Decomposition of the schrodinger equation for two identical particles and a third particle of finite mass
Schroedinger equation angular momentum partials for three body problem
THREE-BODY PROBLEM↗
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A SYMMETRIC REPRESENTATION FOR 3-BODY PROBLEMS. I. MOTION IN A PLANE
A symmetric representation for 3-body problems motion in a plane
PARTICLE TRACK↗
PERIODIC SOLUTIONS OF THE RESTRICTED THREE BODY PROBLEM REPRESENTING ANALYTIC CONTINUATIONS OF KEPLERIAN ELLIPTIC MOTIONS
Periodic solution of restricted three body problem as analytic continuation of keplerian elliptical motions
KEPLER LAW↗
THE RESTRICTED THREE BODY PROBLEM. I. THE SURFACES OF ZERO VELOCITY IN REGULARIZED COORDINATES. 2. THE EULER PROBLEM BY GRAPHICAL ANALYSIS
Three body problem zero velocity curves - euler two center problem by graphical analysis - guidance systems
EULER EQUATION↗
THE HAMILTON-JACOB I FORMULATION OF THE RESTRICTED THREE BODY PROBLEM IN TERMS OF THE TWO FIXED CENTER PROBLEM
Three body problem by hamilton-jacobi perturbation theory - guidance systems
HAMILTON-JACOBI EQUATION↗
Lunar Flight Study Series: Volume 6. A Study of Geometrical and Terminal Characteristics of Earth-Moon Transits Embedded in the Earth-Moon Plane
This report represents the results of a study of coplanar earth-moon transits. The study was initiated to provide information concerning coplanar geometrical characteristics of earth-moon trnasits. The geometrical aspects of transit behavior are related to variations injection conditions. The model of the earth-moon system used in this investigation is the Jacobian model of the restricted three body problem. All transits considered in this study are restricted to the moon-earth plane (MEP).
TRAJECTORY MEASURING SYSTEM↗
The Restricted Three-Body-Problem as a Perturbation of Euler's Problem of Two Fixed Centers and Its Application to Lunar Trajectories
The restricted Three-Body-Problem considers the motion of an infinitesimal mass under the gravitational attraction of two finite masses, which revolve about their common center of gravity in coplanar circles. It is well known that Euler's problem of two fixed centers, consisting of the motion of an infinitesimal mass under the gravitational attraction of two finite masses fixed in space, can be solved by elliptic functions. The idea presented here is to take the solution of Euler's problem as the solution of the restricted Three-Body-Problem by allowing the initial values to be functions of time now. Differential equations for the perturbed initial values are established. These equations can be given in closed form by using the fact that the transformation to the perturbed initial values of Euler's problem is canonical. Thus, an approximation can be obtained for the solution of the restricted Three-Body-Problem. The method can also be used to represent classes of neighboring trajectories for guidance purposes.
Euler equation↗
Lectures in Applied Mathematics. Volume 5 - Space Mathematics, Part 1
The present Proceedings should acquaint the reader with the current state of research on the behavior of nonpropulsive space vehicles, indicate the more pressing unsolved problems, and furnish examples of mathematical techniques which are currently useful. It is hoped that the reader will be stimulated to make contributions of his own, either in the way of developing better mathematical techniques, or finding more ingenious uses of existing ones.
Three-Body Problem↗
DETERMINATION AND SURVEY OF PERIODIC TROJAN ORBITS IN THE RESTRICTED PROBLEM OF THREE BODIES
Determination and survey of periodic trojan orbits in the restricted problem of three bodies
ORBIT↗
THREE-BODY COLLISION RATES IN ATOMIC RECOMBINATION REACTIONS
Three-body collision rates in atomic recombination reactions
COLLISION RATE↗
Lunar Flight Study Series: Volume 3. Earth to Moon Trajectory Investigation for Mission Profiles Involving a Lunar Parking Orbit
Three-body moon-earth satellite orbit and trajectory calculations for injection and periselenum
THREE-BODY PROBLEM↗
ON THE ELLIPTIC CASE OF THE RESTRICTED PROBLEM OF THREE BODIES AND THE REMOTE HISTORY OF THE EARTH-MOON SYSTEM
Jacobi integral and the elliptic case of the restricted problem of three bodies, and study of the remote history of the earth-moon system
THREE-BODY PROBLEM↗
A group of earth-to-moon trajectories with consecutive collisions.
Set of earth to moon trajectories and its relation to apollo mission trajectories
THREE-BODY PROBLEM↗
Instructions for the use of the marquardt ibm 7040 computer program. controlled tethering in space
Computer program for orbiting three body system simulation in Fortran
THREE-BODY PROBLEM↗
Decomposition of the schroedinger equation for two identical particles and a third particle of finite mass.
Angular momentum decomposition of Schrodinger equation extended to case of two identical particles and third particle of finite mass
PARTICLE THEORY↗
The restricted problem of three bodies. II.
Periodic solutions for sputnik motion in gravitational field of two other bodies of finite mass
GRAVITATIONAL FIELD↗
Coupled-channel approach to isotensor π π π scattering from lattice QCD
The quest to understand three-body dynamics from first-principle QCD includes the study of nonresonant and resonant systems. The isospin I = 2 system is of particular interest having no three-body resonance but featuring a resonance in a subchannel, while also being a coupled-channel problem. In this study, we calculate the finite-volume spectrum from lattice QCD at two different pion masses, map the amplitude to the infinite volume through a generalized Finite-Volume Unitarity three-body quantization condition, investigate the limit of a narrow ρ , and compare with an effective Lagrangian prediction at leading order. Chiral extrapolations between different pion masses are performed.
Feng, Yuchuan [The George Washington University] (↗
Toward scalable bound-to-resonance extrapolations for few- and many-body systems
In open quantum many-body systems, the theoretical description of resonant states of many particles strongly coupled to the continuum can be challenging. Such states are commonplace in, for example, exotic nuclei and hadrons, and can reveal important information about the underlying forces at play in these systems. In this work, we demonstrate that the complex-augmented eigenvector continuation (CA-EC) method, originally formulated for the two-body problem with uniform complex scaling, can reliably perform bound-to-resonance extrapolations for genuine three-body resonances having no bound subsystems. Here, we first establish that three-body bound-to-resonance extrapolations are possible by benchmarking different few-body approaches, and we provide arguments to explain how the extrapolation works in the many-body case. We furthermore pave the way towards scalable resonance extrapolations in many-body systems by showing that the CA-EC method also works in the Berggren basis, studying a realistic application using the Gamow shell model.
Ab initio calculations↗