منابع مشابه
The Gravitational Million-Body Problem
We review what has been learned recently using N -body simulations about the evolution of globular clusters. While simulations of star clusters have become more realistic, and now include the evolution of single and binary stars, the prospect of reaching large enough N is still a distant one. Nevertheless more restricted kinds of simulations have recently brought valuable progress for certain p...
متن کاملChaos in the one-dimensional gravitational three-body problem.
We have investigated the appearance of chaos in the one-dimensional Newtonian gravitational three-body system (three masses on a line with -1/r pairwise potential). In the center of mass coordinates this system has two degrees of freedom and can be conveniently studied using Poincare sections. We have concentrated in particular on how the behavior changes when the relative masses of the three b...
متن کاملVariational Integrators for the Gravitational N-body Problem
This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared time steps, the algorithm is momentum conserving and symplectic. We generalize the algorithm to handle individual time steps; this introduces fifth-order errors in angular momentum conservation and symplecticity. We show that using adaptive...
متن کاملShadowing high-dimensional hamiltonian systems: the gravitational N-body problem.
A shadow is an exact solution to a chaotic system of equations that remains close to a numerically computed solution for a long time. Using a variable-order, variable-time-step integrator, we numerically compute solutions to a gravitational N-body problem in which many particles move and interact in a fixed potential. We then search for shadows of these solutions with the longest possible durat...
متن کاملOrbital Divergence and Relaxation in the Gravitational N - Body Problem
One of the fundamental aspects of statistical behaviour in many-body systems is exponential divergence of neighbouring orbits, which is often discussed in terms of Liapounov exponents. Here we study this topic for the classical gravi-tational N-body problem. The application we have in mind is to old stellar systems such as globular star clusters, where N ∼ 10 6 , and so we concentrate on spheri...
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ژورنال
عنوان ژورنال: Symposium - International Astronomical Union
سال: 2003
ISSN: 0074-1809
DOI: 10.1017/s0074180900207043