SCIENTIFIC ABSTRACT NEYMARK, YU. - NEYMARK, YU. I.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001136820010-9
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 99
• Document Creation Date: January 3, 2017
• Document Release Date: August 1, 2000
• Sequence Number: 10
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

NIKITIN, Konsiantin Filippovich; NEYMLLK, Yefrem Zinovlyevich;
FXUKOIJ, M.Ye., red.
[Problems in the hydrogen sulfide therapy of nervous
diseases3 Voprosy serovodorodnoi terapii nervn-;kh za-
bolevanii. Moskvap Meditsina, 1964. 210 p.
(91RA 17:5)

AW-,RC".'C,V A.
.-L I
"On the Movements of an rdeal Clock System ',,Ith Two
Degrees of Freedom."
Reports of thc.- Acad. of Sci. of the USSRP 1946, New series,
vol. 51, no. 1, pp. 17-(~, illuf-tr. 3, Mbli. - 3

I&Yluu~K, )'U. I. 11i '/6TIB

Jul/Ang 48
Turbines, Water
TLxbo Regulators
"Problem of the Effect of Hydraulic Thrust an T'Ah"a
RegulaUon of a Turbine " Yu. I. NOymark, Physiao-
tech inat, Gor'kiy U, 21 pp
"Avtcmtika i Telemekh" Vol 32, No 4
G. V. Aronovich, in a previous article (76T47)
on this subject, reduced the problem to the
equation- C(P.+P,),.h i:~ +(PS-ZPI.)Ch 111F.0.
Stability of system was Investipted vith respeot
to the compound paimmeter + OL and the
13/49T33
UM/Magineering (Otntd)
Jul/Aug 48
JM 7* . Rare Neymark Izvestigates system with re
to parameters CC and r, using a method previously
described (76T3.8). Submitted 29 MP-r 1948,
13/49T3~---

6t AW 9T
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VU*'8lvTmoult,od-T9vnb jo covdo v jo -4.vq,4 Iloool;
"UDTPY49 TVDT'4p=d q-4TA tdDTQDla
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JO tCOT40UUJ MUpVUQO9U=!t V JO 840OX GIC4 JO 2
Wlmnd X*Td=DD Qq4 al UOT=vd= aqq, ;o AW49 *qjt
-oz oonpoi z4TTTqvqc uOTlvrrl9= uT =aTqomd XuW
It ON c= TOA WEGK T 4=041H POPUA&
cld TE gn-04ng 44.=o 131xmtcg -1 0AX.,
T=tdtOJ-Tfjvrtb ;0 QOvdS cqq~ jo ooTag-q, DIM.
NOT

NEYMARK, YU. 1.
MSR/Engineering - Hydraulics, Structures Apr 52
"Theory of the Vibration Sinking of Sheet Piles,"
Yu. I. Heymark, Cand Physicomath Bei
"Gidrotekh Stroi" No 4, pp 24-27
On the basis of simplified process, develops the the-
ory of pile sl:*.ing by vibration, establishing re-
lationship amo-ag sinking rate, parameters of driviag
installation, its power and experimentally detd para-
meters of ground. Vibratory method for driving obeet
piles, suggested by D. 1%,~ BarkjLn, Laureate of StalLn
Prize, is ~_,sed in constr of a number of hydro-
elec power stations.
219w6

.-"or ti.-
"Invc.,;tigation ?crj-(,,dic Proceo!3os an, Thnix t;JGII
Disti-ibutoc' SYstorr, of 1~clay Regul:aticn of Tompernt,,xe", Avt,,;..ati.:a i
Televiekhan!~'~-'a, Vol 14, 1.,,o 1, 195), pp -J,4-43.
Di!xur,ses pericKlic 3oll:tj-on.,~ of an equationcf COrI6L:CtiVty
satI-,,fy1Lnj, the boundai"/ cor,63,Ions:
when f(T) 0 ~;Ith T>TI. f(T)=1 with T/T"
An investilrati n of perlodic solut!,-ms is conducted for
and 3tudyin;, the relation bct,,ieen cccfficl,~ntr~ cif thf~ Folirior sarics, ccr--
resnonc:irv- 'r ~,-'T,ticns cf c(-,uatj.o-. of conc'ucfiv~-.~,, at f(T) Z
am. f (T) C' -'-ivel~r.

C~~nti.
This connection is consIderecim a Pointtransfory.'o',lbn of infl-ni4te
dimen.sion space, TI, 1mioldle point of tld.,; tran.-iforn.-i t ion cort-c-spon-da
to a perindic solutlon.
An invu-stit'ation of the stability- of periodic solutions leal"s to an
J.nvc.-JJ(,,%tJ.on 9f the stabj-lj~t.,- ~-,f lm,toblLe point,,; at mmvil-l cl-,irv-Ds of' the-~T
coordinatou. The cmabililly of bmiob-Alo )olrlt.9 i.s I.y tLe dirAr-!-
but-lon root:3 c-f -, certain transcendont uquiU,on in mnrect W tit) olrcje
of a unit rad-lus.
A nuverical exar..rle and f-rc-~ms are -,rcsenll-~,-~,. (RZbl-iel:h, No U, 1954)
SO- Sur- No. 5 Az~r. 55

ONDUH
~~-
1j. Gal'perin works on structural stabilit7 conditions of ilyn,=Ic
systems. Avtom. j telam. 14 no.1:88-92 J&-F '53- (KIR4 10:3)
(AUtomatic control)

Irb-fl-L111K. YU. I.
"Periodic Gycles and the Stability of Relay Systems", AvtojTatika i
Telemekhani1ca, Vol 14, No 5, 1953, pp 556-569.
Discusses a relay system of automatic regulation, consisti:rk:7, of -a
linear element with a transfer coefficient K(P)
and a relay elermant, the generaliz-A coordi=te of which may acquire
on2,y two vaLues.
In a puriodic operatingoomlition the tijrz intervals form a periodic
sequence whon the trily
?ing
time of th- relay is 1, Repetition takes
place after m. trippinGs of Ite rela,'; the duration of the period is
T = -;-,' Ir I
-;E ; . . , - ~ ic.
In the simplest case (m ~ 1) ... are
equal.

Conti.
The output coordimte cDf the linear elen, ent y(t) is constricted ac-
cordjmg to the transfer c oef f irient of the linear element and to t he
values ...,tri-2, tn-l. tn. .., precedirC the specified instant. Tri PIIC
of the relaj occurs 't I Y(t) - S and at the correspondirZ s ien of y I (t~
Kmling ..., tn-2. tn-l, tn, the Instant of 'ripping of t lie rel.rr
tn ~l ir.V be found as the root of t he equa 'L. ion y(t) = (_l) n ~I (" .
For m unkn(nm Trn m transcendent equatiorw were
derived y(0) y(L I
ftAjagaut equations were do-rived for cases of forced oscillations.
The stability of the periodic operating conditi-on at tjjies
is determined inthe fhlowinG way: for the initial time se-
I IS
qd~n_c6..., n the sequence I", 't built;
the system, mrrespohding to the initial s equence -is stable.
if for snall disturbances ...,Lt, Al.correspondinE; 0 All, tend to
zero,

Cont.i.
Finally, the investigation of the stability 7f free anc.' forced periodic
operatilig, cor4itiorm of the discussed relay system leadq-',to a clarifica-
I
tion of the distribution of roots of the type
with respoct to a unit circle (a as constants).
The problem of D - expansion with respect to unit circle for the
th,aracteristic equation is briefly analy, ze~. Examples are -,iven.
(RZILTIekh, Ao 11, 1954) SO: 3um No. 443, 5 Apr. 55

NZYMARK, Yu.I. (Gorlkiy).
Thaory of vibmtions used in pile driving and pulling. Inzh.sbor.
16:13-48 '53. (KI-RA 7:3)
(Pile driving)

7

e t.-La t P- n-
t a t
!-iarl.
roi xavov I s ar --icle a
1 -
-1:7
re
:~u
ns~? n~~
~ic4si-
to ~i
.
j . c
a re a t~I:ort cs 3r~u c1c, a
:I )e r 17L' -UL e, a 11 f .0 of 0 L' 10 C L~ m S
r v -IV5
9. Monthly List of Russian Accessions, Library of Congress, -1953. Unclassified.

NE Y M,9 K
USSR/Physics Singing flame FD-2202
Card 1/1 Pub. 146-7/25
Author Neymark, Yu. I., and Aronovich, G. V.
Title Conditions for self excitation of a singing flame
Pe-iodical Zhur. ek3p. i teor. fiz. 28, 568-578, May 1955
Abstract The authors consider the problem of the stability of a singing flam
by proceeding the representations of Rayleigh and taking account of the
phenomenological lag in combustion. They find their resulte in close
qualitative agreement with the well known experimental facts. The
pres&nt work was completed in 1952 (results appearing in Otc:het GIFTI
[Reports of the Gorlkiy Sci.-Res. Physicotechnical Institute]). In
1953 a related work appeared on the problem of the excitation of
vibrations during slow propagation of a flame in tubes (B. V. Rau-
shenbakh, Zhur. tekh. fiz. 23, 358, 1953). Six references: e.g. Yu. I.
Neymark. Uch. zap. GGU, 14, 191, 1950; Ustoychivost' linearizovannykh
sistem (Stability of linearized system ), LKWIA (Leningrad Red Banner
Military Aviation Engineering Academy), 1949.
Institution Gor'kiy State University (GGU)
Submitted May 10, 1954

112-57-7- 1450 3D
Translation from: Referativnyy zhurnal, Elektrotekhnika, 1957, Nr 7, p 146 (USSR)
AUTHOR:_ Ney!T~ark-,-Yu. 1.
TITLE: Dynamics of the Relay Systems of Automatic Regulation (Mechanical
Automatic Systems With Dry Friction, Regulation Systems With Hydraulic
Constant-Speed Servomotor, and Other Similar Systems) (Dinamika releynykh
sistem aVtomaticheakogo regulirovaniya (mekhanicheskiye sistemy a,.rtornatiki
s sukhim. treniyem, sistemy regulirovaniya s gidravlicheskim servornotorom
postoyannoy skorosti i inyye sistemy podobnogo roda) )
ABSTRACT: Bibliographic entry on the author's dissertation for the degree of
Doctor of Technical Sciences, presented to In-t avtomatiki i telernekivin. AN
SSSR (Institute of Automation and Telemecha.nics, AS USSR), Moscow-Gor'kiy,
1956.
ASSOCIATION: In-t avtomatiki i telemekhan. AN SSSR (Institute of Automation and
Telemechanics, AS USSR)
Card 1 / I

501, . 14 Z--4
Translation from: Referativnyy zhurrial. MekharlLka, 195-1 , Nr 4, p(USSR)
AUTHOR: Neymark, Yu. 1.
T I T L E: On the Connection Between the Stability Characteristics of Open arid
Closed Dynamic 5ystems (0 svyazi ustoychivostey razoniknutoy i
7.amknitoy dinamicheskikh sistem)
PERIODICAL: Tr. 3-go Vses. matem. s"yezda. Vol 1. Moscow, AN SSSR, 1956,
p 61
ABSTRACT: Bibliographic entry
Card I/ I

L i rjy i,A-tr,I~,uriy ~s~, c;or I n I v i-1- -A -,!),,rl,evs',J -
aviarded sci de,-,ree -.f' Toc Sc lo" J~-,n t'-lt'~,nse -)t j. ~;s rt
,ynFnAcs ol r, s~,~~tr,.ms for ai,t-,,i~itic
t i ".b
systerns of aut or-~~;tjc s wi th cr,l i rio ti on, s,,rstems o; rr~ t~.
silvle-!ipo,-~d llyrlrvfu~i- sf~rvo uriit~i, wid otKor sirill x nt the
:tnki Tetifit.-chanics; AS, Prot 6,

NZYMAn, Tu.I. (Gor'kir)
V-110. 11 -On sliding process in control relay systems. Avtom. i telan.18
no-1:27-33 Ja 157. (tfiaA lo: 3)
(Zlectric r6lars)

HEyN)1)Ry\', ~u I -
AUTIM: None Given.
TITLE: c)f 33
jan--,-,ry - :uj-y ~'Zarn-a~- -7,11 lq-~
Sect 1 on eric F..,, er. t, r2 J kh
i~N, 33~21d, ~--)57, V-1 Nr 12, pp.
-.i' e f an -3 av,,omatikl
.ISTRACT.' itt th-; lns~lit, . .~;r arid -1
i tel3ne.',- n-'kj'. d~-gree---,f f -T-lciinical
3cLences! N. N. jautin Ncn!-,nP--7r problew of the aL:LjTatic -,~ntrol
thecu which aril-er- A-c~ c-.-rpe-Aior. vr),-,h thsi dyn-Lmics cll~:o-~kwork
regu atcl cf Wcl-k-,-ng zadmchi regulF
rtc~ulyatorov
-khoda), Yi.-. IT. ~V-rar~k- Dy,,,P-mirs of' '.1!9 ra-iay 3y5te!T12 (if rla',lc cOn=
trol ~)f dry fric!~isr,, t t--W with
a hYd.-lau:~~-c velo~~ity, ancl,
,DinamiL-.3. rp
-,~5?teq, a7r-,O-M9-tl0-,9lkOgD
kiye SiSt,(iffly ;.-,I k 3
dr;:~-,- I i c h e -, Ke r jr- %n r.-)
:f
go ro~a, AFplicat~
ces.' N. 0. - Thp
Card 1/1, tric, tract);-
eaekt rotralftox-,).

Defense of Dissertatiom.
,a
T nuary July 1957.
Section If Techni,;al Sc
3(D-12-4o/'t5
-.f I,he building priric4p!--.~l of - control sy=
V, P. Kazakor _ Elp~j)-
3tem vrith many 'Hazrab:tka -o3trDycr;--'Y;i mn-,gakanall=
rnreEtig,~t:-on --f tmo me=
noy siotsri5, M. A. Kc)rl-'.e-i _ T --
th--,d3 of 6tab-`liz :Lng th~l ~z~ptem~~ of automiati-c contr3l (Iissledova=
rt')e ivuY:ft 13 p,,. 1; 3bc, j7, 3 4i rp.'-~3ynyk~- 3:v~,7,matichesk,)go regu-
ii-rovaniya
At the Insti-tu'l- frr
the &q-(~
LrmEtigatf= of wa!~hlf-,,! de-p3ait6 ty G" ant
coal-rlninr_
A. D. f *~he e-P,"i teel.
ly decl-'P.'-ng layer,.: -,f lraving a f 2) m
lIssl-~d,:;vaniye k--~-*.-~paday-izhc'i-'k,-i rlastov
rp.
ilt thc.
nical V, K. -nlre5tigatic,n of the jj-cc..!:!s3 -)i* he-
-,erl:,7rantye
,.ing c' 11-Y meann, ~f -ur--ent (TS9
Uglya
Card 2/4 tses3a

Defense of Dissertation.
January July 1957.
Section Df Technical Sc -I
3c,-12-4o,/-J45
AL the Ins.it-.ite for of TransD:,-I, rrist~tut kompleks=
nykh trarsportrykh pi-c-blem'). Auplir~~tion fo." the degree of Doctor of
Techn-41-al Scienc!as: A. A. Sovuzclr of In-1-and water
transportation aperationo % a part --f TBM gk& tx--TY#rtaMx1 uuWo3:Iq'Organi=
zatsiya raboty v--iuIrE;rnF-.g-7) vnzdnf~gc, I,ran3pcrta kak chasti- YEdinw trans=
portncy set, 'SSSR).
At the Institut.p. for 11-acni.ne lr-cienoe (In,911-itut ma.:-:h!.nov9dp-nJya),, appli=
catiom for the deg.rpe of or-- _
i Technicai Science--,; M. A. Kitsparov-
The produ~~tion of a coupled hyzi-roturbine w-fth sluabie -,ranpa for high
pre83ure, and 4.-,s -Lnveatigat:~J:n 'Sozd,~-niye soc3noy povorotno-lopastnoy
gidrotuxbiny na vysokiye nappory i yeye issledo-ianiye). lu. B. Tqvis -
The study of the process of thp, grind,,ng of cylindrical teeth (Iss'Ledo=
vaniye prct3e,3sa zu'7,otocheniya teiiindi-icheskildh zul,~--hatykm koles).
Applicatiorl.3 fc-- th~ degree -~f Cand-idate c1f Tech.-.4-cal 3riences.' M. L.
DP-Ychi'," - "Tenso-netri~ation' (Terzometr-i-wan-,ye) and
generators -cLotlzrbin i G. Ly-ut=
tsau - Ii-vestig-at-l'or. c.-" th, re'laxation cf meta!3 at room tem=
perat,.2re by meafkiying methud,~ of the transversal. deformation and X-ray
Card 3/4 analys4-s (IssI.-dnvaniye napr3,azhc;n'Y v metallakh pri komnat--

Defense of Dissertation. 3o-12-4o/45
January Ju4 1957.
Sectio-a f Tech-nical Scienc,~f.
noy temperatur-. me-~,-,dam, i--,-~ereniya F,cperec.nnoy deformaTsJ-i i rentgeno=
analiza).
At the institat~~ fc.;- imeri A. A. Baykov .-Istit'it metaaur=
P
gil Lmeni A. c, iT,,- 'on e of Doctor of Tech
nica-- Sciences'. P. A. AJ-~k-qan,.~.rc- - Contradic-,,i:~r;3 in the modern deve-
lopment of blo-ming, and wa:,,3 of solving the problem (Protivorech a v
sovrerriefuiom napravleni-i bly'-m-inacv i put-i razresheniya, ikh).
M. A. Kekelidze - Irive.;t4.ga+,--'-on of ;Tiangane,3e ores from the me=
tal"urgical. prLn' of -,riew (1-Q91edo-.,&niye cii-at-,rskilch margantsevy1ch rud
F) meta1lxf-rji?hP,.skoy to,-.hK4-, 2~rpniya). Applin at ions for the degree of
Candidate c-f Terhnical Scierit-F'F,*. L. I. Ivanov - Elaborat4c,n and appli=
cation of the ineth~.,ds o1" .'ac~topo exchange for the f,horm,).1yn'amiCAl irrven
stigation of so:iie do-,-ibie al,-,y3 (Razrab-tka- ~~. primenenlye metoda izotopz
nogo obmena d1ya terTrndinaM4rhF!:.-~kog,, issledr-raniya nekotcrykh dvoy-nykh
splalrov). I. Yu. K(.)zhevn-;)(,-,%, - Investigation of the ther-modynamic reac=
tion of the deph031~h0r-'-,,ation of iron (Iss-1--dovan-'ye termodinamAki re-
aktsii d.~fo.3forat3li zheieza). G. A. Sckol.Dv - Visccslty, cris tall iz ativ.
on proce!~ses, and (-,.f primiary and finite blast-
furnace slags (VyazkDgt.'+, p---tses!~y kTi7,t.a.1-lizats1i i -,nineralogicheskiv
sostav pervirhriykh -~ k,:~np(.Ihr~~kh dwennyki,
AVAILABLE! Lib-rary of Congress.
Card 4/4 1. Control vmatioz- 2. Telemetry 3. Ceology
4o Inlard waterg-Trazisporte.tial 5. MetaUurgr

06515
SOV/141-58-L-5/14
AUTHOR: i.eymark, Yu..J.
TITLE: blethod of Point Transformations in the Theory of Nonlinear
Oscillations, Part I.
FERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy, Radiofizika,
1958, Nr 1, pp 41-66 (USSR)
JLBSTRAICT- The article attempts to give a systematic representatioi-_
some general problems related to the method of point
-i~ransformations as applied to the systems with an arbit-
rary number of aegrees of freedom. This is only the first
part of the whole work; the second part is to follow later.
The method of point transformations was first proposed by
A. A. Andronov and his collaborators (Refs 1-10) and was
applied by them to the problems of automatic control. The
importance of this method in the theory of nonlinear oscili-
ations and the theory of automatic control systems spurred
the author to collect the available material from various
sources and to construct a complete unified theory. The
paper is prima ily concerned with the problem of the stab-
ility of fixed points in a point transformation and its
relationship to the problems of the stability of non-
periodic motion and the states of equilibrium. The point
Card 1/7 transformation is defined as follows. Each point

06515 1'30V/141-58-1-5/14
Method of Point Transformations in the Theory of Nonlinear Oscillat-
ions, Part I.
M(XII X2,000xn ) of a geometrical system 6% is transforme'l
into another point M(Rll 22'...Rn of the system by means
of:
x1 fl(xl' X2,-'-Xn)
~2 f2 (xl,) Y-2,...Xn) (1.1)
xn =.fn(X11 X29..Oxn)
The coordinates x1, x2, ""Xn are the coordinates of IA
while X1. X21 ...xn are the coordinates of M The tran3--
formation is denoted by T so that the system of Eqs (!,I)
can be written as it - TM which means that the transformat;L)-
T is applied to the point M and transforme it into the
Card 2/7

06515 SOV/141-58-1-5/14
Method cf Point Transformations in the Theory of Nonlinear Oscill.,
ions, Part I.
point The transformation T can in turn be applied
to the point so that this is transformed into the poii-,L
9 . The point M is thus obtained by a double transformat,-
ion so that TE - T(TM) . The transformation which
i-,-7--_nsforms the point M into point M may be denoted by
Similarl . the m-th transformation is denoted by Tn . A
point 9.is said to be a fixed point of the traqsformation
T if the transformation transforms the point M* into itseIi4'.
that is, TM* M4 (1,2)
The coordinates x* xW ...X* of the fixed pcint M'O~ obe,-I,
1 2 n
the relationships defined by Eqs (1.2), which can be regard';
as formulae representing coordinaces of the fixedpoints if
the transformation. The e-region of the point M*~ is d.- ~f
ined as the ensemble of the points M for which the relatiun-
ship expressed by Eq (1-3) is fulfilled. The left-hand sidc~
terms of this equation can be denoted by O(M, M*) and it
Card 3/7 represents the distance between M and MII~. The fixed poirit.

06515 SJV/141-58-1-5/14
Method of Point Transformations in tne Theory of Nonlinear Oscitl.'i,
ions, Part I.
M* is said to be asymptotically stable ~dil "'ferentially) it'
it is possible to find a certain E;-region (e >0) for the
point M* which, when subjected to a multiple T trans-
formation COnVE!rges on to the point M* . This means that
for a4 arbitrai-y point not belonging to the small E-region
of M* it is necessary that:
p(Tmll, M*) < em (1.4)
where em4O for m-:),oo and max E;m40 for E-'010 The
fixed Doint M is said to be unsuable wlien for a certain
E;> 0 in the vicinity of the point M*' , there are points
M which go outside the limits of the E-reFion when the
T-transformation is applied. The stability problem is d1Js-
cussed on the basis of "Utle above definitions and it is de-
monstrated in a number of theorems. It is shown that the
Card 4/7

06515 30V/141-53-1-5/1,;
ME-thod of Point Transformations in the Theory of Nonlinear Oscill.,,--
ions, Part I.
coordinates of the point M* can be represented in a ca-non--
ical form by means of Eqs (3 2) which are derived by means
of the Taylor-series expansi;n ~see Eq (3.1)). When the
non-linear terms in Eq (3.2) are neglected, a linearized
transformation is obtained; this is represented by Eq (4.1).
employing this transformation it is possible to constrac.
So-called Lyapunov function which is given by Eq (4.~~"
0
The Lyapunov function is used to establish tLe stability
criterion for a fixed point. The criterion is used to a-na-
lyze the case of a linear transformation, i.e. when a strail-iit
line is transformed into a straight line. In this case it
is possible to give a geometrical representation of the
formation. If the motion of a system is represented by a s~..t
of differential equations of the type:
dxi X (X11 x t) (i 2,...n) (6.1
dt i 21,',x,;
where the functions I 1---Xn are either independent of time
Card 5/? or are periodic functions of time, then the system is

06515 1 -1-5/14
3011/141-58
Method of Point Transformations in the Theory of Nonlinear ascillat-
ions, Part I.
autonomous in the first case and non-autonomous in ttle latt~_,2.
It is shown that the motion of an autonomous system, repres-
ented in the phase space by a closed curve r , is asympt-
otically orbitally stable, if all the phase trajectories near
to the curve r tend to it asymptoticaily for t -> + ao A
periodic motion xi = (Pi(t) is asymptotically stable (in
terms of the Lyapunov criterion), if, for an arbitrarily
small positive e it is possible to find such 6 >0 that
for every perturbation displacement xi (t)'...R (t) for
t4GO the following is -always true:
1-i
x W - (Pi(t)l<
It is shown that the problem of determining and investigating,
the stability of periodic motion can be reduced to the proble,,2
of investigation of the stability of the fixed points of the
transformation. The relationship between the stability of a
Card 6/7

o6515 SOV/141-58-1-5/14
Method o' Point Transformations in the Theory of Nonlinear Oscilln-
ion,s, Part I.
fixed point of a transformition and the stability of the
equilitrium state of a sys*i~em is investigated and the resuit~,
are stated by means of theorems. The linearization of a poiji,,
transformation and its relationship to the variation probleml-q
is also discussed. The solution of linear differential equat,-
with periodic coefficients is investigated and its rel~ii-
1_)uship with the roots of the charELCteristic equation of a
corresponding point transformation is analyzed. Further, tbLe
relationship between various types of mapping (transformat-
ions) is dealt with and the Andronov-Vitt theorem is demon-
strated. The paper contains 9 figures and 31 references, of
which 4 are French, 2 Italian and 25 Soviet.
ASSOCIATION4. Issledovatellskiy fiziko-tekh-nicheskiy in3titUt Dri
Gor'kov universitete (Physics Engineering Research In5tal.
ute of WWGor'kiy University)
SUBMITTED: May 5, 195?.
Card Y?

MUKARK, Yu. 1.
Point tranaformatlou method in the theory of nonlinear 09011latiOnse
Part@ 2t Isvovyaouchebosav.1 radlofis. I no.2:95-227(,,158.
MA 11: U)
1. Issladavatellekly ftsiko-tekhnicheekly institut prl Gorlkavskom
univeraltate,

06!-476
AUTHOR: D~~ymark,__Xm,t_:K. SOV/ 141~ -L 5-6-20/28
TITLE: The Method of Point Reflections in the Theory of Non-
linear Oscillations~ 111.
PERIODICALS Izvestiya vysshikh uchebnykh zavedenly, Radiofizika.,
1958, Vol 1, Nr 5-6 pp 146 - 165 (USSR)
ABSTRACT~ A further instalment of the author's previous two papers
(Refs 40, 41) devoted to the stability and dependence on
parameters of periodi.c motions,~ Dynami~cal systems des-,
cribed variously as piecewise-linear, impulsive interaction
and discontinuously oscillating may be represented in terms
of the phase spaces (.1.11 where the transition from one
space to another must satisfy (1.2) and (1*3) in accordance
with the transformation (1.4). For systems with a small
number of degrees of freedom the geometrical interpretation
of this description is of spaces "glued together" as in
Figures la and 1b. The transi-tion between the closed
trajectories on the surfaces in Figure 2 is represented
Symbolically in (1.5). The motion described by a
trajectory is stable if all the roots of its reflection
in a surface lie within the unit cArcle and unstabla if
Cardl/3

06476
soy/ l.4 1-1-- 5 -6-201 ?8
The Method of Point Reflections in the Theory of Non-.1inear
Oscillations. III.
even one root lies out. side. In order to construct a
reflection a solution must be known to Eq (2.1) describing
the motion., This is best obtained as anacpan ion in terips
of a small parameter. This is best done if Sq (2.1) first
suffers a change of variable as in Sq (2.6). The
reflection of surfaces S and 9 in the neighbourhood of
points M 0 and R 0 can beabhieved by using the inter-
mediate t--surfaces as in Figure 3. Previous qualitative
discussions of the behaviour of single-dgree-of-freedom
systems (Refs 61-.68) have been presented in two-dimensional
phase-space. A study of theTay in which parameter values
influence more complicated systems leads to aft Lixterest
in the incidence of bifurcation. Two broad divisions may
be observed; autonomous, i.e. in wh:Lch. time does not
appear explicitly in Eqs (1.1) to (la2) inclusive, and
non-autonomous. The former may be further divided into
those cases in which the construction of point reflections
are posstble or not. rhe stability of a system is
Card2/3 conveniently determined by the manner in which it becomes

(-606
SOV/141, -.1-5-6-20/28
The Method of Point Reflections In the Theory of Non-linear
Oscillations. III.
unstable. The asympto-tic phase trajectories may vanisli
(Figure 6b) Or C011trikCt to Withill ft pdrtiCUldir rogiLon
(Figure 6a.),, The application of the method of small
parameters is much facilitated by the derivation of two
theorems in Section 5. There are 8 figures and 46
references, of which 4,,i are Soviet and 2 international.
ASSOCIATIM Issledovatel:skiy fi7-iko-tektLn1cheskiy institut pri
Gorikovskom universitete (Physico-teckinical Research
Institute of Goz-kiy University)
SUBMITTED: December 25. 1958
Card 3/3

SOV/109-3-11-2/13
AUTHORS: Neymark. Yu.I., Itaklakov, Yu.K. and Yelkina, L.P.
TITIE: The Circulation of Pulses in a Highly Non-linear System
Having a Delayed Feedbac,~ With Losses
(Tairkulyatsiya impul'sov v sillnoneiineynoy sisteme s
zapazdyvayushchey obratnoy avyazlyu, obladayushchey
dispersiyey)
PERIODICAL: Radiotekhnika i Elektronika, 1958, Vol 3, Nr 11,
pp 1348 - 1360 (USSR)
ABSTRACT: The generators with a delayed feedback have a certain
practical interest in radio engineering. A. generator
of this type (Figure 1) consists of the following
elements: 1) a non-linear circuit which can be described
by a non-linear fumetion, f(u) such that the input
signal can be expressed by
X(t) = f [u (t)j (1)
2) a linear circuit with constant parameters which can
be described by a linear response (p(t) so that the
relationship between its input signal and its output is
expressed by:
Cardl/6

SOV/109-3-11-2/13
The Circulation of Pulses in a Highly Non-linear System Having a
Delayed Feedback With Losses
Y(t) = (P ( t d (3)
-00
and 3) a delay circuit which is described by:
UM = At - 00 (4)
where m denotes the delay time. Eq (4) does not take
the dispersion (losses) into account but, together,
EqB (1), (3) and 00 can be used to describe also a
losay system having a delayed feedback. The solution
of a number of problems relating to the generator of
Figure 1 can b7e effected by employing the method dev-
eloped by one of the authors (Refs 12, 13, 14 and 15).
For the purpose of analysis, it is assumed that the
characteristic of the non-linear element of the generator
is of the 3-type, such as shown in Figure 2. This means
that for any input signal u(t) , the output signal
x(t) will be in the form of a train of rectangular
Card2/6 Pulses. Consequently, the output signal can be expressed

SOV/109-3-11-2/13
The Circulation of Pulses in a Highly Non-linear System Having a
Delajed Feedback With Losses
by Eq (6), where t are the time instants at which u(t)
reaches a value 6 and at which x(t) changes abruptly
from Izer6' to bnd or rrom "ond' to Izere. The signal at the
output of the linear element can be expressed by Eq (7) and
the output signal is given by Nq (8). The above equations
can be used to analyse the operation of various generator
systems. In particular, when each operating cycle of the
system consists of I pulse (this is shown in Figure 5),
the basic formulae are given by Eqs (9) and (10). In these,
tn and t a denote the instants of the commencement and
1 2
the termination of a pulse corresponding to the n-th
cycle. Eq (9) shows that the leading edges of the pulses
have a repetition period, as expressed by Eq (11).
Eq (10) determines the duration of the n-th pulse in
terms of the duration of (n--l)-th pulse. Eq (10) can be
written as Zq (14), where -~- a denotes the duration of the
n-tb pulse. This can further be written as Eq (15). On
the basis of the theory of oscillations and the problem
Card3/6 of iterations (Refs 16, 17 and 18), it follows that the

SOV/109-3-li-2/13
The Circulation of Pulses in a Highly Non.-linear System Having a
Dela,yed Feedback With Losses
solution of Eq (15) is stable provided the conditions
expressed by Eqs (l?) and (19) are fulfilled. If the
system contains multil--pulBe cycles, the relationships for
the inception instant and the termination of the i-th
pulse are expressed bj Bqs (22) and (23). These instants
for the n-th cycle (consisting of m pulses) can also be
expressed by Eqs (24). If rM . t 2m.-1 -t2m-2 and
zm = t2m - t2m-1 I where rm denotes distance between
m-l and m-th pulses imd -C M is the duration of the m-th
pulse, Rqs (22) and (25) can be written in the form of
Rqs (27) and (28). In order tv-o determine the cycle, it is
necessary to find the solution of these equations for the
case:
n n n-l r
r = r
M M B1% M M MRP
where the subscripiB i~kp relate to the threshold values.
Card4/6

SOV/109-3-11-2/13
The Circulation of Pulse8 in a Highly Non-linear System Having a
Delayed Feedback With Lossen
This leads to Eqs (29) and (30). The stability of the
system is therefore described by Eqs (31) and (32). The
above equations can be used to construct the so-called
cyclic function for Bingle-pulse and multi-pulBe cycles
for various values of 6 . The function is represented
graphically in Figure 7 where the duration of the n-th
pulse is expressed by. ~n-l)-th pulse. From the figure, it
is seen that for 6,,~ 0.5 , each pulse introduced into the
system gradually becomes smaller and finally disappears.
On the other hand, for values-of 6 0 and is independent of e .
Cardl/6 It is assumed that tiie input and output variables x(t),

80133
S/141/59/002/06/015/024
E196~E~8
Investigation of the Stability of Some s ri2buted Linear Systems
and y(t) can undergo Laplace transformations and that
the relationship between them can be expressed by:
Y(P) = K(p)x(p) (1.1) .
It is known that from the condition expressed by Eq (1.2)
it follews that the transformation F(p) of the function
f(t) is an analytic function of p in the semi-plane
Rep > d' and that for an arbitrary dl~ (Y , it is possible
to wri.te: 00
00
rf = I f 12 e-21-t dt f f 2 e- 2 Mt dt (1-5)
0
If rf = pf , thei following theorem is true: "In order
that a linear system be stable with respect to all the
perturbations x(t) , for which p x < +~ oo , it is necessary
that the function K(p) should be analytical for Rep > y
Card2/6

80133
S/141/59/002/06/015/024
F-6?2
Investigation of the Stability of Some XPRUted Linear Systems
and it is sufficient for the function to be analytical
in any semi-plane Rep _1- yl where y' O e_Yt jf(t)~ , 9f = Sup t N 0o- 't ~ f (t) (1-7)
for r= y it is necessary that the system should be
stable in accordance with Eqs (1-5) at r = Y and it is
sufficient that the function K(p) should be analytical
in any semi-plane Rep > y1 for y1.4 0 and that the
integral:
'~JdKj dp 12 P=iw dw
_00
should be convergent'. A system described by
Card3/6

80133
5/141/59/002/o6/oi5/024
36?2~pj�2t
Ixivestigation of the StOility of Some 3 u ed Linear Systems
2 %
8 u 2 du
a - - b- - c u f (u) (1-9)
at2 8x2 ax 0
dti n a! t. f (~lq
-L is ~n)
dt s=1 1, 2, 2) (1.10)
is considered as a general example. The system can be
linearized and the equations are then written as
Eqs (1.11) and (1.12). If it is assumed that the initial
conditions are 0 , Eqs (1.11) and (1.12) can be written
as Eqs (1.13) and The solution of this system can
be written as:
Card4/6 0 = K(p)A

80133
S/14l/59/oo2/o6/ol5/024
3b2j4V_j�2t
Investigation of the Stability of Some r u ed Linear Syqtems
where A and B are vectors and K(p) is expressed
by the matrix given by Eq (1-17). It is shown that the
solution of the stability problem is equivalent to the
investigation of the roots of the so-called characteristic
equation; this is expressed by A (P) = 0 . The above
theoretical results are employed to investigate the
stability of several systems. First, the so-called
problem of I.N. Voznesenakty is considered. The system
is described by Eq (2.1). It is shown that its
characteristic equation is in the form of Eq (2-7).
Secondly, a feedback amplifier containing a lossy delay
line in the feedback loop is investigated. The
characteristic equation of the system is in the form
of Eq (3.1), where J(p) is the transfer function of the
feedback loop. The stability of an automatic. co-mpressor
station operating between input and output mains of a gas
supplN system is investigated. The operation of this
Systeii/described by Eqs (4.1), (4.2) and (4-3)
Card5/6 A temperature controller is also considered. -The operation
L.-r

80133
S/141/59/002/o6/ol5/024
Investigation cf the Stability of Som�18234N829uted Linear Systems
of the system is described by Eqs (5-1) and (5*5).
There are 11 figures and 24 references, I of which is
English and 23 are Soviet.
ASSOCIATION: Nauchno-issledovatel.'skiy fiziko-tekhnicheskiy
institut pri Gor1kovskom universitete (Scientific-
research Physics-engineer-ing Institute of Gor'kiy
Universityj
SUBMITTED: July 2, 1959 V~
Card 6/6

80134
16, 9500 S/14l/59/002/o6/ol6/o24
AUTHOR: _Ujgqa~- ,k I- Yu. I. E031/E335
TITLE: A NA~merical Method for Determining Periodic Motions in
an,,,:'Automatic-control Syste 1~
PERIODICAL, Izvestiya v-ysshikh uchebnykh zavedeniy, Radiofizika,
.,1959, Vol 2, Nr 6, pp 989 - 994 (USSR)
ABSTRAC,t: A control system consisting of a linear loop and a non-
linear element is considered. It is assumed that there
is a periodic excitation at the input and that as a result
a periodic regime is possible. Then the output of the
nonlinear element is also periodic and Fourier series can
be written in all three cases. Further relations are
obtained by noting that the output from the nonlinear
element is the input to the linear loop. Apart from the
difficulty of writing down the equations explicitl-.-, a
further difficulty arises in that the system of equations
is infinite. The solution is approached by neglecting
higher harmonics and by making suitable approximations
in the non-11near terms. The period of the input excitation
is divided into a number of equal parts and the values
of the output of the nonlinear element at these times are
Cardl/3 I a -.I-

80134
S/141/59/002/06/016/024
A Numerical Method for Determining Perio�012100Mns in an
Automatic-control System
obtained by the method of least squares. After
substitution of the input expressions in the output
expressions we arrive at the required approximation.
This will give equations for the amplitudes of the
harmonics and a similar procedure will give equations
for the values of the input excitation at the discrete
moments of time. A particular example is considered
consisting of a linear centrally stable loop and a non-
linear loop with a symmetric characteristic. Two sets
of equations are obtained, each of which is inconsistent
(corresponding to two guessed values of the frequency).
Each set is solved by omitting the last equation and
after substitution in the last equation, interpolation
gives a new value of the frequency. Thus, eventually,
a value of the frequency is obtained for which a consistent
set of equations exists. This is then the required
frequency.
Card2/3

A Numerical Method for Determining
control System
80134
S/l4l/5q/oo2/o6/oi6/o24
Per'100HLOANions in an Automatic-
There are I figure and 21 Soviet references.
ASSOCIATION: Nauchno-issledovatellskiy fiziko-tekhnicheskiy
institut pri Gorlkovskom universitete (Scientific-
research Physics-enginecring__Institute of Gorlkiy
University
SUBMITTED: July 2, 1959
Card 5/3

NZY19, RK, Yu. T.
Numerical method for determining the periodic motions of
automatic control systems. 1-,.v. vys. acheb. zav.; radio'ltz.
2 no.6-gRg-994 '59. (MrRA 13:6)
1. NAw-hno-tonledovatel'okly fiziko-toklinicheAty inatitut
pri Gorlkovnkom univerettete.
(Antomatic control)

-A

Thc

a ria 1 y
n
r i v;

2 1
a bc

Or; the
of Different-Lai Eq--~a~j? is c
".asc- Oc~-1,11-5 wi.~-~%
Eq 2, 1) s ;.-t-
Eq
def ined 'by E-1 k
Eq5 (2.22) h;,
~la
~ y t -0 m n
2
rhere art 1/ -~f~
'~- a r e F-, e n -I- ~i .
SUBI,,'T ETED: june I.- .

7
30V/20-127---6/-8
AUTHOR: -Ne YMSEt-4-~- -
TITLE- On the Permissibility of Linearization in Studying Stability
PEIRIODICAL% Doklady Akademii nauk SSSR,1959,vol 12711!r 5,PP 961-q64 (US3R)
ABS'MACT: Let the values of the functions u(t) and ,)(t) belong to the
linear normed functional spaces U and I-L . The operator which
makes correspond uniquely a u t) to every w( '-,), V!~-t , is
called a dynamic system W ~t is called the input and u(t)
the output. Let the out;ut u t~ = 0 correspond to the input
i")(t) - 0. The motion of the dynamic system which corresponds
to the input Q(t) 0 is called stable, if 11 u(t)1! < E
if 11 W (t) 11 9 Theorem : The linear dynamic system
t
(1) u(t) - G t '[7) Li (Z) d V
where G(t,11 is a linear operator, is stable, if
t 1
(2) sup 11 G(ti 9V-) 11 dC < + oo
t t0 to
Card 1/2

On the Permissibility of Linearization in "tudying
Stability
Then the equation
t
(4) u(t) ~ G(t,tvf(-U,U(-,)) +w(-t))dZ'
-00
is considered; let the solution for t