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Results for “THREE-BODY PROBLEM”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1967

Theory of Orbits.

Book on theory of orbits covering restricted problem of three bodies, two bodies in rotating coordinate system and periodic orbits

LIBRATIONAL MOTION↗
NASA NTRS1973

Minimum impulse three-body trajectories.

A rapid and accurate method of calculating optimal impulsive transfers in the restricted problem of three bodies has been developed. The technique combines a multi-conic method of trajectory integration with primer vector theory and an accelerated gradient method of trajectory optimization. A unique feature is that the state transition matrix and the primer vector are found analytical without additional integrations or differentiations. The method has been applied to the determination of optimal two and three impulse transfers between the L2 libration point and circular orbits about both the earth and the moon.

D'Amario, L.↗
DOE OSTI2026

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] (↗
DOE OSTI2025

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↗
NASA NTRS1978

A model for close encounters in the planetary problem

A model is proposed for single close encounters between two small masses, m1 and m2, which orbit a much larger mass, M. The main new feature of the model is the assumption of conic motion of the center of mass of m1 and m2 in the gravitational field of M. Comparisons of the model with the three-body equations of motion indicate that the model is a useful approximation for m1, m2 not exceeding 0.00001 M. The model is therefore applicable for encounters between bodies of the order of an earth mass or smaller in the presence of the sun. Comparisons are also made of outcomes obtained by the model with outcomes of numerical integration for a large variety of close encounters. The above comparisons reveal that for many purposes the model is an adequate approximation for encounters with an eccentricity of the hyperbolic orbit of m1 about m2 not less than 4.

Cox, L. P.↗
DOE OSTI2025

Improved structure of calcium isotopes from ab initio calculations

The in-medium similarity renormalization group (IMSRG) is a powerful and flexible many-body method to compute the structure of nuclei starting from nuclear forces. Recent developments have extended the IMSRG from its standard truncation at the normal-ordered two-body level, the IMSRG(2), to a precision approximation including normal-ordered three-body operators, the IMSRG(3)-N 7 . This improvement provides a more precise solution to the many-body problem and makes it possible to quantify many-body uncertainties in IMSRG calculations. We explore the structure of 44,48,52 Ca using the IMSRG(3)-N 7 , focusing on understanding existing discrepancies of the IMSRG(2) to experimental results. We find a significantly better description of the first 2 + excitation energy of 48 Ca, improving the description of the shell closure at N=28. At the same time, we find that the IMSRG(3)-N 7 corrections to charge radii do not resolve the systematic underprediction of the puzzling large charge radius difference between 52 Ca and 48 Ca. We present estimates of many-body uncertainties of IMSRG(2) calculations applicable also to other systems based on the size extensivity of the method.

39 ≤ A ≤ 58↗
NASA NTRS1968

Research in the Restricted Problems of Three and Four Bodies Final Scientific Report

Seven studies have been conducted on research in the existence and nature of solutions of the restricted problems of three and four bodies. The details and results of five of these research investigations have already been published, and the latest two studies will be published shortly. A complete bibliography of publications is included in this report. This research has been primarily qualitative and has yielded new information on the behavior of trajectories near the libration points in the Earth-Moon-Sun and Sun-Jupiter-Saturn systems, and on the existence of periodic trajectories about the libration points of the circular and elliptical restricted four-body models. We have also implemented Birkhoff's normalization process for conservative and nonconservative Hamiltonian systems with equilibrium points. This makes available a technique for analyzing stability properties of certain nonlinear dynamical systems, and we have applied this technique to the circular and elliptical restricted three-body models. A related study was also conducted to determine the feasibility of using cislunar periodic trajectories for various space missions. Preliminary results suggest that this concept is attractive for space flight safety operations in cislunar space. Results of this research will be of interest to mathematicians, particularly those working in ordinary differential equations, dynamical systems and celestial mechanics; to astronomers; and to space guidance and mission analysts.

Richards, Paul B.↗
NASA NTRS1973

Optimality of incompletely measurable active and passive attitude control systems

Passive attitude control systems and active systems with incomplete state measurements are only suboptimal systems in the sense of optimal control theory, since optimal systems require complete state measurements or state estimations. An optimal system, then, requires additional hardware (especially in the case of flexible spacecraft) which results in higher costs. Therefore, it is a real engineering problem to determine how much an optimal system exceeds the suboptimal system, or in other words, what is the suboptimal system's degree of optimality. The problem will be treated in three steps: (1) definition of the degree of optimality for linear, time-invariant systems; (2) a computation method using the quadratic cost functional; (3) application to a gravity-gradient stabilized three-body satellite and a spinning flexible satellite.

Schiehlen, W.↗
NASA NTRS1974

User's guide to four-body and three-body trajectory optimization programs

A collection of computer programs and subroutines written in FORTRAN to calculate 4-body (sun-earth-moon-space) and 3-body (earth-moon-space) optimal trajectories is presented. The programs incorporate a variable step integration technique and a quadrature formula to correct single step errors. The programs provide capability to solve initial value problem, two point boundary value problem of a transfer from a given initial position to a given final position in fixed time, optimal 2-impulse transfer from an earth parking orbit of given inclination to a given final position and velocity in fixed time and optimal 3-impulse transfer from a given position to a given final position and velocity in fixed time.

Pu, C. L.↗