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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 NTRS1976

On the stability of the solutions of the general problem of three bodies

The extent through which the initial conditions of a given three-body system may be varied without completely changing the qualitative nature of the subsequent system evolution is investigated. It is assumed that the three masses are equal, all initial velocities are zero, the first two bodies initially lie on the x-axis, and the position of the third body is confined to a specific region of space. Analysis of the system evolution for different initial positions of the third body shows that there is a whole area or 'island' in the x-y plane throughout which the initial position of the third body may be moved in a continuous fashion to produce an evolution which also changes in a continuous manner. A Monte Carlo approach is adopted to determine the full extent of this island in the general problem. It is concluded that the stability of a full solution may be directly related to the size of its island in phase space.

Standish, E. M., Jr.↗
NASA NTRS1967

Systems analysis

Selenodesy experiment, data compression, Mars and Venus mass data, Earth-Moon mass ratio, orbits for three-body problem, and unbraked impact time for lunar landing mission - systems analyses

THREE-BODY PROBLEM↗
NASA NTRS2015

Seasonal Variations of the James Webb Space Telescope Orbital Dynamics

While spacecraft orbital variations due to the Earth's tilt and orbital eccentricity are well-known phenomena, the implications for the James Webb Space Telescope present unique features. We investigate the variability of the observatory trajectory characteristics, and present an explanation of some of these effects using invariant manifold theory and local approximation of the dynamics in terms of the restricted three-body problem.

launch windows↗
NASA NTRS2021

New Tools for Tour Design: Swiss Cheese Plot, Invariant Funnel, and Resonant Encounter Map

We define a new set of tools for tour design introduced in previous work: the”Swiss Cheese Plot,” ”Invariant Funnel,” and ”Resonant Encounter Map.” These tools promise to be useful in designing, analyzing, and navigating low-energy trajectories through multi-body systems. We review and clarify methods for generating the swiss cheese plot and invariant funnels in the Circular Restricted Three-Body Problem. We introduce the resonant encounter map as a graphical representation of the three-body design space, similar to the pork-chop plot for the two-body problem. We also discuss some interesting characteristics of the resonant encounter map and its connection to the invariant manifolds of periodic libration orbit

Close, Sigrid↗
NASA NTRS1973

Global stability and the restricted 3-body problem.

Global stability regions are found for class i orbits of the circular restricted three-body problem for primary masses equal and Jacobi constant K greater than 15.5. It is found that, this constant decreases, the stability region shrinks extremely rapidly.

Mullins, L. D.↗
NASA NTRS1963

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↗
NASA NTRS2011

Flyby Design Using Heteroclinic and Homoclinic Connections of Unstable Resonant Orbits

Tour designs using flybys have traditionally been studied using two-body patched conic methods. Previous work has shown that trajectories designed using these techniques and with optimization methods follow the invariant manifolds of unstable resonant orbits as they transition between resonances. This work is continued here by computing heteroclinic and homoclinic trajectories associated with these unstable resonant orbits. These trajectories are used with multiple resonances to design flybys that transition between these resonances in the circular restricted three-body problem without the need for two-body approximations.

three body problem↗
NASA NTRS1973

Periodic solutions of a spring-pendulum system.

A study has been made of a dynamical system composed of a pendulum and a harmonic oscillator, in order to show the remarkable resemblance with many classical celestial mechanics problems, in particular, the restricted three-body problem. It is shown that the well-known investigations of periodic orbits can be applied to the present dynamics problem.

Broucke, R.↗