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Non-linear stability zones around triangular equilibria in the plane circular restricted three-body problem with oblateness
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In this paper, non-linear stability zones of the triangular Lagrangian points are computed numerically in the case of oblate larger primary in the plane circular restricted three-body problem.Abstract:
Non-linear stability zones of the triangular Lagrangian points are computed numerically in the case of oblate larger primary in the plane circular restricted three-body problem. It is found that oblateness has a noticeable effect and this is identified to be related to the resonant cases and the associated curves in the mass parameter μ versus oblateness coefficientA
1 parameter space.read more
Citations
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Journal ArticleDOI
Existence and stability of triangular points in the restricted three-body problem with numerical applications
TL;DR: In this article, it was shown that the locations of the triangular points and their linear stability are affected by the oblateness of the more massive primary in the planar circular restricted three-body problem.
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
The three-body problem
Z.E. Musielak,Billy Quarles +1 more
TL;DR: A review of the three-body problem in the context of both historical and modern developments is presented in this article, where the authors describe the general and restricted (circular and elliptic) three body problems, different analytical and numerical methods of finding solutions, methods for performing stability analysis and searching for periodic orbits and resonances.
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The effect of oblateness in the perturbed restricted three-body problem
TL;DR: In this article, the effects of oblateness of the three participating bodies as well as the small perturbations in the Coriolis and centrifugal forces are considered, and the existence of equilibrium points, their linear stability and the periodic orbits around these points are studied under these effects.
Journal ArticleDOI
Linear stability of equilibrium points in the generalized photogravitational Chermnykh’s problem
TL;DR: In this article, the authors considered the photogravitational Chermnykh's problem with the bigger primary as a source of radiation and the small primary as an oblate spheroid.
References
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Book
The Three-Body Problem
TL;DR: In this paper, the authors present a series of simple solutions of the three-body problem, including the Hamilton and Delaunay formulation, the Lagrangian and Eulerian solutions, and the Jacobi formulation.
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Stability of the triangular points in the elliptic restricted problem of three bodies
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Stability of the triangular lagrangian points
TL;DR: In this paper, it was shown that the set of exceptional mass ratios for which stability remains to be proved or invalidated contains only one point besides the critical mass ratios of order two and three.
Journal ArticleDOI
Stationary solutions and their characteristic exponents in the restricted three-body problem when the more massive primary is an oblate spheroid
TL;DR: In this article, the locations of the five equilibrium points were investigated by taking into account the effect of oblateness of the more massive primary for some systems of astronomical interest, and the periodic solutions of the linearized equations of motion around the five equilibria were analyzed.