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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 NTRS1991

Symplectic maps for the n-body problem

The present study generalizes the mapping method of Wisdom (1982) to encompass all gravitational n-body problems with a dominant central mass. The rationale for the generalized mapping method is discussed as well as details for the mapping for the n-body problem. Some refinements of the method are considered, and the relationship of the mapping method to other symplectic integration methods is shown. The method is used to compute the evolution of the outer planets for a billion years. The resulting evolution is compared to the 845 million year evolution of the outer planets performed on the Digital Orerry using standard numerical integration techniques. This calculation provides independent numerical confirmation of the result of Sussman and Wisdom (1988) that the motion of the planet Pluto is chaotic.

Wisdom, Jack↗
NASA NTRS1992

Symplectic maps for the n-body problem - Stability analysis

The stability of new symplectic n-body maps is examined from the point of view of nonlinear dynamics. The resonances responsible for the principal artifacts are identified. These are resonances between the stepsize and the difference of mean motions between pairs of planets. For larger stepsizes resonant perturbations are evident in the variation of the energy of the system corresponding to these stepsize resonances. It is shown that the principal instability of the method can be predicted and corresponds to the overlap of the stepsize resonances. It is noted that the analysis suggests that other artifacts will occur. For example, the overlap of a stepsize resonance with a resonance of the actual system may also give a region of chaotic behavior that is an artifact. It is pointed out that the fact that the principal artifacts corresponds to a particular set of stepsize resonances suggests that it may be possible to perturbatively remove the effect when the stepsize resonances are nonoverlapping.

Wisdom, Jack↗
NASA NTRS1999

Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions

We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.

Rauch, Kevin P.↗
NASA NTRS1992

Polynomial approximation of Poincare maps for Hamiltonian system

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Froeschle, Claude↗
NASA NTRS1994

A mapping method for the gravitational few-body problem with dissipation

Recently a new class of numerical integration methods - 'mixed variable symplectic integrators' - has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of magnitude faster than conventional ordinary differential equations (ODE) integration methods. Here we present a simple modification of this method to include small non-gravitational forces. The new scheme provides a similar advantage of computational speed for a larger class of problems in Solar System dynamics.

Malhotra, Renu↗
NASA NTRS2014

Coordinated Mineralogical and Isotopic Analysis of a Cosmic Symplectite Identified in a Stardust Terminal Particle

Comet Wild-2 samples returned by the Stardust spacecraft contain a chemically diverse mixture of material, underscoring the complex nature of comets. Studies of entire Stardust aerogel tracks afford the opportunity to examine the fine-grained particle fragments distributed along the length of the track as well as the terminal particles. Previous TEM characterization of a terminal particle (TP) in track #147 revealed a symplectically intergrown iron sulfide and oxide assemblage. Mineralogically similar assemblages, known as cosmic symplectites (COS, formerly termed "new-PCP"), have only been identified in the primitive carbonaceous chondrite Acfer 094. Meteoritic COS have isotopically heavy O compositions (delta (sup 17), O-18 = 180per mille) that point to interactions with early solar system primordial water. In this study we report mineralogical and O isotopic measurements of the Wild-2 COS assemblage. Experimental: Track #147 is a "bulbous"-type track (4600 microns long) containing 7 terminal particles. The TPs were removed from the track, embedded in epoxy, and ultramicrotomed. A JEOL 2500SE 200 keV field-emission scanning-transmission electron microscope was used to obtain quantitative elemental maps and detailed mineralogical characterization. Following TEM analysis, two thin sections of TP4 (12 microns) were analyzed for O isotopes by raster ion imaging with the JSC NanoSIMS 50L. All three O isotopes were measured simultaneously using electron multipliers. San Carlos olivine grains were used as isotopic standards. Results and Discussion: The COS in the Wild-2 track #147 TP4 sample consists of symplectically intergrown pentlandite and nanocrystalline maghemite which coexists with high-Ca pyroxene with Na and Cr (kosmochlor component). This kosmochlor component could have a nebular origin and be precursors to type II chondrules in ordinary chondrites. Yet pentlandite is not a stable phase in the nebula. The COS in Acfer 094 also consists of pentlandite, but contains magnetite [4] rather than the more oxidized maghemite observed in the Wild-2 COS. The Acfer 094 COS display heavy O isotopic compositions that are the result of sulfidization and oxidation of Fe, Ni-metal grains and sulfides by O-17- and O-18-rich water in the solar nebula or possibly on the parent body. The O isotopic composition of the Wild-2 COS, however, is indistinguishable from terrestrial, indicating it was not altered by the same primordial aqueous reservoir as the Acfer 094 COS. The alteration could have occurred on the parent body by isotopically equilibrated ice. The mineralogy and petrography of Wild-2 samples suggests an incomplete or nascent hydration process. In future work we will analyze S isotopes in the track #147 TP4 COS and search for additional COS in Stardust samples.

Nguyen, A. N.↗
NASA NTRS1991

Mapping the stability field of Jupiter Trojans

Jupiter Trojans are a remnant of outer solar system planetesimals captured into stable or quasistable libration about the 1:1 resonance with the mean motion of Jupiter. The observed swarms of Trojans may provide insight into the original mass of condensed solids in the zone from which the Jovian planets accumulated, provided that the mechanisms of capture can be understood. As the first step toward this understanding, the stability field of Trojans were mapped in the coordinate proper eccentricity, e(sub p), and libration amplitude, D. To accomplish this mapping, the orbits of 100 particles with e(sub p) in the range of 0 to 0.8 and D in the range 0 to 140 deg were numerically integrated. Orbits of the Sun, the four Jovian planets, and the massless particles were integrated as a full N-body system, in a barycentric frame using fourth order symplectic scheme.

Levison, H. F.↗