LOCATION OF LIBRATION POINTS IN THE GENERALISED PHOTOGRAVITATIONAL ELLIPTIC RESTRICTED THREE BODY PROBLEM
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1 ISSN: 9-7 Ittiol Joul of Iovtiv Rsch i Scic, Egiig d Tchology ( ISO 97: 7 Ctifid Ogiztio Vol., Issu, Octob LOCTION OF LIBRTION POINTS IN THE GENERLISED PHOTOGRVITTIONL ELLIPTIC RESTRICTED THREE BODY PROBLEM D. Om Pksh Rm, D. Rmshk Shm Rd, Dpt. of Mthmtics, L.S. Collg, Muzffpu, Idi Lctu, Dpt. of Mthmtics, St Kbi Collg, Smstipu, Idi bstct: I this pp th loctio of libtio poits, tigul s wll s colli libtio poits i th glizd photogvittiol lliptic stictd th body poblm hs b studid. Th poblm is glizd i th ss tht th bigg pimy is tk s oblt sphoid d th smll pimy is cosidd s souc of ditio. It hs b foud tht tigul d colli libtio poits difft fom thos i clssicl cs. Ky wods: Libtio / Glisd / Photogvittiol / Rstictd I. INTRODCTION Rdzivskii [] studid th loctio of th uilibium poits by tkig mo mssiv pimy s th souc of ditio i th stictd poblm of th bodis. Dby [] xmid th stbility of tigul poits i th lliptic stictd poblm of th bodis. Shm [7] studid th photogvittiol stictd th body poblm kig smll pimy s oblt sphoid. Hu d Ishw [] xmid th o-li stbility i th ptubd photogvittiol stictd th body poblm. Mkllos, Pdios d Lbopoulou [] studid th li stbility of th tigul uilibium poits i th photogvittiol lliptic stictd poblm. Khs [] discussd th libtiol solutios to th photogvittiol stictd th body poblm. I th pst pp w hv studid th loctio of libtio poits tigul s wll s libtio poits i th glizd photogvittiol lliptic stictd th body poblm. W hv tk th bigg pimy s oblt sphoid d th smll pimy libtio poits coti ccticity, obltss d ditio fcto which difft fom thos i clssicl cs. THE EQTIONS OF MOTION OF CONSIDERED PROBLEM RE - -.( II. LOCTION OF TRINGLR LIBRTION POINTS: Copyight to IJIRSET
2 ISSN: 9-7 Ittiol Joul of Iovtiv Rsch i Scic, Egiig d Tchology ( ISO 97: 7 Ctifid Ogiztio Vol., Issu, Octob Copyight to IJIRSET WHERE /. ( IS THE OBLTENESS COEFFICIENT, THE RDITTION PRESSRE, E THE ECCENTRICITY OF THE ELLIPSE ND N THE MEN NGLR VELOCITY GIVEN BY ; / BEING THE SEMI-MJOR IS OF THE ELLIPSE. MLTIPLYING THE BOVE EQTIONS BY ', & RESPECTIVELY, DDING ND INTEGRTING C, WHERE C IS THE JCOBI CONSTNT. I.E. F(,, + C WHERE F(,, C / (... ( FOR EQILIBRIM POSITION, WE HVE f f f WHICH GIVE ( /... ( ( / ( & ( IF, WE HVE PLNNR LIBRTION POINTS, OTHERWISE WE WILL GET OT OF PLNE LIBRTION POINTS.
3 ISSN: 9-7 Ittiol Joul of Iovtiv Rsch i Scic, Egiig d Tchology ( ISO 97: 7 Ctifid Ogiztio Vol., Issu, Octob LET THE PLNNR LIBRTION POINTS WY FROM -IS BE DENOTED BY L ND L WHICH RE CLLED TRINGLR LIBRTION POINTS. WE HVE WHICH GIVES (7 IT IS OBVIOS THT, THE DISTNCE BETWEEN TWO PRIMRIES SO THT WITH THE HELP OF (, ( & (7 ND PTTING THE VLES OF & / & / SING THESE VLES IN + + / / LSO FROM ( / / / / HENCE THE COORDINTE OF L ND L RE &, ND (9. IF WE PT E & Q, THE COORDINTES OF L RE OF MC CSKEY [].,... (9, RESPECTIVELY WHERE ND RE GIVEN BY (, WHICH GIVES THE SME RESLT III. LOCTION OF COLLINER LIBRTION POINTS: TO FIND THE LOCTION OF COLLINER LIBRTION POINTS ON THE -IS WE SBSTITTE & ND WE GET IN f Copyight to IJIRSET
4 ISSN: 9-7 Ittiol Joul of Iovtiv Rsch i Scic, Egiig d Tchology ( ISO 97: 7 Ctifid Ogiztio Vol., Issu, Octob Copyight to IJIRSET ( /. ( WHERE WE CONSIDER SO THT SBSTITTING THESE VLES IN ( FINLLY WE GET THE SOLTION FOR THE LOCTION OF COLLINER LIBRTION POINT L S! V V Y + V Y WHERE IS THE VLE OF, THE DISTNCE BETWEEN L ND THE SMLLER PRIMRY IN CLSSICL CSE. - 7 Y V 7 IF WE PT, THE SME RESLT IN CLSSICL CSE OF MC CSKEY.
5 ISSN: 9-7 Ittiol Joul of Iovtiv Rsch i Scic, Egiig d Tchology ( ISO 97: 7 Ctifid Ogiztio Vol., Issu, Octob SIMILRLY FROM f ND f WE GET THE SOLTION FOR LOCTION FOR COLLINER LIBRTION POINTS L & L WHICH RE LSO FFECTED BY ECCENTRICITY, OBLTENESS & RDITION FCTOR. REFERENCES [] Dby, J.M..(9: sto. Joul 9, -7. [] Hu, M.N. d Ishw, B.(99: Bull stv. Soc. Idi, 9-. [] Khs, S.N.(99: Cosmic sch vol., No., -. [] Mkllos, V.V., Pdios, E. d Lbopoulou, P.(99:, stophysics d spc scic 9, 7-. [] Mc Cusky, S.W.(9: Itoductio to Clstil Mchics, ddiso-wsly publishig Compy, Ic. Nw Yok. [] Rdzivskii, V.V.(9: sto. Zh.,. [7] Shm, R.K.(97: stophysics d Spc Scic,, 7-. [] Ry Rmshy: Ph. D. thsis, submittd to B. R.. B. ivsity; Muzffpu,9. Copyight to IJIRSET
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