Results 221 to 230 of about 161,781 (262)

Restrictions on the Motion of the Three-Body Problem

SIAM Journal on Applied Mathematics, 1974
It is shown in the three-body problem of Newtonian mechanics that there exist values of the constants of motion which define regions in physical space where motion cannot occur.
openaire   +2 more sources

Resonant motion in the restricted three body problem

Celestial Mechanics and Dynamical Astronomy, 1993
The resonant structure of the restricted three-body problem for the Sun- Jupiter asteroid system in the plane is studied, both for a circular and an elliptic orbit of Jupiter. Three typical resonances are studied, the 2:1, 3:1 and 4:1 mean motion resonance of the asteroid with Jupiter.
openaire   +1 more source

The Restricted Three-Body Problem

1990
The determination of the motion of N point-like masses under their mutual gravitational forces is the basic problem in celestial mechanics, with important applications to fundamental astrophysical problems, like the dynamical structure of planetary and satellite systems and the evolution of multiple stellar systems, ranging from multiple stars to ...
Bruno Bertotti, Paolo Farinella
openaire   +2 more sources

The Restricted Three-Body Problem

2016
An important particular solution of the three-body problem results when one of the three masses is so small, in comparison to the other two, that its gravitational effects can be neglected. This may be called an infinitesimal body compared with the two finite bodies. This is the restricted three-body problem (Szebehely 1967), as mentioned in Sect.
Pini Gurfil, P. Kenneth Seidelmann
openaire   +1 more source

The Restricted Three-Body Problem

2018
Celestial mechanics has a long history, see for example the encyclopedic works of Hagihara [109] and Szebehely [231], or the Scholarpedia article on the threebody problem by Chenciner [53] or on Celestial Mechanics by Ferraz-Mello [83] and the references therein.
Urs Frauenfelder, Otto van Koert
openaire   +1 more source

Saari’s conjecture for the restricted three-body problem

Celestial Mechanics and Dynamical Astronomy, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Roberts, G. E., Melanson, L.
openaire   +2 more sources

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.
openaire   +2 more sources

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
openaire   +3 more sources

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
openaire   +2 more sources

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.
openaire   +1 more source