Related papers: Three-body problem -- from Newton to supercomputer…
The 3:1 mean-motion resonance of the planar elliptic restricted three body problem (Sun-Jupiter-asteroid) is considered. The double numeric averaging is used to obtain the evolutionary equations which describe the long-term behavior of the…
We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability…
Since the earliest proposals for artificial neural network (ANN) models of the mind and brain, critics have pointed out key weaknesses in these models compared to human cognitive abilities. Here we review recent work that uses metalearning…
The problem of $N$ particles interacting through pairwise central forces is notoriously intractable for $N\geq3$. Some quite remarkable specific cases have been solved in one dimension, whereas higher-dimensional exactly solved systems…
The 2:1 mean motion resonance orbit was integrated at the restricted planar 3-body problem in absolute frame. Orbit of Jupiter was assumed circular. Initial Jupiter longitude was assumed zero. The Runge-Kutta method was used. The start of…
The planetary restricted three-body problem (RTBP) is considered. The primary mass M is much more than another masses mj, i=1..N, which revolve around M. The massless probe particle m moves on elliptic orbit, is perturbed by mj. It is well…
Achieving maximum scientific results from the overwhelming volume of astronomical data to be acquired over the next few decades will demand novel, fully automatic methods of data analysis. Artificial intelligence approaches hold great…
We develop computer assisted arguments for proving the existence of transverse homoclinic connecting orbits, and apply these arguments for a number of non-perturbative parameter and energy values in the spatial equilateral circular…
The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as…
We provide an analytical approximation of a periodic solution of the three body problem in celestial mechanics, the so-called figure eight solution, discovered 1993 by C. Moore. This approximation has the form of a Fourier series whose…
The rectilinear elliptic restricted Three Body Problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity $e'=1$, but the collision of the…
A computational approach is developed for the design of continuous low thrust transfers in the planar circular restricted three-body problem. The transfer design method of invariant manifolds is extended with the addition of continuous low…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…
Variational quantum eigensolver ans\"atze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis…
Braids are periodic solutions to the general N-body problem in gravitational dynamics. These solutions seem special and unique, but they may result from rather usual encounters between four bodies. We aim at understanding the existence of…
The restricted three body problem is well-known and very important for dynamics of binary, multiple stars and also planetary systems. We extend the classical version of this problem to the situation that there are some external forces from…
Towards the end of nineteenth century, Celestial Mechanics provided the most powerful tools to test Newtonian gravity in the solar system, and led also to the discovery of chaos in modern science. Nowadays, in light of general relativity,…
Continuing work initiated in earlier publications [Ichita, Yamada and Asada, Phys. Rev. D {\bf 83}, 084026 (2011); Yamada and Asada, Phys. Rev. D {\bf 86}, 124029 (2012)], we examine the post-Newtonian (PN) effects on the stability of the…
The classical simulation of quantum systems typically requires exponential resources. Recently, the introduction of a machine learning-based wavefunction ansatz has led to the ability to solve the quantum many-body problem in regimes that…
Advancements in the implementation of quantum hardware have enabled the acquisition of data that are intractable for emulation with classical computers. The integration of classical machine learning (ML) algorithms with these data holds…