scholarly journals Numerical study of the relativistic three-body quantization condition in the isotropic approximation

2018 ◽  
Vol 98 (1) ◽  
Author(s):  
Raúl A. Briceño ◽  
Maxwell T. Hansen ◽  
Stephen R. Sharpe
Keyword(s):  
Numerical Study ◽  
Quantization Condition ◽  
Isotropic Approximation ◽  
Three Body

scholarly journals Numerical Investigation for Periodic Orbits in the Hill Three-Body Problem

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 72 ◽  
Author(s):  
Vassilis S. Kalantonis
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Numerical Study ◽  
Three Dimensional ◽  
Earth Satellite ◽  
Mission Design ◽  
Special Importance ◽  
Three Body Problem ◽  
Three Body ◽  
The Hill

The current work performs a numerical study on periodic motions of the Hill three-body problem. In particular, by computing the stability of its basic planar families we determine vertical self-resonant (VSR) periodic orbits at which families of three-dimensional periodic orbits bifurcate. It is found that each VSR orbit generates two such families where the multiplicity and symmetry of their member orbits depend on certain property characteristics of the corresponding VSR orbit’s stability. We trace twenty four bifurcated families which are computed and continued up to their natural termination forming thus a manifold of three-dimensional solutions. These solutions are of special importance in the Sun-Earth-Satellite system since they may serve as reference orbits for observations or space mission design.

scholarly journals Numerical Simulations of Planetary Systems of the Jupiter-Saturn Type

1992 ◽  
Vol 152 ◽  
pp. 33-36
Author(s):  
R.A. Broucke
Keyword(s):  
Numerical Study ◽  
Close Approach ◽  
Major Axis ◽  
Two Dimensions ◽  
Semi Major Axis ◽  
Statistical Estimates ◽  
Long Time ◽  
Unit Radius ◽  
Series Of Experiments ◽  
Three Body

We made a numerical study of the General Three-Body Problem in two dimensions, with the intention to obtain some statistical estimates of the outcome of the system after a long time. Two different sets of masses were used. In the first series of experiments we use masses in the ratio of 0.95, 0.04 and 0.01. In the second series, we use masses that are exactly in the Sun-Jupiter-Saturn ratio. To facilitate the discussion, we use the names Sun, Jupiter and Saturn for the three masses, in both cases. In all our experiments, the orbit of Jupiter starts with zero eccentricity and with a unit radius. However, the orbit of Saturn varies in two ways: the initial value of the semi-major axis varies from 1.1 to 3.5 and the eccentricity from 0.0 to 0.75. In total about 4000 cases were run for the two series of masses. All the numerical integrations were done with the method of recurrent power series of order 14, in a heliocentric frame of reference, integrating thus eight simultaneous first-order differential equations. All integrations were performed for a maximum of 12,500 canonical units of time, corresponding to about 2000 revolutions of Jupiter. The cause of termination or type of catastrophe for the system has been determined in all cases. In most cases, this is a close approach of Saturn with Jupiter, followed by ejection of Saturn from the system.

scholarly journals Extracting observables from lattice data in the three-particle sector

2018 ◽  
Vol 175 ◽  
pp. 11006
Author(s):  
Akaki Rusetsky ◽  
Hans-Werner Hammer ◽  
Jin-Yi Pang
Keyword(s):  
Finite Volume ◽  
Energy Shift ◽  
Bound State ◽  
Effective Field ◽  
Quantization Condition ◽  
Unitary Limit ◽  
Lattice Data ◽  
Volume Energy ◽  
Three Body

The three-particle quantization condition is derived, using the particle-dimer picture in the non-relativistic effective field theory. The procedure for the extraction of various observables in the three-particle sector (the particle-dimer scattering amplitudes, breakup amplitudes, etc.) from the finite-volume lattice spectrum is discussed in detail. As an illustration of the general formalism, the expression for the finite-volume energy shift of the three-body bound-state in the unitary limit is re-derived. The role of the threebody force, which is essential for the renormalization, is highlighted, and the extension of the result beyond the unitary limit is studied. Comparison with other approaches, known in the literature, is carried out.

scholarly journals Three-particle system in a finite volume: formalism, quantization condition, spectrum and energy shift

2020 ◽  
Vol 241 ◽  
pp. 02005
Author(s):  
Jin-Yi Pang
Keyword(s):  
Finite Volume ◽  
Bound States ◽  
Particle System ◽  
Energy Shift ◽  
Effective Field ◽  
Quantization Condition ◽  
High Current ◽  
Scattering States ◽  
Three Body ◽  
Hadronic Process

Lattice QCD calculations provide an ab initio access to hadronic process. These calculations are usu ally performed in a small cubic volume with periodic boundary conditions. The infinite volume extrapolations for three-body systems are indispensable to understand many systems of high current interest. We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. Our work shows a powerful and transparent method to read off three-body physical observables from lattice simulations. In this paper, we review the formalism, quantization condition, spectrum analysis and energy shifts calculation both for 3-body bound states and scattering states.

Sign in / Sign up

Export Citation Format

Share Document