturbed flow,
e.g. in a multi-stage rocke~ where the disturbance is
caused by the main stage of the rocket� Suppose it is
required to de~ermine the shape of a body of revolution
having diameters 2Ua and �~0 o~r an axial length XO
(Fig.l.plane ~,X) resulting in the minimum wa~ drag in
a supersonic stream as defined by the parameters of
Eqol, where f[(X,~) are given continuous function,s
determined everywhere in the flow ups~am star~ing with
the characteristic (of the first family) ad originating
at a (Fig.2), in the plane (X,$) in which $ is the stream

ABSTRACT:

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SOV/1~?-58-5-1/t8
~n the Solution of A Variational Problem in Supersonic Flows

function. Let ~(f) be the unknown i~nction giving the
main shock wav~ originating at as then, because of the
shock, the flow in the triangle acd changes. With the
notation of Ref.1, the wave drag of the segment ab is
given by Eq.3, where T. is the contour based on t
ab. Assu m~. he se nt
.... - n~ow as the contour L the curve acb ~w~ o~
~onsis~l~ o~ t ~ -~
g he shock ac and the characteristic ~of the
second family) bc originating at b. Eq.3, is v~lid also in
the case when the functions of the g~s dynamics have
discontinuities in the region of integration, hence Eq.5
can be integrated along ac by taking the left limits of
the fun.9.tions involved. The ~ ......
� ~z.~ aloHg ac
~l(~,f) + ~(f)X2(~,f)] df ' being
and that~along bc being (as shown tn Ref.1 and 2)
$1v(o~) ~/X sin ~ sin (~-.~) _ cos ~] df
The total waw drag of the segment ab is given by Eq.~
and the length of the sought body of revolution is given
by Eq.6. The f~uction ~(~) may be expressed in terms of

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$OV/l ?-SS-3-1/18

On the Solution of a Variational Problem in Supersonic flows
prope~ies of the incident stream and of the angle of
the tangent to the shock wave in the physical plane
(X,W), this angle given by Eq.7. Taking into account the
standard relations through the shock wave as expressed' by
the next three equations and the relation 7, w~ can now
obtain expressions as given in Eq.8 and 9 and these
finally lead ~o Eq.lO. Along characteristics of the
second family there are two non-holonomic relations:
Equations ll and 12. Thus we arrive at the following
variational p~oblem: with the given parameters of the
incident stream (Eq.1) and the given magnitudes ~a.~y15
and.Xo we ham to determine the functions ~(~),
5(~), ~(~) and ~(~) 8ivin8 the minimum wave drag (Eq~4)
wi~h the constant length Xo (Eq.10) and non-holonomic
relations of Eq.ll and 12. For the cases when the shock
is attached and there are no shocks or rarefaction waves
inside the triangle abc and on the aesumption that the
speeds along the characteristic remain supersonic
throughout then, in accordance with the methods described
by the author (Ref.1) and Shmyglevs'kiy (Ref.2), four
~lations are obtained as given by Eq.14, in which

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SOV/I~?-SS-5-1/lS
On the Solution of a Variational Problem in Supersonic Flows

k and ~ are respectively the constant and the v~riable
multipliers of Lagrange. The lower indices denote
partial derivatives with respect to the pertinent
variables. With the use of the first three of these
rel~.tions the fourth one can be transformed to read as
in h~.lS. These four equations together with Eq.ll will
enable us to determine the five i~nctions ~(, ~,1-, ~ and
~. Equ.15 is of the second order with respect to ~
hence the general solution of the system will contain
four arbitrary constants vJ~ich can be determined by the
given magnitudes ~a, Y~o , Xo with the help of Eq.13 and
by the two boundary conditions at the free end (7 = ~c)
which can be obtained from the general form of the first

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SOV/1~7-58-3-1/18

On the Solution of a Va=iational Problem in Supersonic Flows
variational ~elation as indicated by the last two
equations. There are 2 �igu~es and 2 Soviet references.
ASSOCIATION: Kazanskiy Aviatsionnyy Institut, Kafedra Aerodinsmiki
(Kazan' Institute of Aeronautics, Chair of Aerodynamics)

SUBMITTED: 19th February 1958.

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Translation from:

AUTHOR ~

TITLE.:

PERIODIC.~L:
ABSTRACT:

SOV/124-59-9-9884
Referativnyy zhurnal, Mekhanika, 1959, Nr 9, P 45 (USSR)

Kostvchev. G.I.

The Potential Flow Around Two Bodies by a Plane Stream of an
Incompressible Liquid

Tr. Kazansk. aviats, ln-ta, 1958, Vol 33 - 34, pp 3 - 6

To solve the problem the author reeommends to map at first the
exterio~ of one of the bodies onto a semiplane, and then to
analyze the 'flow around the profile, which is near the plane
boundary. The author does not present examples of calculations
in his article.

G.Yu. Stepanov

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/0, ~ O0 o 67060
.4.0.~ $0v/44-59-9-9007
Translation from: Referativnyy zhurnal.Matematlka~1959~Nr 9,P 69 (USSR)
AUTHOR: Kostychev,G.I.

TITLE: On the Construction of Grids According to a Given Velocity Distribution
~Part of the Dissertation Maintained in 1952]
PERIODICAL: TroKazansk.aviatsoin-t%1958,3~-34,7-18
ABSTRACT: Let a grid with straight axes consist; o� infinitely many congruent
profiles and let it be in the potential flow of an incompressible fluid~
The author considers the determination of such a grid from the velocity
of flow given as a function of the profile arc on the profilec The
conditions of the problem permit to determine the absolute value of the
derivative of the complex potential W as a f~lnction of the boundary point
of an infinitely connected domain of the W,-plane which corresponds to the
external region of the sought grid. The mentioned domain of the W-plan~
is also a grid consisting of rectilinear lines; the parameter'of.this
grid are detez~ined from the conditions of the prob!em. In this manner the
dW
real part in-~z on the boundary of the infinitely connected domain is
d~
known. For the determination of in ~z the author maps the exterior of the

grid in the W-plane onto the exterior of concentric unit circles lyin~n
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67060
lO(4), 16( 1 ) sOV/44~59-9-90o?
On the Construction of Grids According to a Given Velocity Distribution
[Part of the Dissertation Maintained in 1952]
a Riemannian surface of infinitely many sheets in the ~-plane; the mapping
function is tl
W 3 '~ e-i~ln ~ + e R~-I '
where t1 is the path, ~1 - the decision of the grid in the W-plane and the
parameter R is determined from a certain transcendent equation. In this
dW
manne= ln~ is determined as a function of ~ by an integral of Schwarz.
In the papers of other authors on this question the analytic funetion
dW
ln~z was determined immediately in the infinitely connected domain of the
W-plane; that caused large computing difficulties, since elliptic functions
were applied.
In an analogous manner the grid is found which consists of m congruent
profiles lying symmetrically around the coordinate origin; here the
velocity distribution is given and in the coordinate origin there lies a
system consisting of the vortex ~ and the source Qo In this case the
domain which corresponds to the flow in the plane W is mapped onto the,//
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lO(4),16(1) 67060
$ov/44 - ~9,-0- ?007
On the Oon~truction Of Or~ds According ~o a O~-,-en Vetccity Distrib~tio~
[Part of the Dissertation ~ain~ined in 195%]
exterior of concentric unit circles on the m-~heeted surface of the plane
~ by the function' ,
2~m ~ + 21Em R~-I ' 2~ R~-I + c .
In this case the function ln~ h~ logarithmic singularities in the points
b~ R and for tho 'dBt~r~ina~ion of it one is compelled to us8 a formula
a generalization of tho formula of Ienzen and the integral of
Schwarz.

V. ::~ P. ogozh i n ;.~.~w/

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..~Kostychev, G.I.

The Fcrmation of the Wi ofile A.-.�ordlng t.o ,+.he
Diagram cf Velocity or Pressure Over *.he Cb. erg

PERIODICAL: Tr. Kazansk. aviats, in-ta, 1958, Voi. ~8, DP. 3-21
p~,~e.,~lal ~n the -plane an.~

~=O

is a functtc, n conformally mapping the exterior of the unit ctrci~
ont.,:, the exterior of the profkle In the ~ -pl~e, and

d~ d~ ~W
~=~ then dz dz ~2 =
~he~e ~is the conjugate veloc!ty.
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8~
s /'l ~ ~ /6 o.looo /oo9 /oo �'oo5
^005/A0O ~
'~ne Fc. rmation of ~he Wing Proflle According t,~ the D~.stribut[en D~a_~ ~, Ve],:,e~-
ty ,:r Pre,sure Over the Chord ..-~:'~m cf

Therefore, if the value of velocisy on the pro. f !lo contour is Frescribed in
f:rm l;'~ = F(x), the problem o~ the dete~inat, lcn of t.ke 5t.~e~ R:i~J Its bounJar.le-~
is reduce~ rot. he determination of the fun,2tion z(~) regul~u' everywhere
t. he region I~ ~ 1, having a simple ~oie !n th~ infln[t.y. &~i saflsf?tng
k:mn~Ary [~[ = 1 the condition

z ' z ' ~ z + z -

Tne sc!uttc, n cf t.he more genera1 ?roblem of 3e~.e~'m[ntng z(~ ~, s~t.~sf~-ing t.ne
::ndit.~cn~ ~t. havl~g bomnJa~,y cond~tLen !n the f.:.:--

where 0~)1~ F'~esente4 in ~he flrs~ ~.~ree ~aragra~k,s of ~.he ar~!cle.
~ssumed that the solution cf ~. (3) is kno'~ for ~= C in the f;rm z

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859~

s/1 ~/60/o00/o09/o01/�o 5
^oo5/^ool

The Formation of ~,he Wing Profile According to, ~he Distribution Diagram of Veloc/-.
~.y ~,r Pressure Over the Cr, c, rd

~he right-hand p~rt cf Eq. (3) in the vlc~nlty of ~= 0 by a set,as In ~.~wers ~f
~, the system of differential eQuaYions c~ be ob,~alned-fcr determining the un-
knc~ functions Zn(~ ) by comparing the cceffLcient.s aL ~ of equal powers. The
conditions are considered for which the solusion c~ be found in the class of
f~otions univalent, in the vlcini%y of th~ infinitely rem~.~e potnt~ the con-
vergence of the successive apDroxlmation process is sho~. ~d the considerations
are presented which simplify the application of ~uhe formulae obtained. It Is
shc'~ that the second approximation gave already practically suitable res[~its fcr
one cf the theoretical profiles, which Is similar to the NACA-2~-iL profile.
~nere arg 5 references.

A.I. Borlsenko

Tra~.slatorZs note: This is the full %ranslatlcn of %.he original Russ:~~. abs~.rac',

Jard ~/'~

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AUTHORS:
TITLE:

S/i47762/000/001/002/015
E195/E~35
Kos~y~_~vk_~.I., Polkovnikov, V.I.
Some variational problems in gas d~amics for
motions other than steady-state

PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy.
Aviatsionnaya tekhnika, no.1, 1962, 11-18
TEXT: Many papers exist which deal with the determination of
optimu:n values of missile design parameters, but which are
applicable only to steady-state conditions. Tile sdlutions thus
obtained do not apply to non-steady states which characterize the
conditions during actual flight. In a previous pal)er (Re�.l:
Ibid, no.~, 1961) the author dealt with such problems, where
aerodynamic characteristics were in the form

u l .... llt
and the equation of motion

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Some variational problems ...

S/1~?/62/000/001/002/015
E195/E~35

where ui(t) - control functions connected with the motion o� the
missile (speed, mass etc); rj(~) - functions which are
independent of time which characterize ~he constructional data
(~
themissile;t0zJ - wit , =on t uctio= or
coordinate). This article is devoted to the consideration of the
influence of motion regime on thc optimum shape of ~'~ missile
some generalization of the problems formulated in thc previous
work. S~ar%ing from ~he Euler-Lagrange equations fo~' several
',ariables and defining a pressure coefficient for the head of
solid of revolution

(1.~)

and

. /

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(1.2)

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Some variational problems .,.

S/lq7/62/000/001/002/015
E195/E%35

;.,'here RI and ~1 - constant coefficients; v and a - velocity
and velocity of sound of the free stream; r' - tangent of the
angle of the tangent to a point on tile surface of the body,
the authors derive in a parametric �orm the equations of the body
profile

(1.8)

(1.9)

where p2 = r'. For a given law of motion v = f(t), the
parameter o is known and the arbitrary constants c and c1
are determined by the boundary conditions r(O) = re, r(1) = r1.
In transition from one regime to another the body profile will
change because of variation in o. With velocity constant
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Some variational problems

v = f(t) = vo, then

o = + v
O

$/Z~?/62/000/001/0o~/01~
E195/Eh35

;gith a given law of resistance, for every motion regime, same
optimum body profile may be obtained by a judicious selection
of "mean" velocity

f{/(t)l"dt '
~P ~ T ~ '
/[/(t)lTM ,tt

The plot of the body profiles of solids of revolution, in
accordance with laws: 5~1 = 25t + 5 and ')12 = (153-13t~ + 11.18}
is sho~ in Fig.2 ( r vs ~ , parabola) these profiles will be
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Some variational problems ...

S/1~7/62/00o/001/0o2/o15
E195/E~35

optimum for a motion with constant bIach numbers
bi1 mean = 22.09, ~2 mean = 19.69. In this example the nose and'
transition to the cylindrical section are not included. The
authors extend the method to the problem of vertical flight, in
particular the determination of optimum body profile for Eiven
initial and final velocities, so that maximum vertical rise is
achieved. They conclude by considering the case of a single
missile subject to flying regimes of varying relative frequency.
There are 2 figures.

ASSOCIATION: Kazanskiy aviatsionnyy institut, Kafedra aerodinamiki
(Kazan' Aviation Institute, Department of Aerodylqamics)

SUBS~ITTED: April 11, 1961

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~.~', .: ..,;' ~
AUTHOR:
TITLE:

$/1~?/~/ooo/oo~/oo~/o~o
EO31/E~35

Kostychev_~_~Ct~I. .

On optimal p~ogrammin~ when there are different
conditions for the realization of a process'

PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy.
Aviat~ionnaya tekhnika, no.2, 1962, 2)-31

TEXT: It may happen that the same unit can operate under
differe~tt conditions but to change the programme of certain of
the components which determine the flight regime is inconvenient
or impossible. Moreover the operating conditions may not be
known in advance and may only be given in statistical.terms.
In %his paper the necessary and sufficient c6nditions are derived
for an extreme value "in the mean" at the end of the interval of
motion of some chosen quantity for ,tifferent re~imes. It is
assumed that there is a vector function u ~ui(t)3 (i = O,1,....,n)
whose components are functions of some argument t in the range
OT describin~ the motion~ which satisfies a system of ordinary
first order differential equations. The problem is to determine
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CIA-RDP86-00513R000825310008-4

On optimal programming

s/j~?/6~/ooo/oo~/oo~/o~o
~o~/~

u so that one of its components takes a stationary value at
t = T. The problem is generalized to q regimes, each described
by_vector functions v ( ) (j = 1,2 ... m) and
uS[u~(t)] (s = 1, ...,q) ,1 . n), where v(t) has the
same value for all motions and u~it) takes different values for
each regime. A further generalization is to the case when there
is a continuous spectrum of regimes depending on some parameter p;
i.e. each flight regime is characterized by vector functions
u(t,p) and v(t). In this case the problem is to determine the
optimum programme for v . This problem may be generalized to the
case where there are several programmes v , each depending ou a
parameter p (the range for p being possibly differdnt i~l each
case). For each of the above problems the Euler-Lagrange
vai'iational ,quations are derived, The theory may be extended
to problems in which the ends of the interval are not fixed or ill

functional whose extremum is sought may also be more complicated.

ASSOCIATION: Kazanskiy aviatsionnyy institut, Kafudra aerodinamiki
Kaza~ Aviation Institut., Department o� Aerodynamics)
SUBHITTED: July 17. 1961
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KOSTYGHEV, G: I.
~t~m~l-'~;�gramming in case of va'riOus conditions for the realization
of a process, Izv.vysouchebozav; avotekho 5 noo2:23-31 '62.
(HIRA 15:7)
1o Kazanskiy aviatsionnyy instituts kafedra aerodinamiki.
(Airplanes~Handling characteristics )

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KOST~OHEV, G.I.

Some varia~ional problems on approaching and interadtton. Izv.-
vys.ucheb.zav.; av.tekh. 5 n~.3~2~-33 '62. (MIRA 15:9)
(Calculus of variations) 04echanicss Analy%ic)

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Necessary extrennzm conditions for a variational problem with a
sitrib,-'ted parameter. Ir~o wy_~o uchebo zavo~ arc tekho 6 nOo2~
124~133 '63o (MIRA 16~8)

(Calculus of variations)

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~.ccEssto~, :