Analysis of the distribution of times of escape in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1826" altimg="si221.svg"><mml:mi>N</mml:mi></mml:math>-body ring problem

Navarro, Juan F.; Martínez-Belda, María del Carmen

doi:10.1016/j.cam.2021.113396

Cited by 6 publications

(5 citation statements)

References 21 publications

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“…, 10. Navarro and Martínez-Belda [26] found an almost linear relation (with negative slope) between the probability of escape from the system and the number of primaries N, in the N-body ring configuration with central body. In this paper, we explore if we find this same linear relation in the absence of a central body.…”

Section: Numerical Explorationmentioning

confidence: 98%

“…The equations of motion of the N-body ring problem without central body are well known and have been described in many works [10,11,15,26]. This problem deals with the motion of a point particle under the Newtonian influence of a configuration of N bodies (called primaries) with the same mass distributed on a circumference occupying the vertices of a regular polygon of N sides.…”

Section: Equations Of Motion and Curves Of Zero Velocitymentioning

confidence: 99%

“…To perform an analysis of the escape in this problem, we integrate each of the initial conditions in the grid S N ,C contained in D N ,C numerically up to a maximum time of T max 10 2 [26].…”

Section: Numerical Explorationmentioning

confidence: 99%

“…Recently, in a previous work, Belgharbi and Navarro [15] perform a numerical analysis to study how the central mass to peripheral mass ratio affects the distribution of times of escape for N 4, finding a sequential pattern in the evolution of the probability of escape per interval of time. Also, Navarro and Martínez-Belda [26] have determined the basins of escape from the N-body ring configuration, for 5 ≤ N ≤ 8, analyzing the percentage of escaping orbits, as well as the way the escape is distributed among the different openings of the potential well.…”

Section: Introductionmentioning

confidence: 99%

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Dependence of the probability of escape on the Jacobi constant in the N-body ring problem without central body

Belgharbi

Navarro

2023

Eur. Phys. J. Plus

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In this work, we perform a numerical exploration of the escape in the N-body ring problem in absence of a central body, for $$4\le N\le 9$$ 4 ≤ N ≤ 9 and ten values of the Jacobi constant. We show how the probability of escape per interval of time varies as a function of the Jacobi constant, finding that, for values of the Jacobi constant smaller than a certain limit value, the probability of escape from the system tends to decrease with time. However, if we consider values of the Jacobi constant larger than this limit value, the probability of escape grows with time, for times of escape smaller than 100 units of time.

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Section: Numerical Explorationmentioning

confidence: 98%

Section: Equations Of Motion and Curves Of Zero Velocitymentioning

confidence: 99%

Section: Numerical Explorationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dependence of the probability of escape on the Jacobi constant in the N-body ring problem without central body

Belgharbi

Navarro

2023

Eur. Phys. J. Plus

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“…[12] have expressed the fundamentals of the Ring Problem of (N+ 1) Bodies: An Overview. [16,15] has studied the analysis of the distribution of times of escape in the N-body ring problem. [1] has discussed about the Equilibrium dynamics of a circular restricted three-body problem with Kerr-like primaries The dynamical properties of the restricted four-body problem with radiation pressure.…”

Section: Introductionmentioning

confidence: 99%

A study of libration points and analysis of their stability behavior in-ring body problem under albedo effect

Kumar

Kushvah

2022

Preprint

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Our intention in this article is to analyze the fundamental analysis of the zones and their existing libration points under the solar radiation pressure and albedo effects. We can feel about albedos at any Nature’s property wherever the Sun rays exist. As we know that important phase of the dynamical system of any celestial body is its stability and the factors which change its behavior of motion. This research article presents an explicit analysis of the albedo effect for ring body problems for a specific value of v = 6, which explains the behavior of existing zone’s stability, shifting of their libration points with monotonicity and the characteristic roots of δ confirms the behavior of stability condition for existing zones as well as their existing libration points in a synodic frame of references. We observed that in this problem from an experimental point of view, a little change in v, changes the complete behavior of the problem and leaves a nice platform of the proof. In this problem, β plays a significant role, which affects firstly the whole dynamics of peripheral primaries, the mass parameters β = 0 and β ≠ 0 generally confirm that this synodic system wears, an absence of a center of mass and the presence of the center of mass, respectively. We have observed in this article is the libration point L0, which exists in the center and has peripheral primary P0, remains unchanged throughout applying the albedo effect. The stability analysis confirms the location of the libration points, whether it is stable, unstable, etc., but here we have seen the more interesting things i.e., most of the locations of the libration points except exceptionals are found unstable. This article also shows the momentum of the position of all the libration points with their existing zone as well as peripheral primaries, by the effect of the radiation pressure and albedo. It is also analyzed here that this complete problem works in a certain short and very sensitive range set (−1.75, 1.75) because this problem is filled with trigonometric periodic functions. In this problem, we have considered only the real roots of the axis x, y, whereas imaginary roots are not considered. For stability analysis, we have taken both real and complex roots of δ. Results of this article for v = 6 may help us to analyze an imaginary behavior of our solar system’s planets in a blank paper, provided by certain rules and regulations by equations of motion because real behavior may be far away from us. By the present study, it is found that the whole behavior of the system for various v whenever change, which can be extended later in another way.

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