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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 NTRS1972

On the elliptic restricted three-body problem.

This article describes the most important features of the elliptic restricted three-body problem. The methods of numerical integration with recurrent power series are developed for both the equations of motion and the variational equations. The conditions for the existence of periodic orbits and families of periodic orbits are also outlined in detail, and finally illustrated with a family of symmetric periodic orbits.

Broucke, R.↗
NASA NTRS2016

Periodic Orbit-Attitude Solutions in the Planar Elliptic Restricted Three-Body Problem

The pitch motion of a spacecraft in the planar elliptic restricted three-body system is studied. Previous studies laid the foundation for spacecraft stability analysis with a small perturbation to the zero pitch motion. In this study, a cell mapping approach that combines analytical and numerical techniques is used to study the global behavior of the full nonlinear spacecraft attitude in which coupling between orbital dynamics and attitude occurs. The effect of gravity gradient torques, orbital eccentricity, and the spacecraft configuration at different Lagrangian points is analyzed. Multiple-period periodic solutions and invariant surfaces are presented for different cases. Reference trajectories around the Lagrangian points are also considered to study coupled dynamics.

Koh, Dayung↗
NASA NTRS1975

Periodic orbits in the Planar General Three-Body Problem

The article contains a numerical study of periodic solutions of the Planar General Three-Body Problem. Several new periodic solutions have been discovered and are described. In particular, there is a continuous family with variable masses, extending all the way from the elliptic restricted problem to the general problem with three equal masses. All our examples have special symmetry properties which are described in detail. Finally we also suggest some important applications to the natural satellites of the solar system.

Broucke, R.↗
DOE OSTI2020

Lattice model of heavy-light three-body system

We present a study of a $1+1$ dimensional heavy-light three-body system in finite volume. The heavy-light system is simulated by a coupled-channel $\phi^4$ type lattice model, and both ground state and excited states of multiparticle energy spectra are measured on various lattices. The lattice simulation data analysis is performed based on variational approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2003

Application of local Lyapunov exponents to maneuver design and navigation in the three-body problem

Dynamical systems theory has recently been employed to design trajectories within the three-body problem for several missions. This research has applied one stability technique, the calculation of local Lyapunov exponents, to such trajectories. Local Lyapunov exponents give an indication of the effects that perturbations or maneuvers will have on trajectories over a specified time. A numerical comparison of local Lyapunov exponents was first made with the distance random perturbations traveled from a nominal trajectory, and the local Lyapunov exponents were found to correspond well with the perturbations that caused the greatest deviation from the nominal. This would allow them to be used as an indicator of the points where it would be important to reduce navigation uncertainties.

dynamical systems theory↗
NASA NTRS1975

On relative periodic solutions of the planar general three-body problem

We describe two relatively simple reductions to order 6 for the planar general three-body problem. We also show that this reduction leads to the distinction between two types of periodic solutions: absolute or relative periodic solutions. An algorithm for obtaining relative periodic solutions using heliocentric coordinates is then described. It is concluded from the periodicity conditions that relative periodic solutions must form families with a single parameter. Finally, two such families have been obtained numerically and are described in some detail.

Broucke, R.↗
NASA NTRS1980

The restricted three-body problem including radiation pressure

The force of radiation pressure is included in the restricted three-body problem by considering the major radial components of the pressure force for the case of a particle in the vicinity of two luminous massive bodies, as well as by introducing the Poynting-Robertson effect for the case of one luminous body. The positions of the Lagrangian points L4 and L5 are found as functions of the ratio of radiation to gravitational forces. The Poynting-Robertson effect renders the L4 and L5 points unstable on a time scale that is long compared to the period of rotation of the two massive bodies. Implications for space colonization and a mechanism for producing azimuthal asymmetries in the interplanetary dust complex are discussed.

Schuerman, D. W.↗
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.↗
NASA NTRS1983

Further studies on criteria for the onset of dynamical instability in general three-body systems

Numerical experiments designed for the elucidation of the conditions under which self-gravitating, three-body systems become dynamically unstable are examined of the cases of four orbital configuration types: circular, prograde, and coplanar; circular, retrograde, and coplanar; circular, direct, and inclined; and eccentric, direct, and coplanar. Results indicate that orbital inclination does not significantly affect stability in 'outer planet' configurations, while the stability of 'inner planet' configurations, where the tertiary is in close orbit about one member of the binary, is markedly less affected, once the relative orbital inclination is greater than 50 deg. It is found that the onset of dynamical instability is only weakly dependent on the eccentricity of either the binary or tertiary orbit, as long as the mass of the tertiary is comparable to the reduced mass of the binary.

Pendleton, Y. J.↗
DOE OSTI2021

A Tidal Origin for a Three-body Resonance in Kepler-221

Over the course of the last two decades, traditional models of planet formation have been repeatedly challenged by the emerging census of extrasolar planets. Key among them is the orbital architecture problem: while standard models of orbital migration predict resonant orbits for short-period objects, most planets do not appear to lie in orbital resonances. Here, we show that the four-planet system Kepler-221, not previously recognized to have active orbital resonances, has a three-body commensurability relation unique within the Kepler sample. Using a suite of numerical experiments as well as a perturbative analysis, we demonstrate that this system likely began as a resonant chain and proceeded to undergo large-scale divergence away from resonance, under the action of tidal dissipation. Our results further indicate that obliquity tides, driven by a secular spin–orbit resonance and mutual inclination, are an excellent candidate for driving this orbital divergence, and that the high tidal luminosity may also explain the anomalous size of planet b, which lies within the Fulton radius gap.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Dalitz plots and lineshape of a 1 ( 1260 ) from a relativistic three-body unitary approach

We formulate the final-state interaction of the a 1 ( 1260 ) resonance decay in a manifestly three-body unitary parametrization and fit it to the a 1 ( 1260 ) line shape measured by the ALEPH experiment. Dalitz plots calculated from this fit are presented. The work demonstrates the feasibility to numerically solve a previously derived amplitude and its generalization to isobars with spin and coupled channels. The model can also be applied to other meson decays and modified for the finite-volume problem as it arises in lattice QCD due to its manifest unitarity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗