Integration of the N body gravitational problem by separation of the force into a near and a far component

1974 ◽  
pp. 313-336
Author(s):  
Afaq Ahmad ◽  
Leon Cohen
Keyword(s):  
Gravitational Problem

Recent developments of integrating the gravitational problem ofN-bodies

1971 ◽  
Vol 13 (2) ◽  
pp. 365-376 ◽  
Author(s):  
Victor Szebehely ◽  
Dale G. Bettis
Keyword(s):  
Recent Developments ◽  
Gravitational Problem

scholarly journals Treatment of Close Approaches in the Numerical Integration of the Gravitational Problem of N Bodies

1971 ◽  
Vol 10 ◽  
pp. 133-150 ◽  
Author(s):  
D. G. Bettis ◽  
V. Szebehely
Keyword(s):  
Numerical Integration ◽  
Body Problem ◽  
Considerable Increase ◽  
Equations Of Motion ◽  
Computer Time ◽  
Tidal Effects ◽  
Basic Ideas ◽  
Gravitational Problem ◽  
Considerable Detail ◽  
Numerical Approaches

AbstractOne of the main difficulties encountered in the numerical integration of the gravitational n-body problem is associated with close approaches. The singularities of the differential equations of motion result in losses of accuracy and in considerable increase in computer time when any of the distances between the participating bodies decreases below a certain value. This value is larger than the distance when tidal effects become important, consequently, numerical problems are encountered before the physical picture is changed. Elimination of these singularities by transformations is known as the process of regularization. This paper discusses such transformations and describes in considerable detail the numerical approaches to more accurate and faster integration. The basic ideas of smoothing and regularization are explained and applications are given.

scholarly journals VII. Note on a gravitational problem

1910 ◽  
Vol 19 (109) ◽  
pp. 91-95
Author(s):  
C.V. Burton
Keyword(s):  
Gravitational Problem

Recent advances in the regularization of the gravitational problem ofn bodies

1974 ◽  
Vol 10 (2) ◽  
pp. 183-184 ◽  
Author(s):  
V. Szebehely
Keyword(s):  
Recent Advances ◽  
Gravitational Problem

A numerical integration scheme for the N-body gravitational problem

1973 ◽  
Vol 12 (3) ◽  
pp. 389-402 ◽  
Author(s):  
A Ahmad ◽  
L Cohen
Keyword(s):  
Numerical Integration ◽  
Integration Scheme ◽  
Numerical Integration Scheme ◽  
Gravitational Problem

Treatment of close approaches in the numerical integration of the gravitational problem ofN bodies

1971 ◽  
Vol 14 (1) ◽  
pp. 133-150 ◽  
Author(s):  
D. G. Bettis ◽  
V. Szebehely
Keyword(s):  
Numerical Integration ◽  
Gravitational Problem

scholarly journals The Binaries from Unstable Triples. Dynamical Processes of Formation

1989 ◽  
Vol 8 ◽  
pp. 143-144
Author(s):  
Joanna P. Anosova
Keyword(s):  
Computer Simulations ◽  
Dynamical Evolution ◽  
Close Binary ◽  
Close Binaries ◽  
State University ◽  
Dynamical Processes ◽  
Triple Systems ◽  
Gravitational Problem ◽  
Three Body

The dynamical processes of formation, evolution and disruption of binaries may be effectively studied by computer simulations in the N > 3-body gravitational problem. As a result of analysis of these investigations of diverse authors, the classification of the dynamical processes of formation of wide and close binaries may be proposed (see Table 1). This Table shows the following general processes: I-triple approaches of the single bodies; II-approaches of binaries with single bodies; Ill-escape from physical triples. The actions of these processes, and kinetics of a frequency of binaries in general field were studied at the Astronomical Observatory of the Leningrad State University (1965-1988) by computer simulations in the three-body problem. More than 3.104 orbits with negative total energy E < 0 and 5.104 with E > 0 have been run on the computers. The film “Dynamical evolution of triple systems” was produced. Part I of this movie shows the evolution of the unstable non-hierarchical triplet as well as the processes of formation, evolution, and disruption of temporary wide and final close binaries inside the physical triples. Part II of film presents in detail the trajectories of the bodies on the triple approaches of “fly-by”-and of “exchange”-types. The triple approach of “fly-by”-type results often in an escape from triple as well as the formation of final close binary. The triple approach of “exchange”-type consists as a rule of a few close double approaches of bodies and rarely results in an escape from triplet, it results in formation of temporary wide binary inside triplet. Part III of movie presents the trajectories of the different-mass bodies: an escape of the minimum-mass body, the intermediate-mass body, and the maximum-mass body as well as a formation of binaries with different-mass components.

On the chiral connection between the ferromagnet, the axisymmetric gravitational problem and the SU(2) vacuum gauge field

1978 ◽  
Vol 66 (5) ◽  
pp. 352-356 ◽  
Author(s):  
Minoru Hirayama ◽  
Hsiung Chia Tze ◽  
Jun Ishida ◽  
Tetsuji Kawabe
Keyword(s):  
Gauge Field ◽  
Vacuum Gauge ◽  
Gravitational Problem
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