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NASA NTRS1985

Meteorites may follow a chaotic route to earth

A numerical integration was employed to show that the 3/1 Kirkwood gap region between Jupiter and the sun can serve as the source for asteroidal debris that strikes the earth as chondrites. A previous study by Wetherill (1968) considered planetary close encounters, secular resonances, collisional destruction in space and subsequent atmospheric abrasion of the chondrites. The factors would have resulted in chaotic trajectories for asteroids in the asteroid belt, i.e., eccentricities large enough to make the objects earth-crossing. A sampling of trajectories which could reach large eccentricities is integrated in terms of deterministic solutions of Hamiltonian systems of equations which behave erratically and are dependent on the initial conditions. The examinations successfully predicted a trajectory with a peak eccentricity of 0.652, a time interval of 340,000 yr, and a semimajor axis between 2.4-2.53 AU that was earth-crossing.

Wisdom, J.↗

NASA NTRS1996

Chiron and the Centaurs: Escapees from the Kuiper Belt

The outer Solar System has long appeared to be a largely empty place, inhabited only by the four giant planets, Pluto and a transient population of comets. In 1977 however, a faint and enigmatic object - 2060 Chiron - was discovered moving on a moderately inclined, strongly chaotic 51-year orbit which takes it from just inside Saturn's orbit out almost as far as that of Uranus. It was not initially clear from where Chiron originated. these objects become temporarily trapped on Centaur-like orbits Following Chiron's discovery, almost 15 years elapsed before other similar objects were discovered; five more have now been identified. Based on the detection statistics implied by these discoveries, it has become clear that these objects belong to a significant population of several hundred (or possibly several thousand) large icy bodies moving on relatively short-lived orbits between the giant planets. This new class of objects, known collectively as the Centaurs, are intermediate in diameter between typical comets (1-20 km) and small icy planets such as Pluto (approx. 2,300 km) and Triton (approx. 2,700 km). Although the Centaurs are interesting in their own right, they have taken on added significance following the recognition that they most probably originated in the ancient reservoir of comets and larger objects located beyond the orbit of Neptune known as the Kuiper belt.

Stern, Alan↗

NASA NTRS2002

Differential Flatness and Cooperative Tracking in the Lorenz System

In this paper the control of the Lorenz system for both stabilization and tracking problems is studied via feedback linearization and differential flatness. By using the Rayleigh number as the control, only variable physically tunable, a barrier in the controllability of the system is incidentally imposed. This is reflected in the appearance of a singularity in the state transformation. Composite controllers that overcome this difficulty are designed and evaluated. The transition through the manifold defined by such a singularity is achieved by inducing a chaotic response within a boundary layer that contains it. Outside this region, a conventional feedback nonlinear control is applied. In this fashion, the authority of the control is enlarged to the whole. state space and the need for high control efforts is mitigated. In addition, the differential parametrization of the problem is used to track nonlinear functions of one state variable (single tracking) as well as several state variables (cooperative tracking). Control tasks that lead to integrable and non-integrable differential equations for the nominal flat output in steady-state are considered. In particular, a novel numerical strategy to deal with the non-integrable case is proposed. Numerical results validate very well the control design.

Crespo, Luis G.↗

NASA NTRS1986

Multiple grid problems on concurrent-processing computers

Three computer codes were studied which make use of concurrent processing computer architectures in computational fluid dynamics (CFD). The three parallel codes were tested on a two processor multiple-instruction/multiple-data (MIMD) facility at NASA Ames Research Center, and are suggested for efficient parallel computations. The first code is a well-known program which makes use of the Beam and Warming, implicit, approximate factored algorithm. This study demonstrates the parallelism found in a well-known scheme and it achieved speedups exceeding 1.9 on the two processor MIMD test facility. The second code studied made use of an embedded grid scheme which is used to solve problems having complex geometries. The particular application for this study considered an airfoil/flap geometry in an incompressible flow. The scheme eliminates some of the inherent difficulties found in adapting approximate factorization techniques onto MIMD machines and allows the use of chaotic relaxation and asynchronous iteration techniques. The third code studied is an application of overset grids to a supersonic blunt body problem. The code addresses the difficulties encountered when using embedded grids on a compressible, and therefore nonlinear, problem. The complex numerical boundary system associated with overset grids is discussed and several boundary schemes are suggested. A boundary scheme based on the method of characteristics achieved the best results.

Eberhardt, D. S.↗

NASA NTRS1999

Advanced Geosynchronous Imager

For improved understanding of chaotic processes and the diurnal cycle, an advanced GOES imager must also have the multi-spectral spectral bands used by low earth orbit (LEO) imagers, with on-orbit calibration for all bands. A synergy between GEO and LEO radiometry would enable earth system scientists to fuse the remote sensing data from all the spaceborne platforms. These additional radiometric capabilities are designed to observe important physical processes that vary rapidly and unpredicably: smoke, fires, precipitation, ozone, volcanic ash, cloud phase and height, and surface temperature. We believe the technology now exists to develop an imaging system that can meet future weather reporting and earth system science needs. To meet this need, we propose a design for a comprehensive geosynchronous atmospheric imager. This imager is envisioned to fly on a GOES-N class spacecraft, within the volume, weight and power constraints of a platform similar to GOES-N while delivering 100 times more data and radiometric quality than the GOES-N imager. The higher data rate probably requires its own ground station, which could serve as a systems prototype for NOAA's next generation of operational satellites. For operational compatibility, our proposed advanced GOES imaging system contains the GOES-R requirements as a subset, and the GOES-N imager capabilities (and the sounder's imaging channels) as a further subset.

Chesters, Dennis↗

NASA NTRS2019

SPARROW: Steam Propelled Autonomous Retrieval Robot for Ocean Worlds

The Steam Propelled Autonomous Retrieval Robot (SPARROW) for Ocean Worlds was a Phase I mission concept study funded under the NASA NIAC program. This report represents the findings of that study and recommendations for future work. SPARROW, envisioned as a soccer ball-sized payload to a primary lander mission, is a propulsively hopping robot for the exploration of Europa's rugged, icy surface. A multi-thruster, passively gimballed robot within a protective, spherical shell, SPARROW is able to freely rotate, self-right, and tumble over chaotic terrains. Europa's abundant surface ice would be harvested as an in situ propellant source. The principal objective of SPARROW is to increase the science return of a Europa landed asset by enabling access to distal, spatially distributed geologic units. The design of mobility systems for Europa is challenging, due in part to its almost entirely unconstrained surface topography and strength. Images returned by Voyager and Galileo yielded resolutions on the order of hundreds of meters per pixel, with localized regions reaching 6 meters per pixelâ€”still far larger than a typical rover. A key benefit of SPARROW's hopping, impact-tolerant design, is that it eliminates the need for a priori information regarding terrain topography and surface strength; no surface reaction forces are required for motion. In this context, SPARROW is believed to be entirely terrain agnostic. In this report we detail the results of three study objectives: i) to quantify the energy required to collect surface ice, change its phase, and maintain propellant temperature, ii) to identify control and estimation strategies that enable SPARROW to successfully reach, and return from, regions of scientific interest, and iii) to characterize the impact of SPARROW's range on likely science return. Five water-based propellant architectures are presented alongside their mass, power, and volume requirements. Monte Carlo simulations of SPARROW hopping and tumbling over 1 km of glacial ice are summarized, characterizing SPARROW's sensitivity to uncertainty in: initial pose, thrust profile, and vehicle-terrain interaction. A science traceability matrix is presented, which details the effect of sortie range on three science goals: constraining Europa's evolutionary morphology, assessing sub-surface ocean habitability, and searching for life and/or biosignatures.

Autonomous↗

NASA NTRS1984

Petrography and classification of Ca, Al-rich and olivine-rich inclusions in the Allende CV3 chondrite

The results of a detailed, systematic petrographic survey of Ca, Al-rich and olivine-rich inclusions in the Allende CV3 chondrite are reported, and a new classification system based on clearly defined and readily applied petrographic criteria is presented. Most Allende inclusions are aggregates containing one or more of three distinct constituents: (1) rimmed concentric objects enriched in Al- and Ti-rich oxide minerals and various amounts of Ca-rich silicates; (2) porous, 'fine-grained' chaotic material enriched in Ca-rich silicates, especially clinopyroxenes and garnets; and (3) porous, 'fine-grained', mafic inclusion matrix, enriched in olivine, pyroxene, and feldspathoids. Two texturally distinct varieties of inclusions consist primarily of inclusion matrix: unrimmed olivine aggregates and rimmed olivine aggregates. Ca, Al-rich inclusions are classified on the basis of the size and abundance of their constituent concentric objects. Some fundamental relationships among Allende inclusions that previusly have not been emphasized are discussed.

Kormacki, A. S.↗

NASA NTRS1978

Physics of the primitive solar nebula and of giant gaseous protoplanets

It has been proposed that the supernova responsible for injecting Al-26 into the early solar system was in fact responsible for triggering the collapse of an interstellar cloud in order to produce a system of stars, one of which would be the solar system. Details concerning the mechanism involved in such a process are discussed. Attention is given to the evolution of the primitive solar nebula, the instabilities in the primitive solar nebula, and the giant gaseous protoplanets. The principal conclusion to be drawn from the material presented is that the primitive solar nebula was a rather chaotic place, highly turbulent, with the multiple formation of giant gaseous protoplanets.

Cameron, A. G. W.↗

NASA NTRS1990

Non-linear dynamic analysis of geared systems, part 2

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Singh, Rajendra↗

NASA NTRS2001

Institution Morphisms

Institutions formalize the intuitive notion of logical system, including both syntax and semantics. A surprising number of different notions of morphisim have been suggested for forming categories with institutions as objects, and a surprising variety of names have been proposed for them. One goal of this paper is to suggest a terminology that is both uniform and informative to replace the current rather chaotic nomenclature. Another goal is to investigate the properties and interrelations of these notions. Following brief expositions of indexed categories, twisted relations, and Kan extensions, we demonstrate and then exploit the duality between institution morphisms in the original sense of Goguen and Burstall, and the 'plain maps' of Meseguer, obtaining simple uniform proofs of completeness and cocompleteness for both resulting categories; because of this duality, we prefer the name 'comorphism' over 'plain map.' We next consider 'theoroidal' morphisms and comorphisims, which generalize signatures to theories, finding that the 'maps' of Meseguer are theoroidal comorphisms, while theoroidal morphisms are a new concept. We then introduce 'forward' and 'semi-natural' morphisms, and appendices discuss institutions for hidden algebra, universal algebra, partial equational logic, and a variant of order sorted algebra supporting partiality.

Goguen, Joseph↗

NASA NTRS2002

The Retrospective Iterated Analysis Scheme for Nonlinear Chaotic Dynamics

Atmospheric data assimilation is the name scientists give to the techniques of blending atmospheric observations with atmospheric model results to obtain an accurate idea of what the atmosphere looks like at any given time. Because two pieces of information are used, observations and model results, the outcomes of data assimilation procedure should be better than what one would get by using one of these two pieces of information alone. There is a number of different mathematical techniques that fall under the data assimilation jargon. In theory most these techniques accomplish about the same thing. In practice, however, slight differences in the approaches amount to faster algorithms in some cases, more economical algorithms in other cases, and even give better overall results in yet some other cases because of practical uncertainties not accounted for by theory. Therefore, the key is to find the most adequate data assimilation procedure for the problem in hand. In our Data Assimilation group we have been doing extensive research to try and find just such data assimilation procedure. One promising possibility is what we call retrospective iterated analysis (RIA) scheme. This procedure has recently been implemented and studied in the context of a very large data assimilation system built to help predict and study weather and climate. Although the results from that study suggest that the RIA scheme produces quite reasonable results, a complete evaluation of the scheme is very difficult due to the complexity of that problem. The present work steps back a little bit and studies the behavior of the RIA scheme in the context of a small problem. The problem is small enough to allow full assessment of the quality of the RIA scheme, but it still has some of the complexity found in nature, namely, its chaotic-type behavior. We find that the RIA performs very well for this small but still complex problem which is a result that seconds the results of our early studies.

Todling, Ricardo↗

NASA NTRS1989

Quantitative computer simulations of extraterrestrial processing operations

The automation of a small, solid propellant mixer was studied. Temperature control is under investigation. A numerical simulation of the system is under development and will be tested using different control options. Control system hardware is currently being put into place. The construction of mathematical models and simulation techniques for understanding various engineering processes is also studied. Computer graphics packages were utilized for better visualization of the simulation results. The mechanical mixing of propellants is examined. Simulation of the mixing process is being done to study how one can control for chaotic behavior to meet specified mixing requirements. An experimental mixing chamber is also being built. It will allow visual tracking of particles under mixing. The experimental unit will be used to test ideas from chaos theory, as well as to verify simulation results. This project has applications to extraterrestrial propellant quality and reliability.

Vincent, T. L.↗

NASA NTRS2003

Dissipating Step Bunches during Crystallization under Transport Control

In studies of crystal formation by the generation and spreading of layers, equidistant step trains are considered unstable---bunches and other spatiotemporal patterns of the growth steps are viewed as ubiquitous. We provide an example to the opposite. We monitor the spatiotemporal dynamics of steps and the resulting step patterns during crystallization of the proteins ferritin and apoferritin using the atomic force microscope. The variations in step velocity and density are not correlated, indicating the lack of a long-range attraction between the steps. We show that (i) because of its coupling to bulk transport, nucleation of new layers is chaotic and occurs at the facet edges, where the interfacial supersaturation is higher; (ii) step bunches self-organize via the competition for supply from the solution; and, (iii) bunches of weakly interacting steps decay as they move along the face. Tests by numerical modeling support the conclusions about the mechanisms underlying our observations. The results from these systems suggest that during crystallization controlled by transport, with weakly or noninteracting growth steps, the stable kinetic state of the surface is an equidistant step train, and step bunches only arise during nucleation of new layers. Since nucleation only occurs at a few sites on the surface, the surface morphology may be controllably patterned or smoothened by locally controlling nucleation.

Lin, Hong↗

NASA NTRS2011

Verification and Validation Plan for Flight Performance Requirements on the CEV Parachute Assembly System

The Crew Exploration Vehicle Parachute Assembly System (CPAS) is engaged in a multi-year design and test campaign aimed at qualifying a parachute recovery system for human use on the Orion Spacecraft. Orion has parachute flight performance requirements that will ultimately be verified through the use of Monte Carlo multi-degree of freedom flight simulations. These simulations will be anchored by real world flight test data and iteratively improved to provide a closer approximation to the real physics observed in the inherently chaotic inflation and steady state flight of the CPAS parachutes. This paper will examine the processes necessary to verify the flight performance requirements of the human rated spacecraft. The focus will be on the requirements verification and model validation planned on CPAS.

Morris, Aaron L.↗

NASA NTRS1999

The Confluence of Gangis and Eos Chasmas (5-12 deg S, 31-41 deg W): Geologic, Hydrologic, and Exobiologic Considerations for Landing Site at the East End of Valles Marineris

Over its 3,500 km length, Valles Marineris exhibits an enormous range of geologic and environmental diversity. At its western end, the canyon is dominated by the tectonic complex of Noctis Labyrinthus; while in the east it grades into an extensive region of chaos where scoured channels and streamlined islands provide evidence of catastrophic floods that spilled into the northern plains. In the central portion of the system, debris derived from the massive interior layered deposits of Candor and Ophir Chasmas spills into the central trough. In other areas, 6 km-deep exposures of Hesperian and Noachian-age canyon wall stratigraphy have collapsed in massive landslides that extend many tens of kilometers across the canyon floor. Ejecta from interior craters, aeolian sediments, and possible volcanics emanating from structurally controlled vents along the base of the scarps, further contribute to the canyon's geologic complexity. Following the initial rifting that gave birth to Valles Marineris, water appears to have been a principal agent in the canyon's geomorphic development an agent whose significance is given added weight by its potential role in both sustaining and preserving evidence of past life. In this regard, the interior layered deposits of Candor, Ophir, and Hebes Chasmas, have been identified as possible lucustrine sediments that may have been laid down in long-standing ice-covered lakes. The potential survival and growth of native organisms in such an environment, or in the aquifers whose disruption gave birth to the chaotic terrain and outflow channels to the north and east of the canyon, raises the possibility that fossil indicators of life may be present in the local sediment and rock. Because of the enormous distances over which these diverse environments occur, identifying a single landing site that maximizes the opportunity for scientific return is not a simple task. However, given the fluvial history and narrow geometry of the canyon, the presence of a single exit at its eastern end provides an opportunity for sampling that appears unequaled elsewhere in the system.

George, J. A.↗

NASA NTRS2019

SPARROW: A Steam Propelled Autonomous Retrieval Robot for Ocean Worlds

This paper presents the results of a NIAC Phase I study into the use of a propulsively hopping robot for the exploration of Europa’s rugged, icy surface. Named the“Steam Propelled Retrieval Robot for Ocean Worlds,” SPARROW is a multi-thruster robot passively gimballed within a protective, spherical shell, which enables it to freely rotate, self-right, and tumble over chaotic terrains. SPARROW is envisioned as a soccerball-sized payload to a primary lander mission. Europa’s abundant surface ice would be harvested as an in situ propellant source. The principal objective of SPARROW would be to increase the science return of a Europa landed asset by enabling access to distal, spatially distributed geologic units. The design of mobility systems for Europa is challenging, due in part to its almost entirely unconstrained surface topography and strength. Images returned by Voyager and Galileo yielded resolutions on the order of hundreds of meters per pixel, with localized regions reaching 6 meters per pixel—still far larger than a typical rover. A key beneﬁt of SPARROW’s hopping, impact-tolerant design, is that it eliminates the need for a piori information on the terrain topography and surface strength; no surface reaction forces are required for motion. In this context, SPARROW is entirely terrain agnostic. In this paper we detail the results of three study objectives: i) to quantify the energy required to collect surface ice, change its phase, and maintain propellant temperature, ii) to identify control and estimation strategies that enable SPARROW to successfully reach, and return from, regions of scientiﬁc interest, and iii) to characterize the impact of SPARROW’s range on likely science return. Five water-based propellant architectures are presented alongside their mass, power, and volume requirements. Monte Carlo simulations of SPARROW hopping and tumbling over 1 km of glacial ice are summarized, characterizing SPARROW’s sensitivity to uncertainty in: initial conditions, thrust control, and cage-terrain interaction. Finally, a science traceability matrix is presented, which details the effect of sortie range on three science goals: constraining Europa’s evolutionary morphology, assessing sub-surface ocean habitability, and searching for life and/or biosignatures.

Phillips, Cynthia↗

NASA NTRS2003

Liquid Propellant Manipulated Acoustically

Fluids are difficult to manage in the space environment. Without gravity, the liquid and gas do not always remain separated as they do in the 1g environment of Earth. Instead the liquid and gas volumes mix and migrate under the influence of surface tension, thermodynamic forces, and external disturbances. As a result, liquid propellants may not be in a useable location or may even form a chaotic mix of liquid and gas bubbles. In the past, mechanical pumps, baffles, and a variety of specialized passive devices have been used to control the liquid and gas volumes. These methods need to be carefully tuned to a specific configuration to be effective. With increasing emphasis on long-term human activity in space there is a trend toward liquid systems that are more flexible and provide greater control. We are exploring new methods of manipulating liquids by using the nonlinear acoustic effects achieved by using beams of highly directed high-intensity acoustic waves.

Oeftering, Richard C.↗

NASA NTRS1981

On the radial structure of Saturn's rings

Voyager 1 cameras revealed that Saturn's B ring appears to be subdivided into hundreds of chaotically spaced narrow rings in a hierarchy that extends to the limit of resolution. A disk model is proposed and applied to Saturn's rings: it is shown that the radial diffusion in a particulate Keplerian disk, under the influence of a viscosity law that decreases more steeply with a certain surface density than with another, will promote the breakdown of the system into an ensemble of thin rings.

Ward, W. R.↗