A variable order method for the numerical integration of the gravitational N-body problem

1974 ◽  
pp. 291-303 ◽  
Author(s):  
Guy Janin
Keyword(s):  
Numerical Integration ◽  
Body Problem ◽  
Variable Order ◽  
Order Method ◽  
N Body Problem

Numerical experiment applicable to planet formation

1984 ◽  
Vol 75 ◽  
pp. 675-676
Author(s):  
Anny Cazenave
Keyword(s):  
Numerical Model ◽  
Numerical Experiment ◽  
Numerical Integration ◽  
Body Problem ◽  
Three Dimensional ◽  
Dynamical Evolution ◽  
The Sun ◽  
Gravitational Perturbations ◽  
N Body Problem ◽  
Fragmentation Processes

A three-dimensional numerical model has been developed with the goal of studying limited dynamical problems relevant to the latest stage of planet growth in the accretion theory. A small number of large protoplanets (~ moon-size) of different masses, moving around the Sun, are considered. The dynamical evolution and growth of the population is studied under mutual gravitational perturbations, accretion and collisional fragmentation processes. Gravitational encounters are treated exactly by numerical integration of the N-body problem. Outcomes of collisional fragmentation are modeled according to the results of Greenberg et al. (1978).

Global Regularization of a Restricted Four-Body Problem

2014 ◽  
Vol 24 (07) ◽  
pp. 1450092 ◽  
Author(s):  
Martha Alvarez-Ramírez ◽  
Joaquín Delgado ◽  
Claudio Vidal
Keyword(s):  
Numerical Integration ◽  
Body Problem ◽  
Binary Collision ◽  
Type Transformation ◽  
Collision Singularity ◽  
Double Collision ◽  
N Body Problem ◽  
Four Body Problem ◽  
Collision Orbits ◽  
Global Regularization

In the n-body problem, a collision singularity occurs when the position of two or more bodies coincide. By understanding the dynamics of collision motion in the regularized setting, a better understanding of the dynamics of near-collision motion is achieved. In this paper, we show that any double collision of the planar equilateral restricted four-body problem can be regularized by using a Birkhoff-type transformation. This transformation has the important property to provide a simultaneous regularization of three singularities due to binary collision. We present some ejection–collision orbits after the regularization of the restricted four-body problem (RFBP) with equal masses, which were obtained by numerical integration.

Taylor series method of numerical integration of the N-body problem

2017 ◽  
Author(s):  
Irina M. Alesova ◽  
Levon K. Babadzanjanz ◽  
Irina Yu. Pototskaya ◽  
Yulia Yu. Pupysheva ◽  
Artur T. Saakyan
Keyword(s):  
Numerical Integration ◽  
Taylor Series ◽  
Body Problem ◽  
Series Method ◽  
N Body Problem ◽  
Taylor Series Method

scholarly journals On frequency estimations in phase fitted variational integrators for the general N-body problem

PAMM ◽  
2013 ◽  
Vol 13 (1) ◽  
pp. 33-34
Author(s):  
Odysseas Kosmas ◽  
Sigrid Leyendecker
Keyword(s):  
Body Problem ◽  
Variational Integrators ◽  
N Body Problem
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