Related papers: Are numerical theories irreplaceable? A computatio…
Many binary systems of interest for gravitational-wave astronomy are orbited by a third distant body, which can considerably alter their relativistic dynamics. Precision computations are needed to understand the interplay between…
We address a fundamental challenge in space mission design and space logistics: planning interplanetary trajectories for missions that must rendezvous with multiple bodies. Such mission occur, for instance, in active debris removal,…
A systolic algorithm rhythmically computes and passes data through a network of processors. We investigate the performance of systolic algorithms for implementing the gravitational N-body problem on distributed-memory computers. Systolic…
The problem of nonintegrability of the circular restricted three-body problem is very classical and important in the theory of dynamical systems. It was partially solved by Poincare in the nineteenth century: He showed that there exists no…
We construct a Nekhoroshev-like result of stability with sharp constants for the planar three body problem, both in the planetary and in the restricted circular case, by using the periodic averaging technique. Our constructions can be…
The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
This paper studies the numerical computation of integrals, representing estimates or predictions, over the output $f(x)$ of a computational model with respect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to the model. For…
Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, one argues that it is not unconceivable that classical physical systems may "compute the hard or even the…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
Trivial choreographies are special periodic solutions of the planar three-body problem. In this work we use a modified Newton's method based on the continuous analog of Newton's method and a high precision arithmetic for a specialized…
The elliptic restricted three body problem has been well studied. However, the previous formulations of the problem have used a rotating coordinate system to keep the positions of the primary and secondary on the x-axis. This requires the…
In spite of the fact that the Newtonian dynsmics of the underlying molecules do not seem to favor one direction of time over its opposite, the non-decreasing entropy of macroscopic physical systems provides a unique direction to 'the arrow…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical…
We compare recent numerical results, obtained within a ``helical Killing vector'' (HKV) approach, on circular orbits of corotating binary black holes to the analytical predictions made by the effective one body (EOB) method (which has been…
We show that for continuous time dynamical systems described by polynomial differential equations of modest degree (typically equal to three), the following decision problems which arise in numerous areas of systems and control theory…
Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly…
Sitnikov problem, consisting two close binaries and a third small body is considered, leading to a rapid ejection of the small body from the binaries. This mechanism is proposed as an explanation of jets in many astrophysical systems.…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…