scholarly journals Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem

2017 ◽  
Author(s):  
Boris A. Percino-Figueroa ◽  
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Keyword(s):  
Angular Momentum ◽  
Body Problem ◽  
N Body Problem ◽  
Weak Kam Solutions

scholarly journals On Topological Stability in the General Three and Four-Body Problem

1983 ◽  
Vol 74 ◽  
pp. 301-315
Author(s):  
A. Milani ◽  
A.M. Nobili
Keyword(s):  
Angular Momentum ◽  
Total Energy ◽  
Reference System ◽  
Total Angular Momentum ◽  
Body Problem ◽  
Topological Stability ◽  
Level Lines ◽  
Change Of Scale ◽  
N Body Problem ◽  
Four Body Problem

By simple symmetry and change-of-scale considerations the topology of the level manifolds of the classical integrals of the N-body problem is shown to depend only on the value of the integral z = c2h (total angular momentum squared times total energy). For every hierarchical structure given to the N bodies the problem can be described as a set of N-l perturbed two-body problems by means of a fitted Jacobian coordinate system; in this setting the Easton inequality, relating potential, momentum of inertia and the z integral, is easily rederived. For N=3 the confinement conditions due to this inequality can be described, in a pulsating synodic reference system, as level lines of a modified potential function on a plane.

scholarly journals INTEGRABILITY OF THE N-BODY PROBLEM IN (2+1)-AdS GRAVITY

2000 ◽  
Vol 15 (27) ◽  
pp. 4361-4377
Author(s):  
P. VALTANCOLI
Keyword(s):  
Black Holes ◽  
Angular Momentum ◽  
Total Angular Momentum ◽  
Body Problem ◽  
Three Dimensional ◽  
Point Sources ◽  
First Order ◽  
Physical Motion ◽  
N Body Problem ◽  
Body Dynamics

We derive a first order formalism for solving the scattering of point sources in (2+1) gravity with negative cosmological constant. We show that their physical motion can be mapped, with a polydromic coordinate transformation, to a trivial motion, in such a way that the point sources move as timelike geodesics (in the case of particles) or as spacelike geodesics (in the case of BTZ black holes) of a three-dimensional hypersurface immersed in a four-dimensional Minkowskian space–time, and that the two-body dynamics is solved by two invariant masses, whose difference is simply related to the total angular momentum of the system.

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

scholarly journals The Use of Integrals in Numerical Integrations of theN-Body Problem

1971 ◽  
Vol 10 ◽  
pp. 40-51
Author(s):  
Paul E. Nacozy
Keyword(s):  
Angular Momentum ◽  
Numerical Integration ◽  
Degrees Of Freedom ◽  
Body Problem ◽  
Center Of Mass ◽  
Integration Step ◽  
Gravitational System ◽  
Systems Of Differential Equations ◽  
Numerical Integrations ◽  
Original Number

AbstractThe numerical integration of systems of differential equations that possess integrals is often approached by using the integrals to reduce the number of degrees of freedom or by using the integrals as a partial check on the resulting solution, retaining the original number of degrees of freedom.Another use of the integrals is presented here. If the integrals have not been used to reduce the system, the solution of a numerical integration may be constrained to remain on the integral surfaces by a method that applies corrections to the solution at each integration step. The corrections are determined by using linearized forms of the integrals in a least-squares procedure.The results of an application of the method to numerical integrations of a gravitational system of 25-bodies are given. It is shown that by using the method to satisfy exactly the integrals of energy, angular momentum, and center of mass, a solution is obtained that is more accurate while using less time of calculation than if the integrals are not satisfied exactly. The relative accuracy is ascertained by forward and backward integrations of both the corrected and uncorrected solutions and by comparison with more accurate integrations using reduced step-sizes.

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