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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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NASA NTRS1978

Numerical integration of nearly-Hamiltonian systems

The reported investigation is concerned with the solution of systems of differential equations which are derived from a Hamiltonian function in the extended phase space. The problem selected involves a one-dimensional perturbed harmonic oscillator. The van der Pol equation considered has an exact asymptotic value for its amplitude. Comparisons are made between a numerical solution and a known analytical solution. In addition to the van der Pol problem, known solutions regarding the restricted problem of three bodies are used as examples for perturbed Keplerian motion. The extended phase space Hamiltonian discussed by Stiefel and Scheifele (1971) is considered. A description is presented of two canonical formulations of the perturbed harmonic oscillator.

Bond, V. R.↗
NASA NTRS1978

Stability of artificial and natural satellites

A quantitative measure of stability based on Hill's definition is evaluated for direct and retrograde satellite orbits. These orbits are known as Poincare's first kind in the restricted problem of three bodies. Onsets of possible instabilities and captures are established. A critical (maximum) value of the satellites orbital radius is found for stability as a remarkably simple function of the mass-parameter. The results are applied to the natural satellites of the solar system.

Szebehely, V.↗
NASA NTRS1978

Comparison between stability limits for satellite motion

Three methods of obtaining stability information on satellite motion are compared by means of numerical and analytical computations. The model of the restricted problem of three bodies is used to describe the motion. Kuiper's (1961) approximate results, Szebehely's (1978) approximate results, and computer solutions obtained by successive iterations show close agreement regarding the maximum values of the orbital radii for stability. The lowest value, i.e., the most conservative estimate, is provided by the simplified form of Szebehely's formula.

Szebehely, V.↗
NASA NTRS1980

Doubly-periodic orbits in the Sun-Earth-Moon system

A series of periodic orbits in the Earth-Moon circular restricted problem of three bodies was found which is ideally suited for exploring the Earth's geomagnetic tail. The mean apsidal motion of the basic highly elliptical Earth orbit was maintained at about one degree per day by a sequence of lunar swingbys, keeping the apogees in the anti-Sun direction. The orbits were periodic in reference frames rotating at both lunar and solar rates. Apogee distances were alternately raised and lowered by the lunar swingby maneuvers. Several categories of these Sun-synchronous double lunar swingby orbits were identified. The strength and flexibility of this trajectory concept was demonstrated with real world simulations.

Farohar, R.↗
NASA NTRS1981

Deformation of a line-element in the phase space at the triangular libration point

The flow in the projection of the phase space into the configuration space is presented in the neighborhood of a neutrally (or critically) stable equilibrium point in the restricted problem of three bodies. The projection is a line-element every point of which has zero initial velocity. After the elapse of various times the mapping (the rotations and elongations) of the line-element is described showing chaotic behavior.

Szebehely, V.↗
NASA NTRS1981

Approximations of satellite stability

Modifications and corrections are presented to relations obtained in an investigation conducted by Szebehely (1978), who has discussed the problem of Hill's (1878) stability of satellites in the restricted problem of three bodies. Attention is given to an approximation of the Jacobian constant for the satellite, the critical value of the Jacobian constant, and approximate solutions.

Markellos, V. V.↗