The Three-Body Interaction Effect on the Families of 3D Periodic Orbits Associated to Sitnikov Motion in the Circular Restricted Three-Body Problem

Ragos, Omiros; Perdiou, A. E.; Perdios, E. A.

doi:10.1007/s40295-019-00193-0

Cited by 11 publications

(2 citation statements)

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“…Indeed, the authors have extended the previous work of the 4-body Sitnikov problem to the N-body case. Moreover, the study unveils the critical Sitnikov periodic orbits from which 3D families bifurcate for different values of N. Recently, Sitnikov three-body problem has been studied by Ragos et al 14 where the three-body interaction has been taken into consideration. Moreover, the effect of this interaction on the evolution of the families of 3D periodic orbits bifurcating from the family of Sitnikov motion of the circular restricted three-body problem are illustrated.…”

Section: Introductionmentioning

confidence: 88%

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On the Sitnikov‐like N ‐body problem with quasi‐homogeneous potential

Suraj

Aggarwal

et al. 2021

Comp and Math Methods

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In the present article, the periodic solutions of the N-body with quasi-homogeneous potential in the Sitnikov sense by applying the multiple methods of scale (MMS) and Lindstedt-Poincaré (LP) technique are obtained. However, these methods are used to find the approximate periodic solutions in the closed form by eliminating the secular terms. In addition of the Newtonian potential and forces, we consider that the big bodies create quasi-homogeneous potentials. We add the inverse cubic corrective term to the inverse square Newtonian law of gravitation, in order to approximate the various phenomena due to the shape of the bodies or the radiation emitting from them. We study the Sitnikov motion in the N-bodies under this consideration. We, further, analyzed the obtain approximate periodic solutions of the Sitnikov motion, for = 2, 7 by using the MMS and LP-method, in closed form. The numerical comparisons are presented in the first and second approximated solutions obtained by using MMS and numerical solutions obtained by LP-method are illustrated graphically. The effect of initial conditions on the solutions of the Sitnikov motion is illustrated graphically obtained by both the techniques. It is observed that the choice of initial conditions plays a crucial role in the numerical and approximate solutions.

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Section: Introductionmentioning

confidence: 88%

“…Using Equations (12)(13)(14) and (16) in Equation ( 11) and equating the coefficients of and its higher order from both sides, we get a series of linear partial differential equations which govern the functions z i (t, T 0 , T 1 ), where i = 0, 1, 2, as follows:…”

Section: The Methods Of Multiple Scalesmentioning

confidence: 99%