A model calculation in a new approach to the three-body problem

1973 ◽  
Vol 258 (1) ◽  
pp. 64-80 ◽  
Author(s):  
W. Glöckle ◽  
K. Ueta
Keyword(s):  
Model Calculation ◽  
Body Problem ◽  
Three Body Problem ◽  
New Approach ◽  
Three Body

A new approach to the three-body problem

1970 ◽  
Vol 141 (3) ◽  
pp. 620-630 ◽  
Author(s):  
W. Glöckle
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
New Approach ◽  
Three Body

scholarly journals On the Quadratization of the Integrals for the Many-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3208
Author(s):  
Yu Ying ◽  
Ali Baddour ◽  
Vladimir Gerdt ◽  
Mikhail Malykh ◽  
Leonid Sevastianov
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Many Body ◽  
Integrals Of Motion ◽  
Quadratic Polynomials ◽  
New Approach ◽  
The Many ◽  
New Variables ◽  
Three Body ◽  
The Relationship

A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed herein. We introduced additional variables, namely distances and reciprocal distances between bodies, and wrote down a system of differential equations with respect to the coordinates, velocities, and the additional variables. In this case, the system lost its Hamiltonian form, but all the classical integrals of motion of the many-body problem under consideration, as well as new integrals describing the relationship between the coordinates of the bodies and the additional variables are described by linear or quadratic polynomials in these new variables. Therefore, any symplectic Runge–Kutta scheme preserves these integrals exactly. The evidence for the proposed approach is given. To illustrate the theory, the results of numerical experiments for the three-body problem on a plane are presented with the choice of initial data corresponding to the motion of the bodies along a figure of eight (choreographic test).

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

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

New Astronomy ◽  
2021 ◽  
Vol 84 ◽  
pp. 101510
Author(s):  
Md Sanam Suraj ◽  
Rajiv Aggarwal ◽  
Md Chand Asique ◽  
Amit Mittal
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

Triple close approach in the three-body problem: A limit for the bounded orbits

1984 ◽  
Vol 32 (1) ◽  
pp. 15-28 ◽  
Author(s):  
Jacques Laskar ◽  
Christian Marchal
Keyword(s):  
Body Problem ◽  
Close Approach ◽  
Three Body Problem ◽  
Three Body
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