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At least 127 records · Page 7
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 NTRS2003

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

Dynamical systems theory has recently been employed for several missions to design trajectories within the three-body problem. This research applied a 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.

local Lyapunov exponent design navigation three-bo↗
NASA NTRS1986

Comment on the three-body theory for period changes in RS CVn systems

In the three-body theory for period variations in RS CVn systems, the timing residuals are interpreted as light-travel time differences as the eclipsing system moves about the barycenter of the triple. These residuals can require a larger orbit than Kepler's law allows, given the time scale of the period variations. For only two of eight systems investigated, SV Cam and V471 Tau, is the theory plausible in that the inferred barycentric motion of the binary is smaller than the orbit of the third body, and the inferred properties of the third body are both reasonable and consistent with its remaining hidden. The theory is thus not a general theory for period changes. Observational testing of the theory is straightforward and may lead to the detection of 'brown dwarfs' associated with eclipsing systems through their kinematic effects.

Van Buren, D.↗
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.↗