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AUTHOR I BXLXTSM VOITY 2- PA - 3o12 THE H Into abi ity of Equations of motion of a Solid Around a Fixed Point wider the Action of a Central Newtonian field of Fore*. (Ob intogriruysmosti uravneniy dvizhoniya tvordigo tola okolo zakre- plennoy tochki. pod daystviyom tsontraltnogo n1yutonovskogo pola ail. Russian) IMIODICAL Doklady Akadomii Nauk S88R91957, Vol 113, Ur 2, pp 287-29o, (U.S.S.R.) Received 6/1957 Reviewed 7/1957 ABSTRACT The present paper investigates the problem mentioned in the title un- der the assumption that the immovable point of the solid is situated in a distance R from the center of gravity large enough with respect to the dimensions of the solid. The equations of-tmotion of the solid under the action of the above mentioned forces are put down explicitly, they are a generalization 'of the equation of the classical problem of motion of a heavy solid round a fixed point. The theory of the last multiplier of JAKOBI can be appleid to the equation hors given and the- refore the integration of those equations is under certain conditions reduced to quadratures. 1) In the general case this system of the equa- tions ofmotion has three primary independent integrals, namely the en- ergy integral, the integral of the moment of the momenta and a relation between-the direc;tion cosines. 2) If the solid has a total kinetic sym- metry, the system of equations has a fourth integral in addition. There is also a four~th integral, if the solid has a kinetic symnetry around Card 1/2 any principal axis of inertia or if the solid is fixed in the center of Integrability of Equations of Motion of a dolid IPA - 3o12 Around a Fixed point under the Action of a Central Newtonian Field of Force.- gravity. The presence of certain terms in the equations of motion and in the primary integrals modfies the graph of motion in some ca- seB in comparison with the conditions in a plane-paraUel field. A solution for the two-dimensional motion of the solid is put down. (Generalization of the problem of the phyaical pendulum). If an ini- tial angular velocity is lacking, a solid fixed in the center of mass (as in the plane-parallel homogeneous field) will not be in equilibrium, but will move periodically. Then the special case of LACRIANGE is redu- ced to a quadrature. (Without illustrations). ASSOCIATION Department for Appleid Mathematics of the Mathematical Institute of the AWemy of Science of the U.d.ti.R. M123ZNTED BY ' *. ' ' L' K=18H, Mov*.* dUBMITTIO 9.9;19~6 AVAILABIJ& Library of Congress Card 2/2 AUTHORt Beletekiyj V.V, (140scow) 40-21-6-3/18 TITLE: 8ome qu estions of the Motion of a So2-td Body in a New-ton Field of Forces (141ekoturz7.~v voprosy dvizheniya tverdogo tela v n1yutonovBkom. pole sil) PERTODICAL: Prikladnaya MatematAlka i Mekhanika, 1957* Vol 21, Nr 6, PP 749-758 (USSR) ABSTRAM The motion of a gyroscope in a radial-symmetric field of gra- vity is investigated. Instead of the rigorous equations there is carried out an approximation so that the measurement3 of the body are assumed to be small compared with the distance of the body from the center of attraction. For practical applications of gyroscopes on the surface of the earth this condition is always satisfied. As in the calculation of the motion of a gyroscope in a parallel field of gravity, also in a radial-symmetric field of gravity different integrals of motion can be found. it is possible to reduce the problem to quadratures similarly as it is done in the cases of the gyroscopic theory calculated by Eitler and Lagrange. Diffe- rences against the well-known gyroscopiO theory are obtained in investigating the stability of a gyroscope which is sup- Card 1/2 Some Questions of the Motion of a S*:Ud Body in a 40-21-6-3118 Newton Field of Forces ported in the center of mass. For very small speeds of ro- tation of the gyroscope there result unstable motions even when the gyroscope rotates around the axes of the greatest or smallest principal moment of inertia. Of course, the gy- roscope becomes already stable for extraordinarily small speeds of rotation, so that the well-known stability behavior of the unsymmetric gyroscope results. The revolutions around the axis of the medium principal moment of inertia are always unstable even in a-radially symmetric field of gravity. The author investigates the case of the spherical gyrbscope and of the symmetric gyroscope. The results formerly obtained can be simplified in both cases. There are 4 figures and 9 references, 5 of which are Soviet, 3 French, and I Swedish. SUBMITTEDs April 29, 1957 AVAILABLE: Library of Congress 1. Bodies of revolution-Motion 2. Gravity-Applications Card 2/2 A Ski IHZI INS vt Az I Sal Vo 312 ", I! !I] JOE 331 2;1 -.' f k, :a V .311 -j- 45 g vh; Will Al BUXTRItTA 'a v jt~a&w.owl~kw-lk- Libration. of a satellite. Isk. sput. zem. no-3:13-31 159. (nU 12:12) (Artificial satellites) (Mechanics, Celestial) VAMIN, V.Ht; INIXTSKITe V.V. '"'a Using the anticipation method In observing an artificial satellite. loke spate soms uo*3t47-53 159. (WRA M12) (Artificial satellites) to, 25984 8/560/61/000/006/oO2/010 E032/E114 AUTHOR: Beletakiy, V.V. TITLEs Classification of the motions of an artificial earth satellite about its centre of mass PERIODICAL: Akademiya nauk SSSR. Iskunstvannyye sputniki Zemli. No. 6. moscow, 1961. pp. 11-32 TEXT: In a previous paper (Ref.l: same journal, No.1, idz-vd AN SSSR, 1958, p.25) the present author considered the motion of a satellite about the centre of mass without taking into account various effects leading to energy dissipation. In the present paper the theory is generalised by the inclusion of gravitational perturbations, aerodynamic perturbations and also orbit regression. The notation employed is said to be the same as that used in Ref.l. The paper is divided into the following sections: 1) equations for the secular motion; 2) interaction between aerodynamic and gravitational perturbational 3) effect of orbit regression. The motion is classified in terms of the locus of the and-point of the angular momentum vector L on a unit,sphere. Detailed classification is given of the various satellite trajectories in Card 1/ 4 25984 Classification of the motions S/56o/61/000/006/002/010 E032/E114 terms of the above locus. This classification depends on the given initial conditions and also the conditions under which the motion takes place. Aerodynamic effects, which would slow down the angular motion of the satellite, are not included. These will be considered in a future publication. The present analysis is based on the following considerations. The motion of the axis of the satellite in space is determined largely by the motion of the angular momentum vector. It was shown in Ref.1 that the equations for the secular motion of the angular momentum vector L can be written down in the form d?, sin a Wn- 0 sin 0 d~ IcTn = - where 2 X SiU2 e + sin Y (e, sin OdO Y - sin 0 ~kncos X'sin w sin i + sin X(kw + kj)cos i)j (1.2) Card 2/4 - coo 0 ks, coo w sin i 25984 Classification of the motions 0060 s/56o/6i/ooo/oo6/002/010 E032/E114 Theme equations describe the motion of the vector L relative to a set of coordinates which is attached to the perigee of the orbiti 0 representn the angle between L and the velocity vector at the perigee, and X tht rotation of L about the velocity vector at the perigee. This angle in measured from the plane of the orbit. In these equations the term containing represents the secular effect of gravitational moment. The secular effect of aerodynamic moments is represented by the function 9(e, %). The remaining terms in (1.2) depend on orbit regression, and hence the rotation of the above set of coordinates in absolute space. It is shown that the equation of the trajectory of the and point of the angular momentum vector on a unit sphere, whose centre coincides with a centre of mass of the satellite, in given byi 1 'V.cOs2 d"com 0 POC023 0 - kn -con Oo F Y This equation in derived subject to certain assumptions which, however, hold in the came of the Soviet satellites. In Eq.(1.8), e in the angle between the angular momentum vector and the Card 3/4 1 Classification of the motions ..... 25984 s/s6o/6l/ooo/oo6/oO2/0l0 E032/Ell4 direction towards the earth's north pole, 01 is the angle between the angular momentum vector and the normal to the plane of the orbit, a and 0 depend on the specific form assumed for the function (p (Ref.1), k(I in the velocity of the node, and k. is the velocity of the perigee. Eq. (1.8) includes effects associated with the simultaneous action of aerodynamic moments, gravitational moments and regression. The entire classification scheme put forward in the present paper is based on the detailed analysis of Eq. (1.8). There are 9 figures, I table and 3 Soviet references. SUBMITTEDs August 1, 1959 Card 4/4 26659 S15 6o/61/000/007/003/010 0 a (11 E032/EI14 AUTHORS: Beletskiyo V.V., and Zonov, Yu~V. ,rITLE: kot'a,tion and orientation of the third Soviet satellite 34,RIODICAL: Akademiya nauk SSSR. Iskusetvennyye sputniki Zemli, No.7, Moscow, 1961, pp. 32-55 .%XT: The third Soviet artificial Earth satellite carried a 'Is,~tlf-orientaringll magnetometer whose function waq to measure the Earth's magnetic field (S..Sh. Dollinor, L.N. Zhuzzov. iN.V. Pushkov, this journal, No.2', Izd-vo AN SSSR, .1956, v.50). ,rhe magnetometer Incorporates a movable frame whose normal is kept parallel to --he magnetic-field vec-tor by special probc-s and the tracking system. The rotation of the frame relatlVe tO fh.~- body of the satellite was measured by two probes and telemetereJ to the j,arth. The motion of the satellite about its cenlr-~ of trwii and also ite orientation in space can bf- ~.k-termined from the tmue d,r-pendence of these angles. The prosent paper descr:P.bes the method t1sed to solve this problem and also tbr- reiuLts ebitained for the rotation and orientation of the satellif-i up to the li,)4th orbit. rhe rotational parameters were determLriRd using these an.1 later otbit data. rhe first part of the prP!,,cn1 paper gives an account (,It I- d 1/ 11 Rotation and orientation of the .... i1560/61/000/007/003/010 E032/E114 of the theory of the method. The mntirin of a satellite about the oentre of mass is affectod by and aerodynamic moments (Ref.2i V.V. Bels~tskiy, thiv, Nc. 1, AN SSSR, 1958, p 215. Ref.3; V.V. Deletskiy, thts io,trnaI, Nr_-- 3, 1rd.vo AN SSSR, 1959, P-13. Ref.11:~ V.V. this iournal, No. 6, izd-vo AN SSSR, 1961, p. 11), m,7jm^n14.T (Ref.5: Yu.V. Zonov, this journal, No. 3, AN SS.SR, 1959, P. -118), possible interactions between womenti associated witl- currents within the socellite itself and the v,arth's magnetic field, e'tc. The mof irwn of the satellite is therefore rather complicated, -Othc_~uch ~.- the rotational kinetic energy is very much greater than tlto~- work done by the external forces so that in a finite incervai Gf time (for example, one complete orbit) the effect of the perturbing forces is small. Hence,in the first approximation -it may be assumed that within such limited interval of -time the motion of th- satellite about its centre of mass is identical with the motion of a free solid body upon which no external forces are act)ng. In particular, in the case of the third Soviet satellite which had two equal principal central moments of inertia, the motion of the centre of Card 2/11. 26659 Rotation and orientation of Che third..,5/56o/6,1/000/007/003/010 E032/Eii4 mass on this approximation wan found to take the form of a regular precession. The satellite's axis z'j which is assumed to coincide with the dynamic symmetry axis, executed a uniform rotation with a tonstant precessional angular velocity tV about the angular momentum vector L which remained fixed In absol-utp- space %'Fig.1). The nutation angle 0 between z and L wan r c, rt,~ 1 1 n t . Furthermore, the sAtellite rotated aboot uritjl~ i tonstant , -, XYZ is thf. abc-ol--t-i artesian frame angular velocity In F ix. I s,icb that the Z axi.s points in the direciion c-f ibe earth's pole, X points towards the Sprinz P'~)int L) i-A 11-e eing.'~ bptween L .-).nd the Y axis, and -jo Is the anje betureati ~hs- LY and XT planes. The problem can fl,.en be redl;ced f.( !1,i, detc~rmination of the parameters 9, f n r e a -.-b and also the determination of the angles 10 -Inij 0(1 c. f7 r .- ii ci n a PA precession as functions of time. The Anfl.-aiinrIr o:-f 1)-e magneto- ineter probes can be used to provAde i1.1 these. por-m('TPts, FiS.2 shows the arrangement of the mairritt-to-motor frampr.. The C,-,:C,,, where A' B and C, ara..,principal central. moments :b fL i~.L.4" ? 4 A r.," J- .2 3 4L Il f~Q ACCESSION.NRe. AT3006839~ inertii:~ o f' th e body., The.', results obtained -are formulated. as f o I..-I I equilibrium o f - -a: bo dy For the -re ative W on a circular- orbii _be-_s_ti6le,.' --:a- Ne ~ --that . -suf f icient T~: - ' o the.- durin :the,,, irection o ~nonpertur e ;nb t r, ax is f the maj ' elli-ps6.1d of, 'i.nertta coi:ncidi ''with, the direction of rtho ' iad iuz'~ve c to r'. of ~the: orbit. that- -th'ar-minor axi - coincide- with th s to... iract on' ot `:t he normal.,.,to the. 6.rb it plane, -',and that the intermAdia '-di _q tang n ' . 4~4 ,,t,o, ..t .,e !or ' ' .~Pd-rticu 9'e .of'~trans at 1 lar, c46 t- tion, ory-rq ary mo ' of whert the orbji - f, s of. -o mes -y the. t s is-plarte and: the -Axi er -11 the body coincides . -normal to~ -th he e. '*rb it plane's is studied t Ori g', art.,~~h . 4 figures :_'ASSOCIATI0N,.,- none- ~'- !' 06.k.ug6 2` DAtk,. ACQs', W- SUB MITTED : .ENCL,., 0 . , . .. ' 6 RE P- S 0 V. 0 11 --~UB OTHER: 002 Cjr ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������L-18275~63.----.'--.-.---EPA(b)/EWT(I)/ECC(w)/FS(v)-2/BDS/~EC---VES( v)---A~F-TC/~,.,- AFmDcFr:SD-3 APGC SSD,4-4/Ps-4/Pi-4/P0-4/Pq-4 'ACCESSION IN41: A-00 S 1%9/63 /000/016/0094/0323 AVMOR: 0khotsimskiyj D, Beletahly.p V, Vo TITLE Use of an earth,~oriented satellite for'oolar investigation SOURCE: AN SSSR. Iskunst, sputniki Zemli., no. 16,, 1963., 94-123 tru- TOPIC TAGS; satellite attitudep 6rbital element,, solar investigation., ins ment 13lumir ion., satellite instrumentation ABSTRACT: An analysis is made of solar Ilumination of instruments mounted on a seellite with triaxial stab to\-'one axis oriented to the earth., the iluat second along the normal to the orbital-plane., and the third along the trans- versal. A slight change occurs in the attitude of the orbit relative to the sun owing to the yearly motion of the earth around the sun and the regression of the orbital node of the satellite due to the oblateness of the earth. The problem of determining the total time of illi-ination is solved 1) by deeterm-1- ing the illumination time at, a constant angle v 1~eAw6en the direction to the sun and the normal to the orbital plane, and 2) by considering changes in' angle V vith time. Mumination time is the time the sun remains within the Card 1/3 L 18275-63 ACCESSION DR: AT3006840 61 i angle of view of the instrument. To solve the first part.. the maximal time of instrument illumination during one orbit of the satellite at given values of angle V and instrument angle.of view p and with a varying angle between the optical axis of the instrument and the axis o:r the vate=te is sought, It is found that the maximal illumination time increases as angle V decreases. The determinati-)n of angle V as a 'function of time makes it possible to establ-Ish its dependence on the angle of orbital inclination to the equatorial plane and on the initial conditions (hour and date) of satellite launching. For's, typical orbit (inclination to equator i = 650; period of rotation T - 90 min) the ;otal~ 0 time of Ulli-i-ation during a satellite lifetime can reach about 60 hr under optimal conditions and only about 15 hr for an instrument, vith an angl~w of viev of 5". Increasing the angle of view increases the iUumination ti=. The tot~_I.- time of illumination depends on the hour and date of lemnehing., the positiop of the.optuical axis of the instrument relative to the satellite., and the inclina- tion of the. orbit to the equatorial plane. - Optimization of the orbital elements', and progre d control of the position of the axis of the instrument can increase illumination time 2-10 times. The analysis rapports the feasibility of using earth-oriented satellites ford solar investigations. Orig. art. has: 25 figures' and 23 formulas. Card 213 ACCESSION NR: Ap4oo9621 S/0293/63/001/003/0339/0386 AUTHOR: Beletskly, V. V. i-TITLE., Evolution of spin In a.dynamIca Ily symmetrical satellite t SOURCE: Kosmichesklye Issledovanlya, v. 1, no. '3, 1963, 339-386 TOPIC TAGS: satellite, dynamically symmetrical satellite, satellite motion, 1i satellite spin, aerodynamic friction, aerodynamic pressure, satelliteshell eddy current, satellite magnetic field, light pressure, satellite shell magnetization, ~i artificial earth satellite ABSTRACT: A complete1system of equations in osculant elements it presented, as a continuation and expansion oY.prevlous reports (V. Ve Seletskly, Sb. lilskus3t- !i venny*ye sputniki Zemli", lzd-vo AN SSSR,.No. 6, 1961, 13-32; lbid, No. 1. 1958, 26-43; i-bld, No. 3. 1959, 13-32). to describe the spin of a dynamically symmetri- cal eatth satellite. The. osculAnt elements (see Fig. I In the Enclosure) are used! as system i n, or where moments of Interference forces are, respectively, indVendentof cc -dependent C, ACCESSION NR: AP40096il' on the angular velocity of Inherent spin Y A method of averaging based on one or two fast variables Is employed for simplification. The concept of "second' approximation" Is introduced and defined as a solution of equations In osculant elements averaged only for the precession period. The evolved theory Is employed I to analyze the motion of a satellite, as affected by gravitational forces, aero- dynamic friction and pressure forces, Its own magnetic field and magnetization of the satellite shell In the Earth's magnetic field, eddy currents in the shell, and! light pressure on a cosmic vehicle travelling In an orbit around the Sun. "rho author expresses gratitude to Do Ye. Okhotsimskly for his evaluatlon*of this -study". OrIg. art. has: i4%fLSures,, I tableg and 236 formulas. ASSOCIATION: none -SUBMITTED: OIjul63. ATD PRESSs 3047 t ENCL: 01 SUB CODE: BV9 ES NO REF SOW 013 orrHER:.o06: 21$ 1 A " S/640/63,/02 0 On, one: caae~;'.o P d. ~ A i 66tis se'd,4 Specl 10 a 19 Ve GV vem ' A iJ Jl, m ;~7 Y~ ka Card:::2/2 A_ BELETSKY. V.V. (Moscow) "Motion of an artificial satellite about its center of mass" report presented at the 2nd All-Union Congress on Theoretical and Applied Mechanics, Moscow 29 Jan - 5 Feb 64. GOLUBKOV., V. Vq YEGOROV~ V. A.; YERSHOV., V. G. (Moscow) "Investigation of flight trajectories with low thrust" report presented at the 2nd All-Union Congress on Theoretical and Applied Mechanics, Moscow., 29 Jan - 5 Fab 19649 S/0293/64/002/003/0360/0391 NR: A?4041562 AUTHOR: Beletskiy. V& V.; Yegorov, V. A. TITLE: Interplanetary flights wish constant-power engines !SOURCE: Kosmicheskiye issledovaniya, v. 2, no. 3, 1964, 360-391 '!TOPIC TAGS. interplanetary flight, space flight, space fl-ight trajectory, constant power flight, interstellar reaction vehicle .!;'ABSTRACT: The problem of interplanetary flight,(between the grivi- itational fields of planets) of a reaction vehicle with-an ion or !plasma-engine is studied, assuming that the'power input for generating ithe jet reaction is constant. A method for linearizing the equationsi ~of motion relative to some suitable known trajectory is used in the This method is called the "method of transporting inVestigation4, trajectories" and was initiated by'T. H. Eneyev. A-"transporting ;Coordinate system" moving translationally along the transporting 1: trajectory is used$, thus taking hecount,-Ln the first approxima-' Ition, of solar --Sravitaition* Plights..with optimum control of the- Card ACCESSION NR: AP4041562 reactive acceleration and flights with,a constant pcceleration vector's changing its direction in space by a sinRle jump are discussed. The speed and high accuracy achieved in computing a large class of interesting tra~cczories are the advantages of this method. The proposed,.method can be used for any type of control of i reactive acceleration. The authors express a sincere gratitude to D.'Ye. Okhotaimskiy and T. It. Eneyev for their assistance and N. D. Hyshetskiy, N. A. Malinina,*,hnd Ye. A. Sidorova for carrying out*the, computg.tiono, Orlg,, art. hos, '11 figures, 81 formulas, and I table,,* ASSOCIATION*. none ENCL: 00 iJ5UbKLTTEDz 20Feb64 A TD PRESS 1 3052 NO REY SOVt 003 OTUERt 001 1 SUB CODE:. 5V, PR 2/1 '!!ACCESSION NRI AP4041563.-.,. S/0293/64/0021003/03i2/0407,1 'AOTHORI Belsiskiy~ A Ve Vo;.Xegor 'V. 'TITLE: Acceleration of a'space vehicle in.the gravitational field of a planet SOURCHt KosmicheskLye; 1saVodoviniya; V, .2, io. 3, 1964, 392-407 TOPIC TAGSt space vehicle.'space vehicle.trajoeto yq reactive P T accelerailons acceior&tLon control, c.onstant, tangcnt'ial acceleration. ABSTRAM Trajectoftes of ii'spaci'.vehicle moving with a'small re- I active acceleration wLthLn.the gravitational. field of a planet are IdLecuseedo -An * approximate a o'Lu t-i dn'is presented for the variational problem of optimum control' of'-..,the -reactive accoliratLon to obtain optimum traJectories after'liftoff'until the parabolic speqd is reachad* Some of these trajectories are- L'I sttenfton',beLhg'~- on"alyzed, with.-aptc a aid to thos 19 CIO9G.T. to the optimal trajectories* Formula@ arb given p _ foi calculating thw, paraU4tAirs-,4of*',ths, trajectory at the and of Its- acceleration sectLons .,RssuIts'of'thig c9uputation of sous trajectorLos-' with constant taigentLa"Vrea'iti4ei acceleration up to~tha p6Lnt at 1/2' i C~rd N NRI AP404150.3. - :i which the parabolic-, sp4d .4s' ached 'argi presented@., " The aetbo lexpress their gratituda, to 0 8, Ry.xhinq, for'carrying out the* -pro- ju Glectroniq -c grammLng and nuu*rLcal(1calcu0tLanm;.ou ' ' omputore , 17 foraul4se d 7,: tables a test, torl; bass 6 41,84 V~ , 'ASSOCIATIONS none ~1059 SUBMITTE6 t 2OFeb6t 28901 IR XNCL 1'" 00 , ' 7 002 SUB CUSS 7 002 OT . ;q Ib ~v. 4t a 212 T. n ACbESSION NR: AP4041564 S'/'O'"293/'64/002/003/0408/0413. AUTHOR: TITLEs Trajectories of cosmic flights with a constant vector of reactive acceleration SOURCE: Kosmicheskiya iss.ledovaniyai v. 2, %~o. 3, 1964, 408-413 TOPIC TAGS: cosmic flightp cosmic-trajectoryp cosmic fligh.t tra- jectory, Newtonian gravitational field, planstrajactory, three dimeniional trajectory ABSTRACT: The possible trajectories of flight.of a cosmic vehicle' within a Newtonian gravitational field with a single'attracting center are discussed. The said'to be propelled by 'an ion., plasma, or similar engine ensuring thrust for a long period: The' I vector of reactive acceleration is assumed to be constant. Through the integration of equations of motion the problem is completely reduced to quadratures, and parametric equations of a trajectory are!- derived. The plane trajectories obtained are of four kindst l)-Un-, bounded., self-crosaing, notenclosing the center of gravitation; Card' 1 1/2 ME- M__ ACCH9SION Ni: AP4041'564*' 2) unbounded, self-crossing, enclosing the center of gravitation; 3) unbounded, not self-crossing; and 4) bounded trajectories* Three- dimensional trajectories can be classified in the same ways, Ori art.. has3 2 figures And 14 formula&. ASSOCIATION: none SUBHITTEDt l4Fob64 ATD PRZSSS,~ 3049 ENCLt 00 SUB COM SV No' REP SOVI 000 OTHERI '001 BELETSKIY, Vladimir Vasillyevich; ABASHEVA, D.A.,, red. (Motion of an artificial satellite relative to the cantor of'M'Age] Dvizhenie iskusstvennogo sputnika, otnositallno I tsentra mass. Moskvap Nauka,_196~. 416 p. (MIRA 19il) tcoe'd ACC NRa AN60122.00 Hionograph ''Beletskiy,, Vladizrdr Vasillyevich ~bvement of an artivicial satellite relative to its center of mms (Dvizheniye iskusstvennogo sputnika. otnositell nogo tsentra mass Moscow, Izd-vo "Ka%W', 65. 0416 p. illus.., biblio. 1,000 copies printed. Series note: Mkhanika kosadcheskogo poleta ...TOPIC TAGS: artificial Earth satellite, scientific satellitep satellite motion,, or-tellite navigation.. Earth satellite orbit., elliptic orbite4Vatorial orbit,, orbit perturbation., orbital aircraft,, artificial satellite PURPOSE AID) CCM=-: After the launching of the first artificial satellite and consequent success in the conquest of space, the interest rose sharply to other prdblems connected with ftu-ther space e-vlorations, in particular,, the important problems are those dealing-with the motion theory of artificial satellites. This book deals vith one pert of the cosmic Mght dynamics - the motion of artificial satellite relative to its center Of mass. The problems discussed in this book axe limited to the dynamics of solids, This book is based on other vowlis published cc presented by the author at the m*echanical and mathematical faculty of Ibscow UhIversity, The results obtained. by so= other authors ere also used in this book, Tipc,629.195.1 ACC NRt A~fO12200 TABIE CF CWBWTS (abridged): roraword -- 8 Introduction 9 Cho 1, AraLlysis of force moments affecting the satellite 17 Ch. II. Stabilization arA libration motion of satel1ite in. Newton field of force - 58 Ch. III, Effects of additional factors on the satellite stabi3ization and libration -- 122, Ch. 1V. Interrelation of, forword and rotation motion of solids in a Newton field of-force -- 145 Ch. V. Satellite's ratatign motion and equations of targent elements -- 175 Ch. VI, Effects of gravitation pertitbationB on rotation motion of a satellite 191 Ch. VII. Effects of aerodynamic perturbations on rotation motion -- 229 Ch. VIII. Analvois of secular perturbations together vith the effeats of 'gravitational and aerodynamic moments and arbit, evolution - 251 Q. IX. Effects of a magnetic field arA force moments of light pressure on the satell.ite's ratation and orientation - 290 Cho X. The motim of some launched artificial oetellites aroxmd their center 0 Maso - 317 ~L 53 Ch. X1. Use of an Earth-criented satelUte for expb=tion of the Sun rd ACC NRt AIAS01 22W ;,pp. I. Motion of a so2id. eround a fixed point in Newton field of force 379 App. II. Or'bits of an equatorial artificial sateLlite - 400 Bibliograj*W 411 SUB CODE SIMM DATE; t 090ct65/ CRIG MW% 073/ Card- 3A ULYUYEV, D.I., inzh.; BOLOTIN, V.I.,, insh., retaenaent;.JZj&jWWj, a&&, inzh., retsenzent; SERGEYEVA, A.I., Inih., red.; KHITROVA, N.A., tekhn. red. I (Handbook for the track maintenance worker] Posobis putevoma rabochemu. Moskva,-Transzheldorizdat, 1963. 322 p. (MIRA 16:8) (Railroads-Traft) (Railroada-Equipment and aupplies) DANILOV, Dmitriy Ivanovich, inzh.; PET.EMKTY- VsAyDjQdjUj%dimjrpjjO, inzb.; GORYANSKIY., Yu.V., kand. tsk~n. nauk,, retsenzent; ORALOV, V.A.,_insh., retsenzent; YFMROV, SiLy-Insh., nauchny7 red.; SOSIPATROV, O.A., red.; CHISTYAKOVA, R.K., tekhn. red. [Trailer and container vessels) Treilernye i konteine*ye suda. Leningrad, Sudpromgiz, 1963. 235 P. (MIRIL 16:5) (Ferries) (Unitized cargo systems) 'rIe4 USW/Gears~- Design. Jun 1947 Mathematics "Certain Problems in the Manufacture of the Crank- gear," V. Ya. Beletskly, 5 pp "'Vestnik Itzhencrov i Tekhuikov" No6 Mathematical treatment, with diagrams of the follov- Ing problems: 1) Designing a crankgear according to a given motion of the slide and. a coefficient of the change of speed in that motion. 2) Designing a crankgear in vhich the angle of transmission of preasure at the time of operation, vith a given motion of the slide, is not less in advance of the ..61yea quantity...,.-,3) Designing a crankgear with given,:,,, ior66 cmtd) jul 1941 Mathematics =tion of the slide, coefficient of change of sp6ed, and a minimum angle of pressure transmission. IOT66' --y- I V. a. teletskiy) V. Y&. - "MovOment of grain in a horizontal sowing bolter", Trudy In-ta (Odes. in-t inzhenerov mukomol. prom-sti i elevator. khoz-va im. Stalim), Vol. 111 1948, P. 53-50, SO: U-3042, March 11, 1953, (letopis Inykh Statey, No. 10, 1949) BMISKIYO V. Y&. Beletskiyj V. Ya. - "Kinatostatics of self-balancing sowing", Trudy In-ta (Odes. in-t inzhencrov mukomol. prom-sti elevator. khoz-va, im. Stalin4p Vol II, 19ap P. 88-103 SO: U-3042, 11 March 1953, (letopis Inykh Statey, No. 10, 1949): BELETSKIY, V. Ya. Beletskiy, V. Ya. - "The kinetostatics of self-balancing sifters," Trudy Vsesoyuz. zerna i produktov ego pererabotki, Issue 16, 190, p. 60-7h. SO: U-4110, 17 July 53, (Letopis tZhurnal Inylch Statey, No. 19, 1949). BmsrsKIY, v. *. K raschetu potrebnoi moshchosti kolebatelinykh mekhanizmov. (Vestn Mash. 1951, no. 3, p. 13-17) Includes bibliography. Calculations of the required power of oscilatirg mechanisms. DLC: TN4-V4 SO: Manufacturing and Mechanical Engineering in the Soviet Union, Library of Congress, 1953. 1. B=MKH, V.Ya. 2. USSR (600) 4. Flywheels , 7. Calculating flywheel masses of oscillating mechanism* with s-,,all amplitudes, Sellkhozmashina no. 4, 1953. 9. Monthly List of Russian Accessions, Library of Congress, APEIL -1953, Uncl. **u Ruzs~i;6~, Tmdl OdessIL to, 1w, Rev. phas a formula was obtalued fat codculAtiag the. osi*t1gi of th'-. aeoced. Cal I~cxfilq of the cam, A number of *iiiubt. cises w-tt -- 7 7 iyi z6r~l' us Reffroov. 124-58-2-6344 Translation from: Refertivnyy zhurnal, Mekbanika, 1958, Nr 6, p 9 (USSR) AUTHOR: B e I e t s k LY__V__Ya_ TITLE: Designing Sliding-block (Slider-crank) Linkages in Accordance With Given Laws of Motion for the Driving and Driven Links (Proyektirovaniye krivoshipno-shatunnogo mekhanizma po zadannym zakonam dvizheniya vedushchego i rabochego zvenlyev) PERIODICAL: Tr. Odessk. tekhnol. in-ta, 1957, pp 57-67 ABSTRACT- Bibliographic entry. See RzhMekh, 1958, Nr 6, abstract 6343. 1. Mechanical drives--Design Card I j I 124-58-6-6343 Translation from: Referativnyy zhurnal, Mekhanika. 1958, Nr 6, p 9 (USSR) AUTHOR: Beletskiy, V. Ya. TITLE: Rendering More Precise the Dimensions of Plane Mechanisms With Lower (Closed) Pairs Which Reproduce a Given Law of Motion (Utochneniye razmerov ploskikh mekhanizmov s nizshi- mi parami, vosproizvodyashchikh zadannyy zakon dvizheniya) PERIODICAL. Tr. Odessk. -tekhnol. in-ta, 1957, Nr 8, pp 37-47 ABSTRACT: A solution. is examined for the problem of designing a hinged four -bar -linkage mechanism intended to achieve a desired re- lationship between the movements of the driving link and the driven (operating) link. In order to calculate three and four para- meters, multiple interpolation is performed with one coupling, the interpolation factor of which equals three and four respectively. In the calculation of five parameters one parameter is determined from the condition of zero deviation Afrorn the given function, and the remaining four parameters are found from the minimum mean-square value of the second derivative of a function which expresses approximately the deviation A. This method for calcula- Card 1/2 ting five parameters is erroneous, because it does not assure at 124-58-6-6343 Rendering More Precise the Dimensions of Plane Mechanisms (cont. even a single point a zero value of the first derivative of the deviation A; in other words, when this method is used, the direction of the tangents to the given function does not coincide with that of the tangents to the approximate function. N. 1. Levitskiy 1. Mechanics--Theory Card 2/2 124-58-6-6345 Translation from: Referativnyy zhurnal, Mekhanika, 1958, Nr 6, p 9 (USSR) AUTHOR: Beletskiy, V. Ya. ----------- TITLE: On the Designing of Plane Mechanisms With Lower (Closed) Pairs Which Reproduce Desired Trajectories (K proyektirovani- yu ploskikh mekhanizmov s nizshimi parami, vosproizvodyash- chikh zadannyye trayektorii) PERIODICAL: Tr. Odessk. tekhnol. in-ta, 1957, Nr 8, pp, 49-56 ABSTRACT: A solution is given for the problem of calculating three and four parameters for a hinged four-bar-lin~ap mechanism and for a sliding-block (slider-crank) mechanism to satisfy the con- dition of the minimum mean-square deviation oi the connecting- rod curve from a desired trajectory. This method differs from the well-known method with respect to the function which charac- terizes the deviation from the desired trajectory. 1. Mechanical drives--Design N. I. Levitskiy Card 1/1 BL.-LETSKIYS V. Ya. RARER, G.O.AZAZJUOJATat;VORONKOV, P.I.;IZHIWV, P.G.;IIZTAI)ZIO, A.M.; DOMMOVSKIT, G.D.*,ZOIDPARET, S.K.;MVCHENKO, I.K.;PIA.TONOV, P.N.; PAY1,113KO6 A.V,;UGOLIK, N.F, V. IA. Girahson. Muk.-elev. prom, 23 no.4:23 Ap 157. (KLRL 10:5) (Girsheon, Vasilii IAkovlevich, 1880-1957) MEMSKIT &~;i doktor takhn. nauk, Prof. designing crankgoare with given coefficient of reverse-running speed change and limit transmission angle. Izv. vys. ucheb. sav.; mashinostr. no.3/4:3-8 158. (MIRA 122-5) 1.Odesskiy takhnologicheskiy institut iment I.V. Stalina. (Cranks and crankshafts) B313TSKIY .0 doktor tekhn.nauk, prof. Synthesis of crankshaft mechanisms at approximately steady speed of the driver. I%7.vys.uchob.zav.; mashinostr. no.6: 1o-14 '58. (MIRA 12:8) 1. Odeaskiy takhnoloelchaskly Institut ims I.V.Stalinae (Cranks and crankshafts) 25 (1) BOV/145-58-7/8-2/24 AUTHOR: Beletgjay..,~Xa. Professor, Doctor of Technical 'M6r6ne- es TITLE: Estimation of Five Parameters for Crank-Connecting Rod Transfer Mechanisms PERIODICAL: Izvestiya vyeshikh uchbenykh zavedeniy - Mashino- stroyeniye, 19589 Nr 7-8, pp 11-16 (USSR) ABSTRACT: The problem of estimation of transfer mechanism five parameters has been analyzed by Professor, Doctor of Technical Sciences, X.I. Levitekiyj in his work "Do- i ding Mechahisms-with Lower Pairs", ASUSSR, 1950p and by Docent, Candidate of Technical Scienceep P. Novodvorskiy'-*in his work "One Method of Syn- th;6is of Mechanisms". Proceedings of the Seminar'on Theory of Machines and Mechanisms, Volume XI, Issue 42, AS USSR, 1951, fZ7. The present article deals with the estimation of five parameters by applying the same method as it was used by the author when Card 1/3 estimating three and four parameters. Reference Z-J7 SOV/145-58-7/8-2/24 Estimation of Five Parameters for Crank-Connecting Rod Transfer Mechanisms "Designing Crank-Connecting Rod Mechanism on the Ba- sis of Given Law of Driving and Working Link Move- ment". Proceedings of the Odessa Technological Insti- tute imeni I.V. Stalin, Volume VIII, 1957. In Fig 1, the author gives a diagram of transfer mechanism and denotes the sought for parameters by r, 1, a, Xo and C~k 00 The final values of parameters are determined P1 by the following expressions: r = - i sin M 0 1 = V(X 0+Xs)2 -2r(X0+Xs)Cos(,D(0 +o~s)+2arsin(cKo+%)+r2+a2 a = P3 _p0 L; X0 = Po; tgoto = Pl, where X s is the P2 P2 P2 relative value of the slide initial displacement;(Xs angle of the crank initial turn; r - relative length Card 2/3 of the crank, a - relative value of displac t. The 7 SOV/145-58-7/8-2/24 Estimation of Five ParameterB-for Crank-Connecting Rod Transfer Mechanisms interrelations between the coefficients po9 P19 P2 and P3 are expressed by the functions: p0 = Xo; p, = rein 0(0; P2 = rcoscxo; P3 = r(acosw_0+Xosino(o). There are 1 figure and 4 references, 3 of which are Soviet and 1 German. ASSOCIATION: Odesskiy tekhnologicheskiy institut imeni I.V. Stalina (Odessa Technological Institute imeni I,V. Stalin) SUBMITTED: November 19, 1958. Card 3/3 SOV/145-58-7/8-2/24 Estimation of Five Parameters~for Crank-Connecting Rod Transfer Mechanisms interrelations between the coefficients po9 P19 P2 and P3 are expressed by the functions: p0 = Xo; p, = rsin 0%; P2 = rco'so(0;P3 = r(acostebi-x0sinoto). There are 1 figure and 4 references, 3 of which are Soviet and 1 German. ASSOCIATION: Odesskiy tekhnologicheskiy institut imeni I.V. Stalina (Odessa Technological Institute imeni I.V. Stalin) SUBMITTED: November 19, 1958. Card 3/3 -BILETSKIT, T.Ta., prof., doktor tekhn.nank Calculating five parameters of hinged four-bar tranonission linViages. Izv.vys.ucheb.zav.; mashinostr. no.6:3-9 159. (MIRA 13:5) 1. Odesakly tekhnologichookly Institut. (Links and link motion) BEIMSKIY, V.Ya.I doktor tekhn.naukp prof. , 04culating six parameters of three-dimensional cra;kgearo having an appro3dmately uniform motion. Izv.vyv.ucheb,zav* mashinootr. no.1:20-23 160o- WRL 1415) 1. Odesskiy takhno.logicheakiy institut imeni I.V.Stalina. (Cranks and arankshafte) BILITSKIY. V.Ya.. doktor tekhn.nauk prof. -, ~ -:.- - , Determining the reduced dynamic coefficient of the external friction of bulk mixtures. Trukt.i s el'khos;maeb- no-1:32 ja 6o. (KM 13.-4) (Friction) 30257- B/145/60/000/009/003/017 D221/D304 AUTHOR: Beletskiyq V.Ya.9 Doctor of Technical Sciencesq lrafe_~~~ TITLE: The analytical method of designing four-bar mechan1sms PERIODICAL: Izvestiya vyeshikh uchebnykh zavedeniy. Mashino- stroyeniyeg no* 99 1960, 29 - 33 TEXT: The author exposes the analytical solution for determining a family of four-bar mechanisms which ensures that the limit angle of pressure should be below a certain value. It is based on the synthesis of four-bar linkages advanced by the author previously. The obtained equations permit computation of mechanism parameters, and thus relieve the designer of selecling linkages by trial me- thods. The extreme two positions of the four-bar mechanism (AB1 C 1D and AB 2C2D) are shown in Fig. 1. The instantaneous ratio of driven and driving linkages is i = A'2 Applying the theorem of sines to Card 110 2 ~B2' 30252 S/145/60/'000/009/003/017 The analytical method of designing ... D221/D304 the triangle DC2B2t the author deduces equations for lengths of cranks, CD and AB9 as well as conrod BC. Repeating the same for the other position of the mechanism and designating by 1 1 the in- stantaneous ratio of speeds of driven and driving linkages, author deduces further equations for the above arms.After mathematical elaboration,, 12 = 0,5 (k + 1) is obtainedp where (14) sin 70 112-11 Yl 2 . - (15) k g-:,nW1 - sin T. which is a known quantity. Substituting 'Y 29 y. and '2 in the ex-- pres'sion of linkageeg it is possible to compute the required lengths of linkages. These calculations are insufficient for the four7bar mechanisms. Thereforep in practice It is simpler to assume some va.- lue of V1 in the limits of 0