Capricious basins of attraction in photogravitational magnetic binary problem

Kumar, Vinay; Arif, Md.; Ullah, Mukhtar

doi:10.1016/j.newast.2020.101475

Cited by 9 publications

(5 citation statements)

References 17 publications

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“…Çà â³ñü õ ïðè é ìàºòüñÿ ë³í³ÿ, ùî ñïî ëó ÷àº öåí òðè ïåð âèí íèõ ò³ë ³ ïðî õî äèòü ÷å ðåç ïî ÷à òîê O; öåíòð ïåð âèí íî ãî ò³ëà P 1 ëå aeèòü íà äî äàòí³é ï³âîñ³ x, à öåíòð ïåð âèí íî ãî ò³ëà P 2 -íà â³ä+ºìí³é ï³âîñ³ x. Ïðÿ ìó, ïåð ïåí äè êó ëÿð íó äî ïëî ùè íè ðóõó ïåð âèí íèõ åëå -ìåíò³â, ùî ïðî õî äèòü ÷å ðåç ïî ÷à òîê êî îð äè íàò, ïðè é íÿ òî çà â³ñü z, à ë³í³ÿ, ùî ïðî õî äèòü ÷å ðåç ïî ÷à òîê êî îð äè íàò O ïåð ïåí äè êó ëÿð íî äî îñ³ x, ïðè é ìàºòüñÿ çà â³ñü y. Îäè íèö³ âèì³ðþ âàí íÿ ÷àñó òà â³äñòàí³ âèáè ðàºìî òà êè ìè, ùîá ãðàâ³òàö³éíà ñòà ëà, äîâ aeè íà ì³ae ïåð âèí íè ìè åëå ìåí òà ìè òà ñóìà ¿õí³õ ìàñ äîð³âíþ âà ëè îäè íèö³. Çã³äíî ç äà íè ìè [8]…”

Section: ð³âíÿí íÿ ðóõóunclassified

“…Ìà òå ìà òè÷ íå ôîð ìó ëþ âàí íÿ íà øî¿ ìî äåë³ îïè ñóºòüñÿ ð³âíÿí íÿìè ( 5), (6). Ïðè j = 1, y = 1, a = 0 ³ b = 1 ö³ ð³âíÿí íÿ ìà þòü âèã ëÿä ð³âíÿíü, ïðåä ñòàâ ëå íèõ â ðî áîò³ [8]. Êð³ì òî ãî, ïðè q = 1 ³ ââà aeà þ ÷è ñï³ââ³äíî øåí íÿ ìàãí³òíèõ ìî ìåíò³â ïåð âèí íèõ åëå ìåíò³â çà ºäè íó ñèëó, ìè îò ðè ìà ëè ð³âíÿí íÿ ðó õó, íà âå äåí³ â ðî áîò³ [23].…”

Section: ð³âíÿí íÿ ðóõóunclassified

“…äå J -ìàò ðè öÿ ßêîá³ f n ( ) X . Äëÿ íà øî¿ êîí êðåò íî¿ çà äà÷³ ìè âè êî ðèñòî âóºìî ñèñ òå ìó ð³âíÿíü (7), (8), ùîá îò ðè ìà òè ³òå ðàö³éíó ôîð ìó ëó Íüþ òî íà -Ðàô ñî íà:…”

Section: áàñåéíè êîíâåðãåíö²ùunclassified

“…[4,5] çà ïðî âà äè ëè ³íñòðó ìåíò äëÿ âèì³ðþ âàí íÿ íå âèç íà ÷å -íîñò³ áà ñåéí³â, ÿêà íà çè âàºòüñÿ åí òðîï³ºþ áà ñåé íó. Äëÿ âèç íà ÷åí íÿ åí òðîï³¿ áà ñåé íó (S b ) òà åí òðîï³¿ ãðà íè÷ íî ãî áà ñåé íó (S bb ) âè êî ðèñ òà íî àë ãî ðèòì [8,9]. Çã³äíî ç âèç íà ÷åí íÿì åí òðîï³¿ ãðà íè÷ íî ãî áà ñåé íó ïðè çíà ÷åí íÿõ S bb > lg2 ãðà íè÷ íèé áà ñåéí º ôðàê òàëü íèì.…”

Section: åíòðîï²ß áàñåéíó òà ²ñíóâàííß ôðàêòàëóunclassified

See 3 more Smart Citations

Perturbations in Coriolis and centrifugal forces and N-R basins of convergence of photogravitational magnetic-binary problem with variable mass

Kumar,

Kumar Marig

2023

Kinemat. fiz. nebesnyh tel (Online)

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Ó ö³é ñòàòò³ ìè äîñë³äaeó âà ëè åôåê òè ìà ëèõ çáó ðåíü êîð³îë³ñî âèõ (j) òà â³äöåí òðî âèõ (y) ñèë ó ôî òîã ðàâ³òàö³éí³é ìàãí³òíî-á³íàðí³é çà -äà÷³, ùî âêëþ ÷àº âïëèâ òðåòü î ãî ò³ëà ó âèã ëÿä³ çì³ííî¿ ìàñè. Ìå òîþ ö³º¿ ðî áî òè º àíàë³ç âïëè âó â³äöåí òðî âèõ ñèë y òà ³íøèõ ïà ðà ìåòð³â (ìàãí³òíî ãî ìî ìåí òó l ³ ðàä³àö³éíî ãî òèñ êó q) íà ³ñíó âàí íÿ òà åâî -ëþö³þ òî ÷îê ð³âíî âà ãè, áà ñåéí³â êîí âåð ãåíö³¿ (ÁÊ), ñòóï³íü íå ïå ðåäáà ÷ó âà íîñò³ ó ÁÊ. Êð³ì òîãî, âèâ ÷åí íÿ âïëè âó j ³ y (ïðè íà ÿâ íîñò³ ³íøèõ ïà ðà ìåòð³â) íà ñò³éê³ñòü òî ÷îê ð³âíî âà ãè òà êîae º îäíèì ³ç àñ -ïåêò³â ö³º¿ ðî áî òè. Äëÿ ð³çíèõ çíà ÷åíü ïà ðà ìåòð³â çà ãàëü íà ê³ëüê³ñòü âè ïàäê³â íå êîë³íå àð íèõ òî ÷îê ð³âíî âà ãè ñòà íî âèòü 3, 5 ³ 7. Âïëèâ ð³çíèõ ïà ðà ìåòð³â íà åâî ëþö³þ òî ÷îê ð³âíî âà ãè äå ìî íñòðóºòüñÿ ãðàô³÷íî. Óñ³ íå êîë³íå àðí³ òî÷ êè ð³âíî âà ãè âè ÿâ ëÿ þòü ñÿ íå ñòàá³ëüíèìè äëÿ äî ïóñ òè ìî ãî ä³àïà çî íó ïà ðà ìåòð³â ö³º¿ ìî äåë³. Çì³íè ãå î -ìåòð³¿ ÁÊ òà êîae ïî êà çà íî òà ïî ÿñ íå íî çà äî ïî ìî ãîþ ãðàô³ê³â. Âïëèâ y, q ³ l íà ñòóï³íü íå ïå ðåä áà ÷ó âà íîñò³ ó ÁÊ äîñë³äaeóºòüñÿ çà äî ïîìî ãîþ ìå òî äó åí òðîï³¿ áà ñåé íó. Ïî êà çà íî, ùî äëÿ ïî âíî ãî ä³àïà çî íó l ³ q ÁÊ ëå aeàòü ó ôðàê òàëüí³é îá ëàñò³, à äëÿ çíà ÷åíü y = 1.37…1.38 ³ 1.40…1.44 ìåae³ ÁÊ ëå aeàòü ó íå ôðàê òàëüí³é îá ëàñò³. Êëþ ÷îâ³ ñëî âà: â³äöåí òðî âà ñèëà, ñèëà Êîð³îë³ñà, ìàãí³òíà á³íà ðíà çà äà ÷à, áà ñåéí êîí âåð ãåíö³¿, åí òðîï³ÿ áà ñåé íó.

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Section: ð³âíÿí íÿ ðóõóunclassified

Section: áàñåéíè êîíâåðãåíö²ùunclassified

Section: åíòðîï²ß áàñåéíó òà ²ñíóâàííß ôðàêòàëóunclassified

See 2 more Smart Citations

Perturbations in Coriolis and centrifugal forces and N-R basins of convergence of photogravitational magnetic-binary problem with variable mass

Kumar,

Kumar Marig

2023

Kinemat. fiz. nebesnyh tel (Online)

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“…Many researchers (Chun and Neta (2015), Daza et al (2016), Zotos (2016), Zotos (2017), Zotos and Sanam Suraj (2018), Osorio-Vargas et al (2020)) have studied Newton-Raphson (N-R) basins of attraction. Kumar et al (2021) studied the MBP in the framework of restricted problem of three bodies. The bigger primary is taken as the source of radiation pressure and smaller primary is taken as point mass.…”

Section: Introductionmentioning

confidence: 99%

Basins of attraction in the photogravitational magnetic-binary problem with oblateness and dissipations

Kant

Kumar

2023

Preprint

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This article investigates the dynamical effect of the dissipation forces, namely the Poynting-Robertson (PR) drag and nebular gas (Stokes) drag on the photogravitational magnetic-binary problem (PMBP) where the smaller primary is an oblate body and the bigger primary is the source of radiation. We have settled the equations of motion. The parametric evolution of the position and existence of equilibrium points and their linear stability are presented. Further, Newton-Raphson (N-R) basins of attraction have been plotted with the effect of Poynting-Robertson (PR) drag and nebular gas (Stokes) drag by Mathematica Software. Numerical results indicate that the ratio of magnetic moment λ has a significant impact on the location, stability of the equilibrium points, and the Newton-Raphson (N-R) basins of attraction of the problem. It is observed that there exist either nine or eleven equilibrium points for different values of mass parameter µ and the ratio of magnetic moment λ. Further, we observed that all equilibrium points are unstable in the Lyapunov sense. It is identified that in every case, the basins of convergence corresponding to the collinear equilibrium points L1 and L3 have infinite extents. Our numerical study suggests that the progression of the attracting domains in this dynamical system is very complicated. It is found that spacecraft is drifted from equilibrium points as a function of time due to instability of equilibrium points and drift is most for L7 point.

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Motion Around Out-of-Plane Equilibrium Points in the Frame of Restricted Six-Body Problem Under Radiation Pressure

Idrisi

Ullah

2022

Few-Body Syst

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Capricious basins of attraction in photogravitational magnetic binary problem

Cited by 9 publications

References 17 publications

Perturbations in Coriolis and centrifugal forces and N-R basins of convergence of photogravitational magnetic-binary problem with variable mass

Perturbations in Coriolis and centrifugal forces and N-R basins of convergence of photogravitational magnetic-binary problem with variable mass

Basins of attraction in the photogravitational magnetic-binary problem with oblateness and dissipations

Motion Around Out-of-Plane Equilibrium Points in the Frame of Restricted Six-Body Problem Under Radiation Pressure

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