This is a preprint, a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Research Article
License:
This work is licensed under a CC BY 4.0 License. Read Full License
In this manuscript, our main focus is to investigate the existence and stability of the libration points in the axisymmetric restricted five-body problem (R5BP) in which the mass of the fifth particle varies with respect to time as per Jeans' law. It has been assumed that the four bodies with masses mi,i = 1,2,...,4 (with m3 = m4 = m̃) form an axisymmetric convex configuration. The equations of motion of the test particle moving under the gravitational influence of the four primaries, have been presented, which are different from the axisymmetric R5BP with constant mass under this configuration. Further, we have determined the in-plane and out-of-plane libration points along with their linear stability. Further, we have drawn the regions of possible motion where the fifth body can move freely. Furthermore, it is observed that the existence of these libration points depends not only on the angle parameters 𝜶 and β but also on the parameters occur due to variation in mass namely γ(0 < γ ≤ 1) and 𝝈 (0 < 𝝈 ≤ 2.2, a proportionality constant occurs in Jeans' law). Moreover, the multivariate version of the Newton-Raphson (NR) iterative scheme is applied in an attempt to unveil the analysis of the basins of convergence (BoC) linked with the libration points as function of 𝝈. Furthermore, in order to measure the uncertainty of the basins, the basin entropy is also determined. It is also revealed that the domains of the basins of convergence (DoBoC) are also related with the required number of iterations and also with the corresponding probability distributions.
Keywords
AR5BP, Variable mass, NR, scheme, Basin entropy
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
This preprint is available for download as a PDF.
Loading...
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
History
CURRENT STATUS: Posted
Version 1
Posted 05 May, 2021
No community comments so far
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Mathematical Physics
Learn more about our company.
This is a preprint. It has not completed peer review.
Research Article
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
History
CURRENT STATUS: Posted
Version 1
Posted 05 May, 2021
No community comments so far
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Mathematical Physics
License:
This work is licensed under a CC BY 4.0 License. Read Full License
In this manuscript, our main focus is to investigate the existence and stability of the libration points in the axisymmetric restricted five-body problem (R5BP) in which the mass of the fifth particle varies with respect to time as per Jeans' law. It has been assumed that the four bodies with masses mi,i = 1,2,...,4 (with m3 = m4 = m̃) form an axisymmetric convex configuration. The equations of motion of the test particle moving under the gravitational influence of the four primaries, have been presented, which are different from the axisymmetric R5BP with constant mass under this configuration. Further, we have determined the in-plane and out-of-plane libration points along with their linear stability. Further, we have drawn the regions of possible motion where the fifth body can move freely. Furthermore, it is observed that the existence of these libration points depends not only on the angle parameters 𝜶 and β but also on the parameters occur due to variation in mass namely γ(0 < γ ≤ 1) and 𝝈 (0 < 𝝈 ≤ 2.2, a proportionality constant occurs in Jeans' law). Moreover, the multivariate version of the Newton-Raphson (NR) iterative scheme is applied in an attempt to unveil the analysis of the basins of convergence (BoC) linked with the libration points as function of 𝝈. Furthermore, in order to measure the uncertainty of the basins, the basin entropy is also determined. It is also revealed that the domains of the basins of convergence (DoBoC) are also related with the required number of iterations and also with the corresponding probability distributions.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
This preprint is available for download as a PDF.
Loading...