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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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Chaotic Motion Of A Two-Link Planar Mechanism

Report discusses global instability in orbital motion of two-link planar mechanism. Principal objective, contributes to understanding of chaotic motions in robot manipulators and other deterministic mechanical systems. Discussion begins with brief review of previous studies of chaotic motion and introduces notion of orbital instability in nonlinear systems. Introduces geometric approach useful in representation of orbital instability.

Lokshin, Anatoly↗
NASA NTRS1990

Chaotic motion of Europa and Ganymede and the Ganymede-Callisto dichotomy

Europa and Ganymede may have undergone an episode of chaotic motion before the establishment of the current Laplace resonance involving the three inner GAlilean satellites. During this episode, the orbital eccentricities of both satellites may have increased dramatically. As a result, the mechanical stresses due to tidal deformation of the satellites' icy lithospheres may have been large enough to result in extensive fracturing, and tidal heating may have melted water ice in the mantles of both satellites, triggering the geological activity that has modified their surfaces since the heavy cratering period. The tidal effects on Ganymede during this episode provide an explanation of the dichotomy between it and Callisto, which have similar bulk properties but very different geological histories.

Tittemore, William C.↗
NASA NTRS2007

Chaotic Motion of Relativistic Electrons Driven by Whistler Waves

Canonical equations governing an electron motion in electromagnetic field of the whistler mode waves propagating along the direction of an ambient magnetic field are derived. The physical processes on which the equations of motion are based .are identified. It is shown that relativistic electrons interacting with these fields demonstrate chaotic motion, which is accompanied by the particle stochastic heating and significant pitch angle diffusion. Evolution of distribution functions is described by the Fokker-Planck-Kolmogorov equations. It is shown that the whistler mode waves could provide a viable mechanism for stochastic energization of electrons with energies up to 50 MeV in the Jovian magnetosphere.

Khazanov, G. V.↗
NASA NTRS2001

Chaotic Motion in the Solar System and Beyond

The motion of planetary bodies is the archetypal clockwork system. Indeed, clocks and calendars were developed to keep track of the relative motions of the Earth, the Sun and the Moon. However, studies over the past few decades imply that this predictable regularity does not extend to small bodies, nor does it apply to the precise trajectories of the planets themselves over long timescale.s. Various examples of chaotic motion within our Solar System and, extrasolar planetary systems will be discussed.

Lissauer, Jack↗
NASA NTRS1986

Chaotic motion in the Jovian atmosphere

Strong nonlinear interactions among unstable waves and the mean flow occur in a simplified quasigeostrophic spectral model of the upper troposphere of Jupiter. The upper boundary of the layer inhibits vertical motion while at the lower boundary perturbations of the potential temperature are not permitted. On an infinite beta plane the forced flow of alternating zones of prograde and retrograde zonal winds, decreasing with height, are linearly unstable and it is shown that the nonlinear terms stabilize the flow by bounding the growth of the eddies. Explicit viscosity terms are not needed. This does not imply that energy would not cascade to the small scale flow but suggests that the nature of the large scale flow is independent of the viscosity at small scales. Numerical time integration shows the flow to be chaotic but, in some cases, with transient propagating features and meandering zonal flow.

Pirraglia, Joseph↗
NASA NTRS1984

Chaotic ion motion in magnetosonic plasma waves

The motion of test ions in a magnetosonic plasma wave is considered, and the 'stochasticity threshold' of the wave's amplitude for the onset of chaotic motion is estimated. It is shown that for wave amplitudes above the stochasticity threshold, the evolution of an ion distribution can be described by a diffusion equation with a diffusion coefficient D approximately equal to 1/v. Possible applications of this process to ion acceleration in flares and ion beam thermalization are discussed.

Varvoglis, H.↗
NASA NTRS2002

Solar System Dynamics

In these 18 years, the research has touched every major dynamical problem in the solar system, including: the effect of chaotic zones on the distribution of asteroids, the delivery of meteorites along chaotic pathways, the chaotic motion of Pluto, the chaotic motion of the outer planets and that of the whole solar system, the delivery of short period comets from the Kuiper belt, the tidal evolution of the Uranian arid Galilean satellites, the chaotic tumbling of Hyperion and other irregular satellites, the large chaotic variations of the obliquity of Mars, the evolution of the Earth-Moon system, and the resonant core- mantle dynamics of Earth and Venus. It has introduced new analytical and numerical tools that are in widespread use. Today, nearly every long-term integration of our solar system, its subsystems, and other solar systems uses algorithms that was invented. This research has all been primarily Supported by this sequence of PGG NASA grants. During this period published major investigations of tidal evolution of the Earth-Moon system and of the passage of the Earth and Venus through non-linear core-mantle resonances were completed. It has published a major innovation in symplectic algorithms: the symplectic corrector. A paper was completed on non-perturbative hydrostatic equilibrium.

Wisdom, Jack↗
NASA NTRS1988

The dynamics of coorbital satellite systems

The dynamical behavior of N coorbital satellites moving with the same average mean motion around a primary has been studied both analytically and by numerical integrations for N from 2 to 9 satellites. Simplified dynamical equations are used to determine the different stationary configurations and their local stability against infinitesimal perturbations. The ring of equally spaced identical satellites is found to be locally unstable for N of six or less, while for N from two to eight there exists another stable compact stationary configuration with separations of 60 deg or less between adjacent satellites. For N of seven or more the equally spaced configuration becomes locally stable, and for N of nine or more it is the only stationary configuration. The motion becomes chaotic for large-amplitude perturbations. The chaotic motion fills a restricted region of phase space whose outer boundary is determined by the maximum velocity curve.

Salo, H.↗
NASA NTRS1991

Chaos and ion heating in a slow shock

An ion heating mechanism is proposed of slow shocks, which is associated with the chaotic motion of particles in the downstream wave field. For a coherent electromagnetic wave propagating along the downstream magnetic field, corresponding to switch-off shocks, the particle motions are not chaotic. For an oblique wave, the interaction between the particles and the wave field may lead to chaotic particle motions. Such particles may be greatly thermalized within one wavelength after they are incident into the downstream wave field. The results can be used to explain the existence of the critical intermediate Mach number observed in the hybrid simulations.

Lin, Y.↗
NASA NTRS1999

Impact of Eccentricity on East-west Stationkeeping for GPS Class of Orbits

There exists a strong relationship between eccentricity and the potential for a repeating groundtrack orbit to exhibit chaotic motion. This is true at all values of eccentricity, but, perhaps most dramatic, is that it is true even for orbits that are nearly circular. These complex motions can have a significant impact on the east-west stationkeeping process for maintaining the repeating groundtrack property of a commensurate orbit. Ely and Howell have shown that traditional stationkeeping (SK) methods are unable to maintain a repeating groundtrack in the presence of complex dynamics, such as with chaotic motion. They developed an alternate SK method that is able to maintain a repeating groundtrack for eccentric, commensurate orbits. The focus of the current study is to investigate orbits with characteristics that are similar to GPS satellites except with modestly larger eccentricities. It will be shown that at eccentricities larger than approx. .01 the chaotic regions become significant, and the need arises for a robust stationkeeping approach, such as developed in. FurtheRmore, the investigation will reveal that the influence of luni-solar perturbations contributes to the growth of eccentricity, thus increasing the probability of encountering chaotic motion during a typical satellite lifetime.

Ely, Todd A.↗
NASA NTRS1994

The broad emission line and continuum variations of Seyfert galaxies. 2: Broad-line region structure and kinematics

Spectroscopic observations of 13 Seyfert 1 galaxies made from 1979 to 1984 at Palomar and Steward Observatories were analyzed for H beta line profile variations. Significant profile changes were detected in five galaxies. These variations are often associated with changes in continuum and/or H beta strength, suggesting a causal connection between variations in the continuum source and changes in emission-line profiles. Moreover, the overall strength of H beta line flux variations is strongly correlated with line width in the far wings, whereas no such correlation was found in the line core. This finding is consistent with previous observations (Shuder 1982) which suggest that higher velocity gas lies closer to the central continuum source, since this inner gas would be expected to track variations more closely. In each of the five galaxies in which H beta line profile variations were detected, particularly NGC 5548 and Mrk 6, only two distinct line profile shapes were observed. Since intermediate profile types were not detected, the transition from one type to the other must occur rapidly (within a few months). These rapid line profile variations are thus consistent with numerous other studies which strongly point to a small broad-line region (BLR) size in Seyfert galaxies. Observational models of BLR kinematics and structure for each of the galaxies in the present sample are presented. Line asymmetries suggest that radial motions exist in the BLRs of most of these objects. Chaotic motions also appear to be quite common. However, evidence for rotational motion was observed in only one case. A model that is consistent with the majority of this sample incorporates both radial and chaotic motions combined with some form of external obscuration such as an optically and geometrically thick torus.

Rosenblatt, Edward I.↗
NASA NTRS1984

The rotation of Hyperion

For almost the entire range of dimensions of Hyperion allowed by uncertainties in the observations, the satellite cannot librate stably about a rotation rate which is synchronous with its orbital mean motion. Rather, the large gravitational torques on the asymmetric satellite coupled with the large eccentricity forced by the orbital resonance with Titan cause Hyperion to tumble in a random manner. Large changes in orientation of body axes relative to inertial space and in the instantaneous spin rate occur on timescales of the order of the orbit period. Numerical evaluation of the exponential divergence of nearby trajectories in the phase space of the motion verifies that the tumbling is truly chaotic. This newly defined state of chaotic rotation for Hyperion is likely to be the only example of confined, continuously observable chaotic motion in the solar system.

Peale, S. J.↗
NASA NTRS1992

Combustion noise and combustion instabilities in propulsion systems

This paper is concerned with some aspects of non-linear behavior of unsteady motions in combustion chambers. The emphasis is on conditions under which organized oscillations having discrete frequencies may exist in the presence of random motions. In order to treat the two types of motions together, and particularly to investigate coupling between noise and combustion instabilities, the unsteady field is represented as a synthesis of acoustic modes having time-varying amplitudes. Each of the amplitudes are written as the sum of two parts, one associated with the random field and the remainder representing the organized oscillations. After spatial averaging, the general problem is reduced to solution of a set of second-order ordinary differential equations whose structure depends on the sorts of nonlinear processes accounted for. This formulation accommodates any physical process; in particular, terms are included to represent noise sources, although only limited modeling is discussed. Our results suggest that random sources of noise have only small effects on combustion instabilities and seem not to be a cause of unstable motions. However, the coupling between the two sorts of unsteady motions may be important as an essential process in a proposed scheme for noise control. It is now a familiar observation that many nonlinear deterministic systems are capable of exhibiting apparently random motions called 'chaos.' This is a particularly interesting possibility for systems which also executed non-deterministic random motions. In combustion chambers, a nonlinear deterministic system (acoustical motions) exists in the presence of noise produced by flow separation, turbulent motions, and energy released by combustion processes. The last part of the paper is directed to the matter of discovering whether or not chaotic motions exist in combustion systems. Analysis has not progressed sufficiently far to answer the question. We report here recent results of processing data taken in one combustor to determine the dimensions of any attractors in the motions. No evidence has been found for chaos in the strict sense, but the method seems to be an important means of investigating the nonlinear behavior of combustion systems.

F. E. C. Culick↗
NASA NTRS1993

Transonic panel flutter

FEM is here used to ascertain the stability and aeroelastic response of thin, 2D panels subjected to Mach 0.8-2.5 flows. In the absence of shocks, it is found that the Euler equations used to represent the unsteady flowfield dynamics predict response behaviors resembling those obtained via potential flow methods. Where shocks do play a significant role in the overall motion of the panel, divergence and limit cycle flutter are observed. In the Mach 1.4-1.5 range, flutter involved the higher modes of the panel, tending toward possible chaotic motion.

Davis, Gary A.↗
NASA NTRS2006

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion by group symmetries of the problem were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. It is proved that the upper boundary of particle stochastic heating is conditioned by intrinsic property of the particle chaotic motion. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Khazanov, G. V.↗
NASA NTRS1994

Topological analysis of chaotic orbits: Revisiting Hyperion

There is emerging interest in the possibility of chaotic evolution in astrophysical systems. To mention just one example, recent well-sampled ground-based observations of the Saturian satellite Hyperion strongly suggest that it is exhibiting chaotic behavior. We present a general technique, the method of close returns, for the analysis of data from astronomical objects believed to be exhibiting chaotic motion. The method is based on the extraction of pieces of the evolution that exhibit nearly periodic behavior-episodes during which the object stays near in phase space to some unstable periodic orbit. Such orbits generally act as skeletal features, tracing the topological organization of the manifold on which the chaotic dynamics takes place. This method does not require data sets as lengthy as other nonlinear analysis techniques do and is therefore well suited to many astronomical observing programs. Well sampled data covering between twenty and forty characteristic periods of the system have been found to be sufficient for the application of this technique. Additional strengths of this method are its robustness in the presence of noise and the ability for a user to clearly distinguish between periodic, random, and chaotic behavior by inspection of the resulting two-dimensional image. As an example of its power, we analyze close returns in a numerically generated data set, based on a model for Hyperion extensively studied in the literature, corresponding to nightly observations of the satellite. We show that with a small data set, embedded unstable periodic orbits can be extracted and that these orbits can be responsible for nearly periodic behavior lasting a substantial fraction of the observing run.

Boyd, Patricia T.↗
NASA NTRS2002

Spin-Up Instability of a Levitated Molten Drop in MHD-Flow Transition to Turbulence

When an alternating magnetic field interacts with induced eddy currents in a conducting body, there will be a repulsive force between the body and the driving coil system generating the field. This repulsive force is the basis of electromagnetic levitation, which allows containerless processing of different materials. The eddy currents in the conducting body also generate Joule heating. Axial rotation of electromagnetically levitated objects is a common observation in levitation systems and often an undesirable side effect of such experiments on 1-g and -g. There have been recent efforts to use magnetic damping and suppress this tendency of body rotation. The first report of rotation in EML drops was attributed to a slight asymmetry of the shape and location of the levitation coils could change the axis and speed of rotation. Other theories of sample rotation include a frequency difference in the traveling electromagnetic waves and a phase difference in two different applied fields of the same frequency. All of these different mechanisms share the following characteristics: the torque is small, constant for constant field strength, and very weakly dependent on the sample's temperature and phase (solid or liquid). During experiments on the MSL-1 (First Microgravity Science Laboratory) mission of the Space Shuttle (STS-83 and STS-94, April and July 1997), a droplet of palladium-silicon alloy was electromagnetically levitated for viscosity measurements. For the non-deforming droplet, the resultant MHD flow inside the drop is inferred from motion of impurities on the surface. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal levitated drop that undergo secondary flow instabilities. As rise in the fluid temperature rises, the viscosity falls and the internal flow accelerates and becomes oscillatory; and beyond a point in the experiments, the surface impurities exhibit non-coherent chaotic motion signifying emergence of turbulence inside the drop. In this work, a background of these set of observations will be given followed by a presentation of our results on the digital particle tracking analysis that has been performed on a number of available videos. The analysis indicates that the levitated drop attains a constant rotational speed during the melting phase and formation of the co-rotating axi-symmetric laminar toroidal structures. However, the rate of axial rotation increases dramatically during the deformation of the toroidal structures anti their breakup into chaotic entities. This new data suggests an interaction between the flow inside the levitated molten drop and the driving coils in the experiments. Possible mechanisms for this interaction will be reviewed. The data will also be used to make an assessment of existing theories on droplet rotation.

Abedian, B.↗