SCIENTIFIC ABSTRACT RUMYANTSEV, V.V. - RUMYANTSEV, YE.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001446020018-5
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 22, 2000
• Sequence Number: 18
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT


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v V,
'-:u -a JE G- IUSSR/MATHEMATICS,,/l)if-Li~~uc-zitiaI aq-txatloua C11M I /I pa 111.
AUTHOR RUUJANZEY V.V.
TITLE The stability of the permaneat rotations of a heavy rigid body.
PERIODICAL Priklad. Xat.Mech. 20.. 51-66 (1956)
r-3viewad 7/1956
The author 4pplies Liapunov's Urect method to the izvostigation of the.
notatilAty of $he totions ~ bf, `4 heavy iigid body *ith a fixed point., The. six
EuIer-Folason equAtions of motion inliegrale v '~- conett
possess car
.1y2- ocnqtj 7. 3 - 0. According to detajoy's arrangement the LispuAor function
is a0ustruated iA.the form
V v 2 63vi + 'T 3 + V3
Here. la the angalar valoaityl *?tis -a aouBtant..depazding on,W the moments
of Inertia and on the- e-oardInates of the -c-enter af. gravityl JA an arbitrary
constant. From Ahis several sufficient exiterin of stability. axe given for
Permanent, rwia:tions. The general.. case of arbitrat7 distribution, of masses is
considered. as. well as a series -of. special aaaes.: In &a illustative way th*
ra.nges of stability are determined on the coze of the permanent axes. The
ol~taJ_ued results are illustated by tumorous exampleat e.g. for the conditions
of S.Kovalevskij, Stecklov, ff.lovaleTakl and in hiriher integrable cases,
INSTITUTIONt Moscow.

L)
SUBJECT USSR/MMMUTICS/Differ-ential equations CARD 1/2 PC -,692
AUTHOR
TITLE On the stability theory of control systems.
PERIODICAL Priklad.Mat.Mech. 20, 714-722 (1956)
reviewed 4/1957
Let the automatic control system with several control elements
n k
b + hip f
z
0(=1
ri
=Z
i-1
be given. Here b h are constants, control parameters and
. i,~zI Pi ep ~
,f A(1~,&).continuous functions which satisfy.all the,conditions which are
necessary for the uniqIueness of the.solutions of (1)) f,5(0) - 0. 1?urther-
more -]::Ek-B>A.
ASSOCIATION: Mechanical Institute, Acad.Sci. USSR (Institut mekhaniki
AN -SSSR)
SUBMITTED; April.8, 1957
AVAILABLE: Library of Congress
~CARD 1/1
1-0

AUTHOR: Rumyantsev, V.V. (110scow) SOV/40-122-3-9/21
~TITLE: yof the Uotions of a Gyroscope in.Cardanic
bilit
On ~ta
~
Suspension cw..ii stoychivosti dvizheniya giroskops. v kardanovom
podvese)
PERIOD16AL: Prikladnaya matematika i mekhanika,1958,Vol 22, Nr 3,
pp 374 - 378 (USSR).
ABSTRACT: Starting from investigations of several authors the.author con-
siders in the present paper:the stability behavior of a sym-
metric gyroscope in Cardanic suspensionand thereby he takes
into account the influence of the masses of the.Cardan rings..
It is assumed that the external Cardan axis is fixed in the
space and vertical'. The internal Cardan axis is assumed to be
able to move in a horizontal plane. The center of gravity of
the system is to lie on the axis of symmetry of the gyroscope.
Under the given assumptions.now the stability of the vertical
position of the, gyroscope is proved by the construction of a
Lyapunov function. The Lyapunov function is obtained thereby
as a linear combination of the integrals of the problem. The
Card 1/ 2 following integrals are applied: 1. Theorem of energy, 2. the

On.the Stability of the Motions of a Gyroscope, SOT/401-22-3-9/21
in Cardanic Suspension
constancy.of the vertical impulse component and 3- the stabil-
ity of Ithe impulse component of the rotor in the direction of
the rotor axis.. I,.t~is shown that,the obtained stability con-
dition is not only sufficient but also necessary*
In a concluding chapter it is investigated how dissipative
forces takeeffect on the stability behavior of the gyroscope
mounted on gimbals. ItAs assum~5d that frictional forces are
effective around,the axes of the Cardanic suspensions. For the
special assumption on which these frictional forces were
based the motions of the system remain asymptotically stable..
This result is.even retained~ if the,masses of the Cardan
rings are subsequently neglected. It i's shown that in this
case the stability is identical.with the secular stability_
given by Kelvin.
There are 3 references, 2 of which are'Sovietg and I is.German.
SUBMITTEDs January 10, 1958
Card 2/2

16(1)
AUTHOR: Rumyantsev,V.V. (Moscow) -22 26
SOVAO -4-10/
TITLE: On the Stability of Motions of a Gyroscope in,Cardanic
Suspension.II (0b ustoychivosti dvizheniya giroskops. v
kardanovom podvese.Il)
PERIODICAL: Prikladnaya matematika i,mekhanika,1958,Vol 22,Nr 4,
pp 499 -503 (USSR)
ABSTRACT: In addition to the first part of the paper the author con-
tinues the stability investigations for.-the motions of a
heavy symmetric gyroscope in Cardanic suspension. While in
the first investigations the fixed external Cardan axis was
assumed to.be vertical, novr this axis is supposed to be ho-
rizontal. This case practically appears in many gyroscopic
instruments applied in navigation.
The investigation method does not differ from the methods
applied in.the first part of the paper. The components of
inertia of the Cardan rings,are considered. Starting from
an expression for.the kinetic energy the author calculates
the equations of motion.according to the method of Lagrange.
The existence of.thefirst integrals from the energy.theorem
Card 1/ 3

on the Stability of Motions of a.Gyroscope in SOV/40-22-4-10/26
Cardanic Suspension II
and from the theorem of momentum allowh the establishment of
a.Lyapunov function as a linear combination of the first iiR-.
tegrals. From the condition for positive definiteness of.the
Lyapunov function and of negative definiteness of its total
derivative with respect.to.the time the stability of the
motions of the gyroscope can be derived according;to well-known
theorems of Lyapunov and Chetayev.
Besides general investigations of this kind also the special
case is considered that the system turns through 90 degrees
around the internal'Cardan axis. In this case the planes of
internal and external Cardan ring coincide so that the system
loses one of its degrees OfLfreedom in this special position.
This motion is unstable as it is well-known. The instability
can be read from'the Lyapunov functions
Furthermore a practically interesting case is investigated in
which.thefixed external Cardan axis is :onnected with a sup-
porting motor. The moment of the supporting motor can be chosen
so that the rotoraxis of.the gyroscopic system maintains a
constant posi-kion.in the space. An investigation of,the sta-
bility of this system shows that stable relations canbe ex-
Card 2/3

1004)
AUTUOR: Rumyantsev, V. V. SOV/20-124-2_~13/71
-------------------------
TITLE: Stability of the Equilibrium of a Solid Body,Which has
On the
,
Cavities Filled With a Liquid (Ob ustoychivosti ravnovesiya
tverdogo tela, i meyushchego polosti, napolnennyye zhidkostlyu)
PEPIODICAL: Doklady Akademii nanuk SSS 1lt,,1959, Vol 124,.Nr2, pp 291-20/4
(USSR)
,ABSTRACT: Short reference is first made to some earlier papers dealing
with thissubject. The present paper deals with the problem of
proving the Lagrange theorem for a solid body with liquid
filling. For this purpose the author.bases his investigations
iipon the fundamental work by A. M. Lyapunov. The aforementioned
liquid is in this connection considered to be homogeneous,
incompressible, and ideal. The position.of the solid with
respect to a certain immobile system of coordinates (Oxyz) can
be determined by, the independent coordinates qi(i = 1,...,n 0, where C C + C A A, +A
0 1 2 2'
W 02 G2z
if mass of the -system. If C > A , C A> O,then the,system is stable
too, even though the rigid 2body, 2alone were unstable for:A 1 >~.C
N~ G. Chetayev, S. L. Sobolev, N. Ye. Zhukovskiy and Lyapunov are
mentioned inthe paper.
There are 6 references: 5 Soviet and IFrench4
SUBILITTED: February 27, :1960
Card 2/2

PHASE I BOOK EXPLOITATION SOV/6201
Vaesayuznyy s"yezd po teoreticheskoy i prikladnoy mekhanike. IskMoscow, 1960.
Trudy Vsesoyuznogo s"yezda po teoreticheskoy I prikladnoy mekhanike,
27 yanvarya -- 3 fevralya 1960 g. , Obzornyye.doklady (Transactions of the
All-Union Congress on Theoretical and Applied Mechanics, 27'January to
3 February 1960. Summary Reports), Moscow, Izd-vo,AN SSSR, 1962.
467 p. 3000 copies printed.
Sponsoring Agency: Akademiya nauk SSSR. NatsionalInyy komitet SSSR po
teoreticheskoy i prikladnoy mekhanike.
Editorial Board: L. 1. Sedov, Chairman; V. V. Sokolovskiy, Deputy Chairman,
~G. S. Shapiro, Scientific Secretary; G. Yu. Dzhanelidze. S. V. Kalinin.
L. G. Loytsyanaldy, A. 1. Lurlye, G. K. Mikhaylov. G. I. Petrov. and
V. V. 11-umyantsev; Resp. Ed.: L. 1. Sedov; Ed. of Publishing House:
A; G. Chakhirev; Tech. Ed.: R. A. Zamarayeva.
Card l/ 6

Transactions of the Ail-Union Congress (Cont.) SOV/6201
PURPOSE; This book is intended for scientific and engineering personnel .~ho
are interested in recent work in theoretical and applied mechanics.
COVERAGE: The articles included in these transactions are arranged by
general subject matter under the following heads: general and applied me-
chanics (5 papers), fluid mechanics (10 papers), and the mechanics of rigid
bodies (8 papers). Besides the organizational personnel of the congress
no personalities are mentioned. Six of the papers in the present colleation
have no references; the remaining 17 contain approximately 1400 references
in Russian, Ukrainian, English, German, Czechoslovak, Rumanian, French,
Italian, and Dutch.
TABLE OF CONTENTS:
SECTION 1. GENERAL AND APPLIED MECHANICS
Artobolevskiy, I. I. Basic Problems of Modern Machine Dynamics 5
Bogolyubov, N. N., and Yu. A. Mitropollskiy.' Analytic Methods of
the Theory of Nonlinbar Oscillations 25
Card 2/ 6

Card 3/6

89383
S/040/61/025/001/002/022
B125/B204
AUTEOR- .-,Rumyantsev, V. V. (Moscow)
TITLEt The stability of the motion of gyrostats
PERIODICAL: Prikladnaya matematika i mekhanika, v. 25, no. 1, 1961, 9-16
TEXT: The author investigates several.motions of,heavy gyrostats with an
immobile point by employing the second.Lyapunov method. The body S1 has a
fixed point 0 at the originof two recItangular s stems of coordinates:
the axis of the immobile system.of coordinates 010 has anupward vertical
direction, and the axes of,the moving system of coordinates Oxyz shift
with the principal axes of inertia.of the gyrostat S with respect to the
latters' fixed point 0. The equations of motion of,this heavy gyrostat.
readi
Card 1/6

89383
S/040/61/025/001/002/022
The stability of the motion... B125/B204
dki
A + Tt + (C - B)qr + qk - rk P(Z y
dt dk2 3 2 o 2 0r3
B~A[ +T- + (A - C)rp + rk, - pk P(x z
t 3 or3 oyl)
C dr +d~ + (B - A)pq + pk - qk P(yoTj - x,f2)
dt dt 2
R is the weight of the gyrostat; the constants x ty 'z are the coordi-
0 0 0
nates of its center of mass; r1IT2 r T3 are the cosines of. the.angles
between the verticals Ofand the fixed axes x,y,z. For the cosines,
d
d ri -r2 Y3
= P r (1.2) holds. These
dt -12 -13' dt r ri -dt
equations (1.1) and (1.2), howeverr in general are not sufficient for a
complete study of the motion of the heavy gyrostat, and,inaddition, the
equations of the relative motion of the body S are required, which
2
depend on the shape of the body S 21 on the characterof the conditions
Card 2/6

S/04 61/025/001/002/022
Y
I T4e stability of the motion... B125
B204
imposed upon it, and on the forces'acting upon it. If the vect6r k s
known from the beginning, or especially if it is constant, (1.1) and (1.2)
suffice for investigating the motion of the gyrostat. The -following are
~
sev6ral first-integral
s of the.equation of motion of the gyrostati If the
internal forces:acting upon S have a force function U, and if the condi -
2
tion!3 are stead one obtains for the integral of the energies
y
2 2 2
-U) + 2P(x +y
Lp , + Bq + Cr + 2(pk +qk +r,k ) + 2(T +Z const.,
2
1
3 2 oyl OT2 oT3)
1
.
H-2re T is the kinetic.energy of S -in its relative motion. With kint cons
2
2 ~'A
j
2 2
the first integral reads: Ap +Bq +Cr + 2P(x const (1-4
ofl+YOT2+'of3

The surface integral is (Ap+,k.,)T,+(Bq+k +1 (Cr +k const (1-5)t
2)T2 1 343 =
and the integral characterizing the constancy of the angulat momentum reads
2 2 2
(Ap k + (Bq k + (Cr + k const (1.:6). From (1.2) follows
+ 2) 3)
2 2
+ + 1. The second part deals with the stability of,the
permanent rotations of a gyrostat (x
i(i 1,20) are given
=yo=zo-O), if k
o
i__SLard

-----------
89383
S/040/61/025/001~6~2/022
i 'The stabili.ty of the motion... B125/R2O4
constants. In this case, N. Ye. Zhukovskiy gave the first geometric
interoretation (Ref. 2). The author, however, studies stability by the
direct Lyapunov method. The- permanent axis is assumed to have an uncbarzed
position within the body, which is assumed to be determined by the direc-
tion cosines d,p,y-in the mobile axes; it then follows from (1.1) that
2 2
(C B)lr?Ta + Gj(pk3 ~k (A-C)ld,(j +W(Tkl-ak,) Of
2) 0'
2
B - A + k 0 (2.2). From hese equations the angular
2
velocity Q may then be determined. The equationsby Staude-Mlodzeyevskiy
follow herefrom as a special case. The equations of the perturbed motion
the first integrals
lead to
V, = A + ~pgl) + B (J,2 + 2qEq-) -c 0 ns t
V2 A2 (~12 + 2PE,) + 2
B2 (t 2 + 2qo~j) + C2 R3' + 2ro~,)
+ 2 + BA~
~3 + C4~ 3) - cODst-_
and the corresponding Lyapunov function reads-
Akj Bkt t. + _~qks E't
V XV, + -W7 r0
A
Card 416

8
S73 3
04
0/61/025/001/002/022

The stability of the motion...
BI 204-
25 13
Ilext, the stability of the rotation o f a symmetric gyrostat (k B,
X0 =YO Of z0/ 0, k1 k2 - 0).is studied. 'Fo rthe f
irst integrals,
therc follows (4-7) and for V (4-8). .
The results fo6d for k const
(i.= 1,2,3) are also applicable.to he avy bodies, multiply connected,
having cavities entirely filled with perfect homogeneous liquids
(Yiith~eddy-free motion).. According to N. Ye. Zhukovskiy, the equations
of motion~of'such a gyrostat have the form of.Eqs. (1.1). There are
6 references: 5 Soviet-bloc and 1 no n-Soviet-bloo.
SUBMITTED: November 14, 1960

Card 616

29408
005
/003/Oo4
S/055/61/000/

4100 ,
,
D205/D303
AUTHOR: Rumyantsev, V.V.
TITLE: On the. motion of some systems with non-ideal constraints
PERIODICAL: Moscow. Universitet. Vestnik. Seriya I. Matematika, Mekhani-,
ka, no. 5,~1961, 67 75
TEXT: The author considers the motion of a system consisting of
points P-9 of~ masses m.9 , with respect to some Cartesian coordinate system,
the coordinates of those points being x -.) 9 Y-0 I ZV (-v = n). The force
acting on the Y..Differentiating.theequ.ation of con-
points is E.,~ (xv YV z-O
straints with ,
respect to time
a x% z + e
b
0
yl~ + e
, B py
,
S V 1
s
s
ey
V
where a .... e are functions of given coordinates velocities x1V alp zt,,
'points P,) and time t. The sum.of elementary work of the reactions of ideal
constraints is

Card 1/4

29408
S/055/61/000/005/003/004
On the motion of D205/D303
+ N Sz 0, (3)
E(N x6X + NVY Sy.P V7,
An assumption is made that displacements determined by
X)) + P rV 6 yy + I-r-Y 46 z v0,r q,
V
are among those possible for a system with non-idial constraintS.C~
are known functions of coordIinates and velocities of.given points..rlyhese
are called (A) - displacements. The necessary and sufficient condition for
their existance is given. The equation
RVxSxIIj + RVY0YV +RVz 6z,)) 0.
can be regarded-as an axiom of non.-ideal constraints. The sum of elemental
'work of forces F9 and the inertia forces on any (A) displacement is equal
tO 7ero. The Gaussian principle is obtained for such systems. Theorem 1 -,
'The deviation of the actual motion of a system with non-ideal constraints
from any (A) motion is less than thedeviation ofthe latterfrom the true
,Card 2/4

:2y)108
-9/055 61/000/005/003/oo4
On the motion of D205YD303
motion of a system free from all constraints. Theorem 21 The deviation of
the actual motion of a system with non-,ideal constraints from.the actual.
motion of a system free from any constraints is less than the deviation of.
the latter from any (A) - displacements. Appell's equations can be derived
from the Gaussian principle and an equation of motion of a system with non-
ideal constraints is obtained
QF + P2 D (22)
gqlo > r rp
r
where Dr are known functions qif q! (j 1 ... k), t and T-_Dr
r p Solving the last equation=16q'I Sq It0
2* r
C 9qIIf (23)
Sqr rs s r P2
s P2+
Card 3/4

16 L39
S/04 61/025/004/018/021
D274%3061
AUTEOR: Rumyantsev,.V.V. (Noscow)
TI 'IU: nie stability of certain types of gyrostats
PERIODICAL. Prikladnaya matematika i mekhanika, v. 25, no. 4.
19611 778-784
TMCT: Four types of heavy gyrostats are considered which are sup-
ported by a fixed horizontaL plane. Type 1; The gyrostat consists
of rigid body S, and rotor S2- : The axis of S2 coincides,with the
axis of.rotation of its inertia ellipsoid. The equationof motion
Of S2 with respect to S I is given. The amount, of momentum G of the
gyrostat with respect to any paint is equal to the, geometric sum
of the moments of momenta ?f.Sl and S,)., A modified, ri-j"id body is
considered, obtained by joinino -to S 7an inf initcly thin rod - of mass
Q L
m2 and -center Of 9ravitY It .02 (m2 and 0,) are also-. the mass and cen-
ter, oEgravity Of S2)-' A formula is obtained for the moment of mo -
:-Ilentum. of the modif ied bodl,t which shous that if the gyrostal: has a
Card 1/6

i?
S/04016L/02.5/004/018/021
Me stability of certain typess.... D2747D306
fixed point 0, then its equation of motion have the forift of.equa-
tions (1.1).of V.V. Rumyantsev (Ref. 1: Ob ustoychivosti dvizheniya
girostatov, PM1, 1961. v. 25, no. 1), all the~results therein con-
tained being applicable to system SIS.3. (for the case- ki '= const.,
ki being the projections of the unit ~e'ctor oil the rotor axis);
'rype 2: M motion of the Gerve Z-Abstracter's note: Russian trans-
literation
"J gyroscope ir. consideredon an absolutcly smooth hori-
zontal plane, under the effect oE gravity. The pertinent theory
was developed by Carvallo on the assumption that S~ has no mass;
taking into account the mass leacts to a more complicated theory.
From the integrals of energy and areas one obtains
(b + e cos29) (1 4 c cos2Q) Gt2 0 - a sin 8) (1 + C C082g)
C2-'., COS g)2 (2.5)
where
a b, =L~" C C - B~ c2 L21 C a 1-112 h, r4 k
B B B 13
M being ~thc mass oil the gyroscope, IL and Iz arbitrary constants.
Card 2/6

2 t I
S/040/61/025/004/018/021
The stability of certain types.... D274/D306
e the angle between zj and z, ti - the angular velocity. Eq. (2.5)
can.be integrated, leading to 'a hyper-elliptical,integral for(t
. '4,
thereupon, the angles '~ and.(X can be found by quadratures. ~ is
the angle between xl and x);~ Type 3. This.type differs from Type
2 by the design of the mounting only, which has an additional'degree
of freedom as com?,ared to Type 2. The stability of.vertical equil-
ibrium is considered, determined by
9 - 0' - 0, const, 0, 0, 0 const
( 34)
The function V is introdUced
2 t2 C,~v2 + ~Igalm2
V ~ V, + 9LV2 ~z AO L 4-
,2 2c_)2~ 316)
+ (C2 IIgl.) 912 +
+ B (1 + 4B) 2~kBGVell!
being some constant. According to Sylvester's criterion, the
V-function is a positive definite if
al .-. 0, C2 2~,2 - Bl,,E(! > 0
(these conditions were obtrilned by an appropriate choice of ,~J; the
Card 316

S/040/61/025/004/018/021
The stability of certain types..., D274/D3061
derivativel ;-rith respect to time, of the V-function.is zero, hence
:the V-function satisfies Lyapunov's sLability conditions. There-
fore condition (3.7) is the sufficient-one for'stability; it is
shown that this is also the necessary.condition. Condition LI 0
means that the geometrical center of the.supporting circular segment
should lie higher than the center of gravity of the instrument. The
second of the conditions (3.7) permits detennining the lowest angu-
lar velocity ~~ of rotor S2, for crhich the gyrostat is stable. This,
condition is compared with Mayyevskiy's stability condition Type
4;, The rigid body Sl has a spherical, base which touches.the support-
horizontal plane at one point only; (S, can be ahollow sphere).
The axis of rotor S2 is assumed as coinciding with the,Oz-axis.,The
equations of motion are Set UD, The V-function is introduced:
V - V1, + 2/AV2 + ~V3 + -L (C - 1~) I 2V3 2 (4.15)~
4
A (p2 4- q2) + 2AX (pyl + (92) + ~L(112 +'122): +
+ Cr" 12 + 2C' 113 JP2 + (C - A) ?,1.2 + 2 2 +
+ 11 (U2 + V2 + W2) + 2C r0 + (C A) 12(ryl.2 +'12 2 + 2)
a ).31 + 2 2
A2
Card,4/6

25139
S/040/61/025/004/018/021
The stability of certain types... D274/D306
where Mgal - (Cr 0 + C 2 COA, a I'beirZ the coordinate of the c6n-
ter 01 of the spherical base i-rith respect to the Oz-ayds.. Sylves-
ter's criterion leadsto condition
C - A A r0 2 + C2wro + Mg alt (4.'18)
t ) a' > 0
w1tich satisfies all the conditions of. Lyapunov* s theorem. If a < 0,
tlLe center of gravity of the body is higher than the acometrical
center 0, of the base. In that, case the rotation will be stable.
for sufiLiciently great angular velocities, if C1 > Aa. If a' -- 01
the center of gravity is above 01; the~rotation.will be 5tablVfor
any angular velocity, In the c Iase,of an absolutely smooth horizon-,
~tal plane, the necessar and sufficient stability condition is "'Tiv-
Y
en by (Cro + 02 ,.))21+ 41ZIgal > 0
There are 6 references: 3 Soviet-bloc and 3 non-Soviet-bLoc, whicF~_
ircludc'2 translation,-, into Russian. The reference to the English-
langua-c -oublication reads- as follows: S. O!Brien, T.L. Synre,.The
Y
instability of the tippe-top explained by sliding friction. Proc.,,
Card 516

B/040/61/025/006/001/021
D299/D304
AUTHOR: Rumyantsev,.V.V. (Moscow)
TITLE: On systems with friction
PERIODICAL: Prikladnaya matematika i mekhanikap v. 25, no..,6,
1961p 969 977
TBXT.- Pailnlevbls general definition of systems with friction is
adopted which holds for any experimental law of friction. Some of
Fainleve"s results are extended to nonholonomic systems. Gauss's
principle of least constraint is formulated for 2 types of such
systems: 'With implicit friction forces and without implicit reac-
tion forces (which is of greater interest). From Guass's principle-
the equations of motion of systems with friction*are derived. By
differentiating the'inithl equationsp one obtains.
+ a z e 0
(a X" + b Yl S. 1-1 ... fPt p Pi + P2)9.
s V. ST Bv 1)
3
where ay bf c and e are known f,unctions of.the coordinates x, y, z,
Card 1/6

.100610011021
S/040 /61/0?f
On systems with friction D299/D304 -
of the velocities of the points Pv(v,=,l, ...,,n) of the 3ystem*,
and of the time t.'The virtual displacements of the points P'V
rV
are determined by p independent relationships
(a Sx + b 0 (s 1#0~0010- (1-4)
V sv~y' + ev 6.z V
Below, an extension of Painlevb's results to.nonholomonic systems.
Mith friction is.giVeno In order that the sum of the elementary
work of a system of forces P P P on every virtual displace-
Vx1 vy, '0Z
Ment:of the system vanish, it is..necessary and sufficient that the
equalities
F~x F,, X'b'? F" I.e.7 (V n)
hold, where are coefficients which are the same ford ali thb
points of the system.,Further,'.the reactions RV are Considered. ft
is established that RV c an be* uniquely decomposeVinto 2 forces N
Card 21/6

;S/040/61/025/006/00.1/021.
On systems with.friction D299/D304
termined by the friction law. Assume the friction law is known.'
Then one obtains as the general dynamical equation of systems with
frictiont the.equation
((X. + Plz MVXV') 6XI + (Y. + ply M,Y.M) 6Y., +
V (2.2)
M,Z,N)6z,) 0
+ (ZV + PVz
From (2~2) it is possible to obtain Gauss's principle of.least con
straint for systems with friction. According to this'principle,
among all the virtual accelerations, the real accelerations of
points of a s_ystem w~th:friction,,minimize the function
i XV+P.~ Y
ZVI ( +PVV z p4i z
,A MV + YVIIY + V
2
c
and ednverBelyp the minimum conditions for the function A, whi h
satisfy-conditions (1.3), lead to the equations of motion. The equa-
tions of motion of systems with friction can also be expressed in
the form of Appellsequations. In.Eq. (2-5), the friction forces
Card 4/6

S/040/61/025/006/001/021,
On,systems with friction D299/D304
are, implicit, being c omponents of the reactions of constraints. It
is of greater interestv,however, to set up G leprinciple for
systems with friction without *implicitly. julding the friction for-
ces in the function A. It is assumed that among the virtual displa-
cementag there are displacements Wa satisfy the conditions
PVX SxV + WY SYV + Pg.szv = 0 (,P 1, n),. (3-1)
For these displacementsp therelation
(R Sx + R By. + R Sz 0 (3o2)
-4 Vx V VY V Vz 19
Z
holds. The set of virtual displacements which satisfy (3-1) are
called (c)-displacementes For any(c)-displacementp Eq. (2,2) becor
mess
((X M,2xvt 1
)Sx 19 + (YV m19 YV 8y" +(Z.~ MI) z 0 (3 o3,),
The.constraint reactionB do not enter this equation which con8titu-
Card 5/6

S/040/6f/025/006/001/021
On Bys,tems.with friction D299/D304
.tesp for systems wit#-friction, a principle analogous to the Eu-
ler-Lagrange prijoiple.,Procefding from Eq,,~(3-3)o Gtjpels princi-
ple is formulated, involving the following theorems. 1).The devia-
tion of the actual system with friction from the virtual (c)-motion
is smaller than the deviation of the latter from the motion of the
system freed of all constrain%. 2)~The deviation of the actual mo-
tion of a system with friction from the motion of a constraint-
freesystem, is smaller than the deviation of the latter from the
(c)-motion. Hence Gauss's principle for systems with friction has
the same formulation as for systems withouttriction, provided that
only ihe virtual (c)-motions are considered. The principle.thus
formulated makes it possible to readily obtain the equations of mo-.
tion of a system with friction. There are 9 references: 3 Soviet-,
bloc and 2 non-Soviet-bloc (in translation).
SUBMITTED: May 25, 1961
Card.6/6

i

----------- - -
AMINOVY M.Sh., red.; BOGOYAVLEXS~- A.A.P red.; KALININ., S.V.,
red.; KUZIMINT, P A., red.;LORIYE, A.I., red.;
MATROSOV, V.M., red.; RUMYANTSEV,,V.V,, red.;
SRETENSKIY, L.N., red.
[Proceedings of ihe iiiteruniversi~y.conference on the
applied theory of the stability of motion and on. analy#c
mechanics] Ti-udy Mezhvuzovokoi konferentsii po prikladnoi
teorii ustoichivosti dvizhenila i analiticheskoi mekhanike.
Kazan', Kazanskii aviatsionrqi in-t. 1964. 144 p.
(MIRA 16:12)
1. Mezhvuzovskaya, nauchnsys, konferentsiya po analiticheskoy
mekhanike i ustoychivosti dvizheniya, Kazan, 1962.

p
Acassion NR- Ar4o43294 6/0040/64/028/004/OT46/OT53
AWHOR: Rumyantsevp Vo V. (Moscow)
TITLE: Stability of motion of asolid body with a liquid possessing surface
tension
SOURCE: Prikladnaya matematika i mekhanika$ Y. 28s no. 4,, 1964,, 746-753
TOPIC TAGS: solid body, liquid, solid liquid., motion stability, surface tension#
satellite dynamics
ABSTRACT: In a previous work of the author (Prikl. matem. i mekhanika 26), ff6
(1962)),, theoremovere formulated which reduced the problem of stability of a
stationary motion including the case of equilibrium,, of a solid body with a cavity
filled completely or partially with an ideal or viscous liquid.. to the problem of
the least.changed potential energy. The surface tension was not considered. How-
ever, the latter is essential in many cases. ITheauthor expands his theory to
'.include the effect of. the surface tension. The., author is grateful to N. N.
Krasovskiy)r N. 11. Molseyer, and 0. K. Pozharitakiy for a dincussion.of the work.,
Orig. art. has: no figures and 22 equations.
-Card 11/2

W
ACC NR, AT60221175 SOURCE CODE:. uR/0000,/65/0.00/00,0/0153/ol6g
,AUIHOR: Rumyantsev, V. V,
iORG: None
TITLE: Investigation of the stability of motion of solid bodies with cavities.fill6'd
with a liquid
SOURCE: Vsesoyuznyy s"yezd po teoreticheskoy i prikladnoy mekhanike. 2d, Moscow, 1964
Analiticheskaya mckhanika. Ustoychivost' dviz,henlya. Nebesnaya ballistika,(Analytical
mechanics. Stability of motion. Celestial,ballistics);.trudy s"yezda, no, 1, Moscow,
Izd-vo Vauka, 1965, 153-169
TOPIC TAGS: motion stability, motion mechanics
ABSTRACT: The authortreviews various nonlinear methods recently developed for study-
jinG the stability OfVltion of solids with cavities partially-or complete~,v filled wit
]a liquid.. Most of the p~_o~~`dures based on development of,the ideas and methods of
Lyapunov. The various approaches to the problem are surveyed and the.effectiveness of
the vHrious method's in practical applications are evaluated. The generally accepted
!
definitions of stability are stated and the problem of stability of steady-state
imotions of a solid with a simply connected cavity partially or completely filled with
a homogeneous incompressible ideal liquid:is solved. Oric-art. has: 49 formulas.
ISUB CODE: 2.0/ SUBM DATE- OltDec65/ ORIG REF: 026
LC. K-:

LX
P
1
t
(_C
M
1
)/_
U, vaa( ~UT~
4
0 -6-7
UR/0040/66/030/001/0051/0066~J
5 1,j
(;
E
C
OD
E
~UR
:
dt~
WTHOR: Rumyantsev. V. V. (Moscow)

ORG:. none

qui
TITLE: On.the-theory of motion.of solids having cavities filled with Ii d
SOURCE: Prikladnaya matematika. I mekhanika v. 30, no. 1 1966, 51-66
XOPIC TAGS: motion equation, body having cavity,:liquid sloshin tmotion stabilityp
fluid mechanics:
YZ
-2114,V I
ABSTRACT: The motion of an absolutel rigid bod having acavitypartially or en-
on
tirely filled with an idealhomogeneous incompressible liquid,with surface tensi s
.analyzed; The.Hamilton Ostrogradskiy-r~rinciple of least action Is used,to derive the
equations of motion of such a body-m-liquid system. A simultaneous system of~differen-,
tial equations in Lagrange form'are.derived which,,with boundary conditions for:the
an
pressure and the kinematic conditions on the walls of the-cavity~~ d on the free sur-
face, describe the motion of the body-liquid.system. Expressions for determining.the
e of the liquid nid air"upon.th ity walls-are derived.
generalized pressure forc a e cav,
First integrals of the motion equations.'are'analyzed.under the assumptions that~the
,
forces applied to the body-liquid system are continuous and that the.coordinates.of.
the liquid particles are functions of their initial values and of time. From thel.-
equations of motion, conditions are sought~ under which the body-liquid system is in
Card 112

ACC NR:
,W6033207 SOURCE CODE: UR/0040/66/030/005/0922/093i-
jAUTHOR: Rumyantsev, V. V. (Moscow)
ORG; none
TITLE: On stability of stationary motions
SOURCE: Prikladnaya matematika i mekhanika,.v. 30,.no. 5, 1966, 922-933~
TOPIC TAGS: Motion stability, motion mechanics, mechanical system, maLhematic
Ianalysis
ABSTRACT: The question of the stability of stationary motions of hol Ionomic mechanicall
systems with cyclical coordinates has been investigated extensively by many authors,
but it.cannot be considered to have been completely exhausted. The presentarticle
examinE-~ the stability of the stationary motions ofholonomic.mechanical systems. Th
theorei,,s of Routh, Poincare, Kelvin, and Chetayev are used and certai n new results
arefound. The example of Yu. I. Newmark and N A. Fufayev (PM, 1966, t. 30, vyp.2
j.is studied as an illustration. It Iis shown tha; with proper selection of.parameters
in this example no peculiarities are discovered. Themethod developed in this paper
is characterized by,uniformity in approach to.investigating the stability of motion
Iof various mechanical systems and makes,it possible comparatively simply to derive the:
necessary and sufficient conditions of stationary motion stability. This paper states,
and proves two.theorems. Given the notation
Lq.,d 2.

ACC NR: AP6033207
> 0
a typical conclusion is that in the case of.stability of stationary,motions of a
pendulum Vnen, in addition to gravity, dissipative forces with complete dissipation,
and constant forces balancing the dissipative forces in the stationary regime act
upon the pendulum, the statioAary motions corresponding to points of arm Cl with any
0 and a < 0, or 5 < a, and a > 0, of am C2 wgeb 8 > al and a 0 are secularly stable, and those corresponding to all other p oints or arms
C. are unstable. Orig. art. has:, 59 formulas and 1 figure.
SUBCODE:10/ SUBM DATE: 04Feb66/ ORIG REF: 014/ OTH REF: 003
Card 2/2

89-4-5-6/26
AUTHORS: Zeytlenot-11G A Rumyantsev, V.-.Y., Smirnov,V. L.,
Fomin L. P., &k'51_ovV. K. Grishayev, I. A.9
I
Zeydllts, P. Lt.
TITLE:, Principles of the Selection of the Basic Parameters of a
Linear Accolerator of.Electrons to fligh Energy (Onnovaniya
dlya vybora osnovnykh parametrov linoyn kh uskoriteley
y
clel~tronov na boltshiye ener-,,ii)
PERIODICAL: Atomnaya Eneraiya, 1950, Vol. 4, Nr 5"
PP. 443 454 (USSR)
A:MRACT: By a comparative analysis the dependence of the accelerator
Ion.--th, the number of sections, the input porler, the con-
strUction co~Asv and the possibilities of uscon the value
of the electric field otren.-th in the axis of the waveGulde
are shown. The section of the wave,-uide in this case is fed
i-idependcrtly T)y.-- high-frequency ~;enerator.
The minimuri of the construction cost and of the possibilities
C, d 1 3 Of use is not determined by the final enerCy of the, electrons.

62-4-5-6/26,
~'rinciples of the Selection of. Vie Chief Pararaetc.ra of a Linear Accelerator
for Electross of H-ii:'-h ErerGy
There is no relation between ti-.-ese points. It could, be shown.
that for the feediiij; of the accelerator sections a hij;h-w
frequency 6-eiierator with a power of nore than 2o IM is best
suited. The problem.of the increase of the duration.of the
useful p,,rt of tlhe.hij~h-frequency impulse.is ventilated. If a
rectan,,Xlar.wavecuide is used,Vae duration of the impulse at
the in-;)-,.it of the excitation line must be increased by the
amount of L/V
- L/C- Inthis case it is as uell necessary
l imit
t:a~ the hioh-frequency impulse reaches the amplifyin-- klystron
of the first section with a deceleration of the a--.1c amount.
For VuA purpose a special synchronizin- scheme is needed which
simultaneously transfers thephase shift to the other sections.
The relation between the duration of the useful part of the
impulse and the total duration of the impulse is independent,
of the final ener,-~y of the accelerated electrons
.There are
~'Card 2/3 .
13 fi..-;ures,l table and.2 references, 1 of whichis Soviet.

/275 /6/000/602/004/032.~;
-,-

JJTF
IORS: R11mvant
Levin Vj i(fiokfil, A~N.

*
~'iepafiov' S.M., Susletato _V K -Fomin
sev ,

-:and Chu
Ya, binskaya,
T V= Line ar'5-35 Mev electron- accdlerator~:~,with X-~ray~ -

:.-head f or
-madica purposes

PERIODICAL:
"Referati
vny'y zAiurnal i- El ektronilia i e' y e
r uskori'
no. 2 1963 -46-', abstract 2AM9 (Elekt on
te Ii,: 2omsk Tobskiy: un. t j .1961 -10 15,"~ 0301166tion))"'.

TEXT: ~u d.,
lse .,~a6 erator, 1~-: described h- 'f
cei T e requency~,.--i
t ie electron; ener y - ca
o,:E the microwave fie Id Is:. about~ 2800, N-c
smoothly,vary ~from o ~ 35 146V; _th6' mean ~:ele6tron, current 'in t ie
entire range- can I b Ie brought to :~18_-microampere.: The technicai':char--~;.
the. ',accelerator: are; described,-:-:. Them
acteristics"and the de1jign of `
accelerating -
system, the microwave aupply, the vacuum -system; and,,.
!
-acce erator~_.
the X-ray. head ~ device
are considerat! in detail'." All
the 1
-elements were .
tested-6ii laboratory_,s~tands and -~the 't-iorlc3*-rg.drawirLcEs.-I,-.,.~.
Card i/2

S~27%563/000/06VO04/02'1_._.
-D
Linear 5-35 M
ev electron: 301
0
f or the ent ire e quipmc:ht were given,over to~ a plant- f or- serial
production.
Z,~3stracter. S.,note: CorVle.te ,translat'lolft2
d,

- - ---------
B/161/62/004/011/020/049
B100102
AUTHOAt Rumyantsevg V. V.
TITU: Multiphonon corrections to the kinetic equation
PERIODICALt Fizika tverdogo tela, v. 4, no. 11, 1962, 3189 3201
TEXTt The investigation of the electron - phonon interaction in first
perturbation-theoretical approximation leads to theusual kinetic equation
1960). This equa-,
(0. V. Yonstantinov, and V. I. Perell, ZhETFj 39p 1971
tion cannot be applied-at high temperatures or where the electrons are
scattered from the impurities. In the present paper the corrections to
.the kinetic equations of the electrons in meta.19 'and semiconductol-a.are
derived for T)>-G, taking account ofthe.two4honon processes in the case of
a Fermi equilibrium distribution1unction by using a graphical method
developed in the above mentioned paper. After a lengthy calculation it is
shown that the corrections are of the type
-4- iS] [(2k-... is])-' X (13),
X 2rio (2k, k-ql-q3 toM
Card 1/2

S/1 BV621004101110201/049
Multiphonon corrections to the ... B104/B102
t
which describe the successive -interactions with two differ.ent phonon8 and
can be attributed, according,,to their magnitude, to terms.that are related
to the single-phonon scattering in the lowest perturbation-theoretical
approximation. One such term is
A-1CLO Ito
where a is the lattice constant, and E the energy. This gives for semj'-:
0
conductors urk/(-tT),and*for'metals aN a i,, found to be small when
the coupling constant, the energy and the,chemical potential are
renormalizable. The results of the investigations into other correction
types are discussed and shown to have little reliability. There are 4 fig-
ures.
ASSOCIATION: Fiziko-tekhnicheskiy institut im. A. F, Ioffe. AN SSSR9
Leningrad (Physicotechnical Institute imeni A. F. Ioffe AS
U55R, Leningrad)
.3 UBMITTED i June 21, 1962
Card 2/2

c-
L 46163-65 EWT(M)/EPA(w)-2/EWA(m)-2 Pt-7/Pab-10 1JP(c) GS
iACCESSION IFR: AT5007930
S/0000/64/000/000/0420/0424
V.
1AUTHOR: Vallter A. rif hayev, 1. Yemmenko, Ye. V.; Kondratenko, V.
lZe Kuznetsov, G. F.; I~vin, V. H.; Hqlyshev._I_
N.-i.; Sem~nov, A. U.; Turkin,-F. F.; Khokhlov. V. K.
TITLEz Ginear travelinp-wave accelerator of electrons with output energy 2 Gov
!50URCM International Conference an High Energy Accelerators. Dubna, 1963.
Trudy. 6-a-cow, Wt-o-mTz7i-at,-i79-64,42d 424
TOPIC TAGS: high energy accelerator, traveling wave electron accelerator, klystrwl.
ABSTRACT: The accelerator consists of an injector and 49 accelerating sections eact
4.5 mters long. The accelerator operates with a traveling 1/2w-wave with constant
phase velocity equal to the velocity of light a and group velocity equal to 0.04e.
The operating frequency of the accelerator Is 2797 we for a temperature of the ac-
celerating section equal to 370C. The-energy of the accelerated electron beam in
2 Gev, the mean current Is 1.2 pamp for a transmission frequency of 50 times per
second and duration of.the high-frequency pulse of T- 2 case, The high-frequency
power supply for each section is independent of the klyst amplifier. The *XCL-
rd 1/3

L 46163-65
~ACCESSIOU 11R: AT5007930
itation of the klystroh5 is carried,out from a common wave -guide line, which is
supplied from a high power klystron excited by a regulated master oscillator. The
,1group velocity of the electromagnetic wave'in the 'excitation line is equal to about
10.905 c. The constant phase of the electromagnetic wave at klystron output Is
maintained by a phaaing system with an accuracy of 4&0= 1120. The accelerating sec-
,tiona am inatalled In a sp,.-cial bunker which has a concrete wall-like shield and
I-) covorad on top by nectionnI rein forced -concre to slabs. The output installation
~in shielded by a special eavthen enclosure covered by minforcod-concrete slobs.
~Purification of the beam from harmful admixtures Is carried out by meano,of a mag-
inetic parallel transfer system and magnetic separators. The present report die-
'Cusses the parameters of the main units, such as: the Injector, the vacuum system
~(2-10~6 mm/Hg), the accelerator's h 'igh-frequency pulsed power supply, the output
~installation. the formation and measurement of the beam, the control of the accele-
irazor. It is planned to store the electrons and positrons which are obtained
by
ithe present accelerator in a suitable ring, but experience must first be,gained
~with small storage rings and colliding breams, under study at the Physicc~technical
Vr
.;Institute, Acadery of Sciences, Ukrainian SSR. The present accelerator was con-
structed-1ii -aci6REaii-ce with the principle of uniform structure. but eot constant
field. The entire adjustment phase of the large acceleiatorla operation is_carried
t_~ord 2/3

ILIX0 -06
ACCESS19N NF: AT5007931 S/0000/64/000/000/0430/0434
AUTHOR: Zeytlenok, G. A.; Lazarenko, Yu. P.; Rupyantsev, V. V.; Ryabtsov, A. V.1
iLevin, V. M. ------------
CD
TITLE: Selection of the optimum parameters of a linear high-ener electron
.celerator
SOURCE: International Conference an High EnermtJoAlaratom Dubna, 1963.
Trudy. Moscow, Atomizdat, 1964, 430-434
TOPTC TAGS: high energy accelerator, electron beam, waveguide
!ABSTFACT: Modern linear high-energy electron accelerators are complex expensive
devices. The problem of lowering their cost for given characteristics of the ac-
celerated beam is of foremost importance. In the present report, which proceeds
from the condition for minimum expenditure for equipment and utilization of the ac-
celerator, its optimum parameters are determined taking into consideration the beam
capacity. It is considered here that the cost of construction and operation of the
accelerator can be described by the formula
d S=A4L+A~V JAIveal
~77,
Car
_V3

where L is the length a in stem'; N is the ~Zumber. of sectiow
of acceler
t-.,g sy -a. and
s ~ t e total'tivia 6f.- rAt6io: A
are constants found from econ6mic analysis,"i is-' h-'
b
al., "Atomnaya ener-
;operation (from start-up to shut-down). [Go A. Eeytlenok et
ya," 4, No 5 (1958); PrOC.
Int'l Conf. High Ehergy Ace. (CERN, 1959)$ p. 349.]
(1) omits fixed expenses which do not affect the position of the minimum
!S and therefore can be disregarded. To formulate the basic problem, let there be
.1given coefficients Ais energy W. and mean current 1 41 of the accelarated*electron
lbeam; as well as the characteristics of the high-friquency power supply', the supply
1power during pulse. P, the frequency of the accelerating field w, the duration of
Ithe Pulse TK, and the.pulse repetition frequency no -It is required to determine the
Ivalues of t e basic parameters of the accelerator which correspond tolminimum cost..
of the accelerator 6: the accelerating field strength E 'averaged over the length
of the section, the length of one section Z, the acceleratorls.effe6tiveness n, the
n
-the problem pot
Igeometrical dimensions of the sections, etc. The solution of ed i
the report is given for two accelerating systems: 1) systdm-with field strength
that does not vary along the la 'ngth, Rz 9 av = const. p, 2) system with a constant
configuration for the wave-guide sections t6oughout the length, It is concluded
Card 2/3

L 12779-66 . EWT(1)/EWA(m)-2 IJP(c) AT
ACC-N-R, _AP5026605 SOURCE CODE., UR/0056765704970047f 33-
AUTHOR: Rumyanegeyj VV. VF 0
ORG: t~tut leniengradskiyl politekhni=g
institut)
.TITLE: Contribution to the theory of reflection of fast electrons
from conducting media
SOURCE: Zburnal eksperimentallnoy-i teoreticbeskoy fiziki, v. 491
no..4, 1965.0 1126-1133
TOPIC TAGS: electron energy, conduction electron,, electron ref lection,
electron interaction, transition probabIlIty
ABSTRACT: The author investigates the influence -of uction,
,~4q,cond
electrons in a solid on the behavior of the el-c Mf 1e a t ion coet-
.ficient as a function of:the energy transferred to the target.- In.
.addition to taking account of the interaction between the fast elec
tron and the latticeand.with the conduction electrons, allowanceis
made for the interaction between tbe,conduction electrons themselves.
The target is taken to be4n. n-type semiconductor,. so that the
electron-electron Interaction and plasma effects can be.allowed.for.
L--card 1/2

W'
A A 4 A %
.1 -----------------------------------------
lie A
p
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90
00 111
)72 MUXCTION AM, COMMM Of WATEPAMM PUT WITH O.K.K.
Sri MACHIRS. RoVantsov, V*Ya. (Torfyannaya ProsWablennost,
1949, (6), 18, 190.
o im coo
!*,,roe
zoo
:ii
40
7100
v
u w AV IS' A
0 r? tp tr OP 14, 1. a, lot a, onaIt a AM ;o
0 !q 0 0 0 0 so o 0 oo 41 00 0 0 Me 0 0 *so 0 0 0 0 es 0 0 6
1
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RUKYANTSEV, V.Ya., inzhener; GINZBURG, L.N., inzhener; RYABCHIKOV, M.Ta.,
A1iDRZOYBVSKIY, A.M., inzhener.
t
Mechanization of block peat production during l953 by enterprises.
of the Main Administration of the'Peat Industry. Torf.prom. no.2-
6-15 154. (MLRA 7:3)
1. Petrovsko-Kobelevskoye torfopredpriyatiye (for Rumyantsev).
2. Sverdlovskiy torfotrest (for Ginzburg). 3. Chernoramenskiy.
torfotrest (for Ryabehikov). 4. Orekhovskove torfopredpriyatiye,
(for Andrzheyevskiy). (Peat industry)