Results 271 to 280 of about 162,417 (306)

Global Regularization of the Restricted Problem of Three Bodies

Celestial Mechanics and Dynamical Astronomy, 2004
The restricted plane circular three-body problem is considered. It is well known that the differential equations of the problem have singularities when the distance between the third body and one of the primaries tends to zero (collisions). Motions near or through collisions can be studied only by using regularized equations of motion.
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STABILIZATION OF CHAOTIC BEHAVIOR IN THE RESTRICTED THREE-BODY PROBLEM

International Journal of Bifurcation and Chaos, 2007
The restricted three-body problem on the example of a perturbed Sitnikov case is considered. On the basis of the Melnikov method we study a possibility to stabilize the obtained chaotic solutions by two bodies placed in the triangular Lagrange points.
Arsen Dzhanoev, Alexander Loskutov
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Dynamics of the Parabolic Restricted Collinear Three-Body Problem

SIAM Journal on Applied Dynamical Systems, 2019
Summary: We give a complete study of the dynamics of an infinitesimal mass under the Newtonian attraction of two point masses -- particles which escape along a line with zero energy -- and a third massless particle moving along the same line (called the parabolic restricted collinear three-body problem).
Joaquín Delgado, Claudio Vidal
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Crash test for the restricted three-body problem

Physical Review E, 2005
The restricted three-body problem serves to investigate the chaotic behavior of a small body under the gravitational influence of two heavy primary bodies. We analyze numerically the phase space mixing of bounded motion, escape, and crash in this simple model of (chaotic) celestial mechanics.
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A Note on the Regularization of the Restricted Three‐body Problem

Astronomische Nachrichten, 1976
AbstractThe requirement that near a singular point of the equations of motion the power series expansions of the old variables in terms of the new ones start with second order terms leads to the transformation z = sin21/2w related to that of THIELE‐BURRAU. Using this new transformation, a derivation of the regularized equations of motion is given.
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The photogravitational restricted three-body problem

Astrophysics and Space Science, 1994
The photogravitational restricted three-body problem is reviewed and the case of the “out-of-plane” equilibrium points is analysed. It is found that, when the motion of an infinitesimal body is determined only by the gravitational forces and effects of the radiation pressure, there are no “out-of-plane” stable equilibrium points.
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The invariance of the restricted problem of three bodies

Celestial Mechanics, 1985
The restricted problem of three bodies in sidereal coordinates is investigated using Lie theoretical methods of extended groups. The application of the theory results in a single scalar generator with an associated invariant - the integral of the motion attributed to Jacobi.
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Generalizations of the Restricted Problem of Three Bodies

1984
This paper offers several generalizations of the restricted problem of three bodies from an analytical and dynamical point of view. First, a short review of the classical restricted problem is offered which is followed by the most general reformulation of the problem. In this most general formulation we consider a dynamical system consisting of several
Victor Szebehely, Arthur L. Whipple
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Out-of-plane equilibrium points in the elliptic restricted three-body problem under albedo effect

New Astronomy, 2021
M Javed Idrisi, M Shahbaz Ullah
exaly  

On the modified circular restricted three-body problem with variable mass

New Astronomy, 2021
Md Sanam Suraj, Rajiv Aggarwal, Md Chand Asique   +2 more
exaly