Analytical solution of the Lagrange quintic equation in the three-body problem in celestial mechanics

1985 ◽  
Vol 55 (3-4) ◽  
pp. 267-272 ◽  
Author(s):  
N. I. Ioakimidis ◽  
K. E. Papadakis
Keyword(s):  
Analytical Solution ◽  
Celestial Mechanics ◽  
Body Problem ◽  
Three Body Problem ◽  
Quintic Equation ◽  
Three Body

The Celestial Mechanics Three-body Problem

1988 ◽  
pp. 79-87
Author(s):  
Erich W. Schmid ◽  
Gerhard Spitz ◽  
Wolfgang Lösch
Keyword(s):  
Celestial Mechanics ◽  
Body Problem ◽  
Three Body Problem ◽  
Three Body

The Celestial Mechanics Three-body Problem

1990 ◽  
pp. 81-89
Author(s):  
Erich W. Schmid ◽  
Gerhard Spitz ◽  
Wolfgang Lösch
Keyword(s):  
Celestial Mechanics ◽  
Body Problem ◽  
Three Body Problem ◽  
Three Body

scholarly journals Analytical Solution of the Bosonic Three-Body Problem

2008 ◽  
Vol 100 (14) ◽  
Author(s):  
Alexander O. Gogolin ◽  
Christophe Mora ◽  
Reinhold Egger
Keyword(s):  
Analytical Solution ◽  
Body Problem ◽  
Three Body Problem ◽  
Three Body

scholarly journals Stability Theory in Celestial Mechanics

1974 ◽  
Vol 62 ◽  
pp. 1-9
Author(s):  
J. Moser
Keyword(s):  
Celestial Mechanics ◽  
Stability Theory ◽  
Recent Progress ◽  
Body Problem ◽  
Homoclinic Orbits ◽  
Perturbation Series ◽  
Three Body Problem ◽  
The Stability ◽  
Three Body ◽  
Positive Results

This expository lecture surveys recent progress of the stability theory in Celestial Mechanics with emphasis on the analytical problems. In particular, the old question of convergence of perturbation series are discussed and positive results obtained, in the light of the work by Kolmogorov Arnold and Moser. For the three body problem, classes of quasi-periodic solutions and doubly asymptotic (or homoclinic) orbits are discussed.

Celestial Mechanics

2018 ◽  
Author(s):  
Prasenjit Saha ◽  
Paul A. Taylor
Keyword(s):  
Celestial Mechanics ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Hamiltonian Form ◽  
Three Body Problem ◽  
Lagrange Points ◽  
Chaotic Orbits ◽  
Orbit Integration ◽  
Numerical Orbit ◽  
Three Body

Celestial mechanics abounds in interesting and counter-intuitive phenomena, such as descriptions of mass transfer between stars or optimal placements of satellites within the Solar System. Remarkably, many such features are already present in the restricted three-body problem, whose assumptions still allow for analytical understanding, and to which the second chapter is devoted. This ‘simplified’ system is discussed first in terms of forces (both gravitational and fictitious), and then using the Hamiltonian form. As well as traditional topics like stable and unstable Lagrange points and Roche lobes, a brief introduction to chaotic orbits is given. Additionally, readers are guided towards exploring on their own with numerical orbit integration.

Rigid-Rotator and Fixed-Shape Solutions to the Coulomb Three-Body Problem

1997 ◽  
Vol 22 (1) ◽  
pp. 37-60 ◽  
Author(s):  
A. Santander ◽  
J. Mahecha ◽  
F. Pérez
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Rigid Rotator ◽  
Three Body
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