Journal ArticleDOI
Equilibrium points and their stability in the restricted four-body problem
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Numerically the problem of four bodies moving in circles around their center of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the vertices of an equilateral triangle, is studied.Abstract:
We study numerically the problem of four bodies, three of which are finite, moving in circles around their center of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the vertices of an equilateral triangle, while the fourth is infinitesimal. The fourth body does not affect the motion of the three bodies (primaries). The allowed regions of motion as determined by the zero-velocity surface and corresponding equipotential curves as well as the positions of the equilibrium points are given. The existence and the number of collinear and noncollinear equilibrium points of the problem depend on the mass parameters of the primaries. For three unequal masses, collinear equilibrium solutions do not exist. Critical masses associated with the existence and the number of equilibrium points, are given. The stability of the relative equilibrium solutions in all cases is also studied. The regions of the basins of attraction for the equilibrium points of the present dynamical model for some values of the mass parameters are illustrated.read more
Citations
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Journal ArticleDOI
Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure
TL;DR: In this paper, the authors used the multivariate version of the Newton-Raphson method to determine the basins of attraction associated with the equilibrium points in a planar circular restricted three-body problem.
Journal ArticleDOI
Equilibrium points in the photogravitational restricted four-body problem
J. P. Papadouris,K. E. Papadakis +1 more
TL;DR: In this article, the authors considered the photogravitational version of the problem of four bodies, where an infinitesimal particle is moving under the Newtonian gravitational attraction of three bodies which are finite, moving in circles around their center of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the vertices of an equilateral triangle.
Journal ArticleDOI
Families of periodic orbits in the restricted four-body problem
TL;DR: In this article, families of simple symmetric and non-symmetric periodic orbits in the restricted four-body problem are presented, and their linear stability in three cases, i.e., when the three primary bodies are equal, when two primaries are equal and finally when we have three unequal masses.
Journal ArticleDOI
Stability regions of equilibrium points in restricted four-body problem with oblateness effects
Reena Kumari,Badam Singh Kushvah +1 more
TL;DR: In this article, the authors extended the basic model of the restricted four-body problem by introducing two bigger dominant primaries m�� 1 and m petertodd 2 as oblate spheroids when masses of the two primary bodies (m�� 2 and m�� 3) are equal.
Journal ArticleDOI
Revealing the basins of convergence in the planar equilateral restricted four-body problem
TL;DR: In this paper, the authors used the planar equilateral restricted four-body problem where two of the primaries have equal masses to determine the Newton-Raphson basins of convergence associated with the equilibrium points.
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Journal ArticleDOI
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Collinear equilibrium points of Hill’s problem with radiation and oblateness and their fractal basins of attraction
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