Stability Analysis of the Rhomboidal Restricted Six-Body Problem
We discuss the restricted rhomboidal six-body problem (RR6BP), which has four positive masses at the vertices of the rhombus, and the fifth mass is at the intersection of the two diagonals. These masses always move in rhomboidal CC with diagonals 2a and 2b. The sixth body, having a very small mass,...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Astronomy |
| Online Access: | http://dx.doi.org/10.1155/2021/5575826 |
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| author | M. A. R. Siddique A. R. Kashif M. Shoaib S. Hussain |
| author_facet | M. A. R. Siddique A. R. Kashif M. Shoaib S. Hussain |
| author_sort | M. A. R. Siddique |
| collection | DOAJ |
| description | We discuss the restricted rhomboidal six-body problem (RR6BP), which has four positive masses at the vertices of the rhombus, and the fifth mass is at the intersection of the two diagonals. These masses always move in rhomboidal CC with diagonals 2a and 2b. The sixth body, having a very small mass, does not influence the motion of the five masses, also called primaries. The masses of the primaries are m1=m2=m0=m and m3=m4=m˜. The masses m and m˜ are written as functions of parameters a and b such that they always form a rhomboidal central configuration. The evolution of zero velocity curves is discussed for fixed values of positive masses. Using the first integral of motion, we derive the region of possible motion of test particle m5 and identify the value of Jacobian constant C for different energy intervals at which these regions become disconnected. Using semianalytical techniques, we show the existence and uniqueness of equilibrium solutions on the axes and off the axes. We show that, for b∈1/3,1.1394282249562009, there always exist 12 equilibrium points. We also show that all 12 equilibrium points are unstable. |
| format | Article |
| id | doaj-art-736d746bb0cc42bd9fae6320a09f6f73 |
| institution | Kabale University |
| issn | 1687-7969 1687-7977 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Astronomy |
| spelling | doaj-art-736d746bb0cc42bd9fae6320a09f6f732025-02-03T06:12:30ZengWileyAdvances in Astronomy1687-79691687-79772021-01-01202110.1155/2021/55758265575826Stability Analysis of the Rhomboidal Restricted Six-Body ProblemM. A. R. Siddique0A. R. Kashif1M. Shoaib2S. Hussain3Department of Mathematics, Capital University of Science and Technology, Zone-V, Islamabad, PakistanDepartment of Mathematics, Capital University of Science and Technology, Zone-V, Islamabad, PakistanSmart and Scientific Solutions, 32 Allerdyce Drive, Glasgow G156RY, UKDepartment of Mathematics, Capital University of Science and Technology, Zone-V, Islamabad, PakistanWe discuss the restricted rhomboidal six-body problem (RR6BP), which has four positive masses at the vertices of the rhombus, and the fifth mass is at the intersection of the two diagonals. These masses always move in rhomboidal CC with diagonals 2a and 2b. The sixth body, having a very small mass, does not influence the motion of the five masses, also called primaries. The masses of the primaries are m1=m2=m0=m and m3=m4=m˜. The masses m and m˜ are written as functions of parameters a and b such that they always form a rhomboidal central configuration. The evolution of zero velocity curves is discussed for fixed values of positive masses. Using the first integral of motion, we derive the region of possible motion of test particle m5 and identify the value of Jacobian constant C for different energy intervals at which these regions become disconnected. Using semianalytical techniques, we show the existence and uniqueness of equilibrium solutions on the axes and off the axes. We show that, for b∈1/3,1.1394282249562009, there always exist 12 equilibrium points. We also show that all 12 equilibrium points are unstable.http://dx.doi.org/10.1155/2021/5575826 |
| spellingShingle | M. A. R. Siddique A. R. Kashif M. Shoaib S. Hussain Stability Analysis of the Rhomboidal Restricted Six-Body Problem Advances in Astronomy |
| title | Stability Analysis of the Rhomboidal Restricted Six-Body Problem |
| title_full | Stability Analysis of the Rhomboidal Restricted Six-Body Problem |
| title_fullStr | Stability Analysis of the Rhomboidal Restricted Six-Body Problem |
| title_full_unstemmed | Stability Analysis of the Rhomboidal Restricted Six-Body Problem |
| title_short | Stability Analysis of the Rhomboidal Restricted Six-Body Problem |
| title_sort | stability analysis of the rhomboidal restricted six body problem |
| url | http://dx.doi.org/10.1155/2021/5575826 |
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