Journal ArticleDOI
Nonlinear stability in the restricted three-body problem with oblate and variable mass
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In this article, the authors investigated the nonlinear stability of the triangular equilibrium points when the bigger primary is an oblate spheroid and the infinitesimal body varies (decreases) it's mass in accordance with Jeans' law.Abstract:
This study investigates the nonlinear stability of the triangular equilibrium points when the bigger primary is an oblate spheroid and the infinitesimal body varies (decreases) it’s mass in accordance with Jeans’ law. It is found that these points are stable for all mass ratios in the range of linear stability except for three mass ratios depending upon oblateness coefficient A and β, a constant due to the variation in mass governed by Jeans’ law.read more
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Book ChapterDOI
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS
Journal ArticleDOI
Out of plane equilibrium points locations and the forbidden movement regions in the restricted three-body problem with variable mass
TL;DR: In this paper, the authors present an analytical study on the dynamics of a third body in the restricted three-body problem and find an appropriate approximation for the locations of the out-ofplane equilibrium points in the special case of a nonisotropic variation of the mass.
Journal ArticleDOI
The great escape - III. Placing post-main-sequence evolution of planetary and binary systems in a Galactic context
TL;DR: In this paper, the authors investigate the interplay between stellar mass-loss, Galactic tidal perturbations and stellar flybys for evolving stars which host one planet, smaller body or stellar binary companion and reside in the Milky Way's bulge or disc.
Journal ArticleDOI
On the triangular libration points in photogravitational restricted three-body problem with variable mass
TL;DR: In this paper, the authors investigated the triangular libration points in the photogravitational restricted three-body problem of variable mass, in which both the attracting bodies are radiating as well and the infinitesimal body vary its mass with time according to Jeans' law.
References
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Book
A treatise on the analytical dynamics of particles and rigid bodies
TL;DR: In this article, a comprehensive account of analytical dynamics is given, starting from first principles with kinematics before moving to equations of motion and specific and explicit methods for solving them, with chapters devoted to particle dyanmics, rigid bodies, vibration and dissipative systems.
Theory of Orbits.
TL;DR: In this paper, a book on theory of orbits covering restricted problem of three bodies, two bodies in rotating coordinate system and periodic orbits is presented. But it does not cover the problem of periodic orbits.
Book ChapterDOI
A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS
Astronomy and Cosmogony
TL;DR: In this paper, the authors present a survey of the universe and the evolution of the stars in terms of light from the stars, gas and liquid stars, as well as the configurations of rotating liquid masses and compressible masses.
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