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At least 487 records · Page 27

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NASA NTRS1992

Non-Hamiltonian perturbations of integrable systems and resonance trapping

This paper studies general, non-Hamiltonian perturbations of integrable systems with two degrees of freedom and derives conditions for temporary and permanent resonance trapping. The analysis involves a noncanonical transformation of variables near the resonant manifold and averaging with respect to the fast phase to investigate oscillatory behavior on the intermediate timescale. The resulting reduced system is Hamiltonian to leading order and permits, after averaging on the intermediate, or libration, timescale, a canonical transformation to action-angle variables in the oscillation zone. The final system so obtained reveals the possible existence of two- and three-dimensional invariant tori in the vicinity of the resonant manifold. An explicit divergence condition for general perturbations to be dissipative on the slow timescale follows from the analysis. An application of this approach to the problem of resonant trapping and escape is outlined for the restricted problem of three bodies subject to dissipative perturbations with a radial symmetry.

Ghil, M.↗

NASA NTRS1994

Nonlinear instability of accelerating shock waves with application to supernovae

We consider the stability of a planar accelerating shock front in an exponential atmosphere, a situation that can be described by a self-similar solution. A previous linear instability analysis showed that there are three regimes, depending on the wavelength of the perturbation along the direction of the shock front: at long wavelengths the shock is unstable, at intermediate wavelengths it is overstable, and at short wavelenghts it is stable, where the characteristic length is set by the initial density scale height. We have carried out numerical simulations of such an accelerating shock front and have confirmed the results of the semianalytic linear analysis in the linear regime. In the nonlinear regime, the evolution again depends on the three wavelength domains. At long wavelengths, the instability continuously grows but the flow remains smooth, and at short wavelengths, the flow is stable. The intermediate wavelength, overstable regime shows more complex evolution. The growing linear oscillations saturate soon after entering the nonlinear regime and the oscillations continue with the same approximate period. The shock front develops moving points of intersection, which generate weak shock fronts and density and pressure structure in the immediate postshock flow. The density fluctuations, with a contrast of a factor of 2-3, become frozen into the downstream flow. The growth of the instability is slow, so substantial initial perturbations are needed; thesemay be present in Type II supernovae with red supergiant progenitor stars which have outer convective regions. The clumping in the outer supernova atmosphere may affect spectral line formation and may play a role in the formation of fast knots.

Luo, Ding↗

NASA NTRS1982

Synthesis of a modern/classical controller for large space structures

The paper is concerned with wide-sense stationary random vibrations of a representative large space structure subject to nonwhite excitations, and with synthesis of its controller amid modeling uncertainties due to truncated modes. Dynamics is analyzed by residue calculus in frequency domain. Steady state variance of a modal coordinate is shown to depend on, among other things, power spectral density of excitation at the modal frequency. Modal cost analysis is performed for an order reduction with a performance objective of attitude, attitude rate and energy control. Optimal and suboptimal output feedback controllers are compared. By treating deleted modes as an additive and a multiplicative perturbation in an idealized transfer function, the low frequency modes omitted according to modal cost analysis are found to cause instability. Finally, the size of the idealized model is shown to be governed by light damping and stringency in performance and stability specifications.

Hablani, H. B.↗

NASA NTRS1979

Origin of longitudinal grooving in Tiu Vallis, Mars - Isolation of responsible fluid-types

Fluid instability analysis developed for the growth or decay of large, longitudinal roller vortex perturbations imposed at the base of fluids of exponentially stratified viscosities is presented. The origin of longitudinal grooving and fluting in a region of converging flow in Tiu Vallis, Mars, is analyzed, and the propensity of fluids, such as water, mudflow/debris flow, and lava, to develop longitudinal roll patterns as part of their flow field is tested. It is found that the grooving pattern in Tiu Vallis was probably formed by vortex motion in a mudflow or debris-laden slurry, but exact representation of sediment/debris concentration or sediment transport machanism is not yet possible. It is concluded that longitudinal vortex motion modelled in this analysis can develop in water, lava, or ice, but that the specific flow characteristics of these models which include the vortex motion are unreasonable for flow in Tiu Vallis.

Thompson, D. E.↗

NASA NTRS1969

Sensitivity aspects of linear digital control systems.

Linear computer-controlled closed loop systems sensitivity analysis, deriving estimation error incremental covariance to demonstrate quality deterioration under perturbed initial conditions, parameters, etc

Christie, L. A.↗

NASA NTRS1972

Definition and application of longitudinal stability derivatives for elastic airplanes

A set of longitudinal stability derivatives for elastic airplanes is defined from fundamental principles allowing perturbations in forward speed. Application of these derivatives to longitudinal stability analysis by use of approximate expressions for static stability and control parameters as well as the dynamic equations of motion is illustrated. One commonly used alternative formulation for elastic airplanes is shown to yield significant inaccuracies because of inappropriate interpretation of inertial effects.

Kemp, W. B., Jr.↗

NASA NTRS1973

Matrix Perturbation Techniques in Structural Dynamics

Matrix perturbation are developed techniques which can be used in the dynamical analysis of structures where the range of numerical values in the matrices extreme or where the nature of the damping matrix requires that complex valued eigenvalues and eigenvectors be used. The techniques can be advantageously used in a variety of fields such as earthquake engineering, ocean engineering, aerospace engineering and other fields concerned with the dynamical analysis of large complex structures or systems of second order differential equations. A number of simple examples are included to illustrate the techniques.

Caughey, T. K.↗

NASA NTRS1975

Switch selector processing

The proper program execution of the switch selector commands that provide sequencing signals to the launch vehicle hardware was verified. Correct execution of each step necessary to activate a switch selector command and maintenance of the minimum timing requirements between steps are verified through analysis of a series of 6D/LVDC intermediate timing cases. Nominal and perturbed switch selector feedback conditions are simulated to verify correct processing of all realistic and timing combinations. A command which is in progress can be properly terminated by issuance of a forced reset. This is verified by forcing the conditions which require a forced reset and observing that the proper termination is completed.

Source record↗

NASA NTRS1977

Gravitational harmonics from shallow resonant orbits

Gravitational constraint (lumped coefficient) equations are derived from GEOS-2 data and a detailed analysis of the shallow resonance problem. The equations follow from elementary perturbation theory and show that all such lumped coefficients are harmonic in the argument of perigee. The best along-track constraints derived from them account for all but about 2% of the 13th-order resonant information in the tracking data. The equations are also in good agreement with recent comprehensive gravity models which use substantial amounts of GEOS-2 data.

Wagner, C. A.↗

NASA NTRS1980

Observations of ULF oscillations in the ion fluxes at small pitch angles with ATS 6

The ultra-low-frequency modulation of ion flux densities at small pitch angles observed by ATS 6 is examined, with particular attention given to a detailed analysis of a representative event. ULF modulation events with maximum modulation at small pitch angles were identified 14 times during the first eight months of operation of the NOAA low-energy particle detector on ATS 6. For the event of October 23, 1974, maximum flux modulation, with a maximum/minimum intensity ratio of 3.7, was observed in the 100 to 150 keV detector at an angle of 32 deg to the ambient field. Spectral analysis of magnetic field data reveals a right elliptically polarized magnetic perturbation with a 96-sec period and a 5-gamma rms amplitude, propagating in the dipole meridian at an angle of about 15 deg to the ambient field and the dipole axis. Proton flux modulation is found to lag the field by up to 180 deg for the lowest-energy channel. Observations are compared with the drift wave, MHD slow wave, and bounce resonant interaction associated with transverse wave models, and it is found that none of the wave models can adequately account for all of the correlated particle and field oscillations.

Su, S.-Y.↗

NASA NTRS1981

Computational problems in autoregressive moving average (ARMA) models

The choice of the sampling interval and the selection of the order of the model in time series analysis are considered. Band limited (up to 15 Hz) random torque perturbations are applied to the human ankle joint. The applied torque input, the angular rotation output, and the electromyographic activity using surface electrodes from the extensor and flexor muscles of the ankle joint are recorded. Autoregressive moving average models are developed. A parameter constraining technique is applied to develop more reliable models. The asymptotic behavior of the system must be taken into account during parameter optimization to develop predictive models.

Agarwal, G. C.↗

NASA NTRS1985

Three-dimensional baroclinic instability of a Hadley cell for small Richardson number

A three-dimensional, linear stability analysis of a baroclinic flow for Richardson number, Ri, of order unity is presented. The model considered is a thin horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The basic state is a Hadley cell which is a solution of the complete set of governing, nonlinear equations and contains both Ekman and thermal boundary layers adjacent to the rigid boundaries; it is given in a closed form. The stability analysis is also based on the complete set of equations; and perturbation possessing zonal, meridional, and vertical structures were considered. Numerical methods were developed for the stability problem which results in a stiff, eighth-order, ordinary differential eigenvalue problem. The previous work on three-dimensional baroclinic instability for small Ri was extended to a more realistic model involving the Prandtl number, sigma, and the Ekman number, E, and to finite growth rates and a wider range of the zonal wavenumber.

Antar, B. N.↗

NASA NTRS1990

On the topology of flux transfer events

A topological analysis is made of a simple model magnetic field of a perturbation at the magnetopause that shares magnetic properties with flux transfer events. The aim is to clarify a number of topological aspects that arise in the case of fully three-dimensional magnetic fields. It is shown that a localized perturbation at the magnetopause can in principle open a closed magnetosphere by establishing magnetic connections across the magnetopause by the formation of a ropelike magnetic field structure. For this purpose a global topological model of a closed magnetosphere is considered as the unperturbed state. The topological substructure of the model flux rope is discussed in detail.

Hesse, Michael↗

NASA NTRS1990

Short-time Lyapunov exponent analysis

A new technique for analyzing complicated fluid flows in numerical simulations has been successfully tested. The analysis uses short time Lyapunov exponent contributions and the associated Lyapunov perturbation fields. A direct simulation of the Taylor-Couette flow just past the onset of chaos demonstrated that this new technique marks important times during the system evolution and identifies the important flow features at those times. This new technique will now be applied to a 'minimal' turbulent channel.

Vastano, J. A.↗

NASA NTRS1991

Energy-heading transients in atmospheric flight guidance for airbreathing hypersonic vehicles

A time-range-fuel optimization problem is formulated for an airbreathing, hypersonic vehicle. Singular perturbation theory is used to decompose the problem into simpler subproblems. Analysis of the cruise-dash problem shows the importance of a Mach-limit. Energy-heading transients are studied and a family of trajectories, fairing asymptotically to a cruise condition, are generated.

Cliff, Eugene M.↗

NASA NTRS1992

The modulation of the low-latitude radiation budget by cloud and surface forcing on interannual time scales

Regionally confined interannual perturbations in the tropical radiation budget associated with east-west circulations are examined along with the forcing mechanisms of these perturbations in relation to surface and cloudiness variability. A zonal harmonic analysis of emitted longwave radiation emphasizes that these variations are largely controlled at the planetary wave scale. The overall effect leads to an approximately 50 deg/yr propagation phase speed that is considerably slower than the oceanic Kelvin wave capable of driving east-west longwave (LW) anomalies through SST feedback. Examination of the time-dependent radiative energetics over the tropics reveals that the aforementioned anomaly LW propagation is mainly due to cloud forcing associated with east-west circulation changes. Diabatic heating associated with coupled ocean-atmosphere feedback appears to be larger responsible for the LW anomaly propagation.

Sohn, Byung-Ju↗

NASA NTRS1996

Pulse Detonation Engine Air Induction System Analysis

A preliminary mixed-compression inlet design concept for potential pulse-detonation engine (PDE) powered supersonic aircraft was defined and analyzed. The objectives of this research were to conceptually design and integrate an inlet/PDE propulsion system into a supersonic aircraft, perform time-dependent CFD analysis of the inlet flowfield, and to estimate the installed PDE cycle performance. The study was baselined to a NASA Mach 5 Waverider study vehicle in which the baseline over/under turboramjet engines were replaced with a single flowpath PDE propulsion system. As much commonality as possible was maintained with the baseline configuration, including the engine location and forebody lines. Modifications were made to the inlet system's external ramp angles and a rotating cowl lip was incorporated to improve off-design inlet operability and performance. Engines were sized to match the baseline vehicle study's ascent trajectory thrust requirement at Mach 1.2. The majority of this study was focused on a flight Mach number of 3.0. The time-dependent Navier Stokes CFD analyses of a two-dimensional approximation of the inlet was conducted for the Mach 3.0 condition. The Lockheed Martin Tactical Aircraft Systems-developed FALCON CFD code with a two equation 'k-1' turbulence model was used. The downstream PDE was simulated by an array of four sonic nozzles in which the flow areas were rapidly varied in various opening/closing combinations. Results of the CFD study indicated that the inlet design concept operated successfully at the Mach 3.0 condition, satisfying mass capture, total pressure recovery, and operability requirements. Time-dependent analysis indicated that pressure and expansion waves from the simulated valve perturbations did not effect the inlet's operability or performance.

Pegg, R. J.↗

NASA NTRS2013

A Resolved Debris Disk Around the Candidate Planet-hosting Star HD 95086

Recently, a new planet candidate was discovered on direct images around the young (10-17 Myr) A-type star HD 95086. The strong infrared excess of the system indicates that, similar to HR8799, Beta Pic, and Fomalhaut, the star harbors a circumstellar disk. Aiming to study the structure and gas content of the HD 95086 disk, and to investigate its possible interaction with the newly discovered planet, here we present new optical, infrared, and millimeter observations. We detected no CO emission, excluding the possibility of an evolved gaseous primordial disk. Simple blackbody modeling of the spectral energy distribution suggests the presence of two spatially separate dust belts at radial distances of 6 and 64 AU. Our resolved images obtained with the Herschel Space Observatory reveal a characteristic disk size of approx. 6.0 × 5.4 (540 × 490 AU) and disk inclination of approx 25 deg. Assuming the same inclination for the planet candidate's orbit, its reprojected radial distance from the star is 62 AU, very close to the blackbody radius of the outer cold dust ring. The structure of the planetary system at HD 95086 resembles the one around HR8799. Both systems harbor a warm inner dust belt and a broad colder outer disk and giant planet(s) between the two dusty regions. Modeling implies that the candidate planet can dynamically excite the motion of planetesimals even out to 270 AU via their secular perturbation if its orbital eccentricity is larger than about 0.4. Our analysis adds a new example to the three known systems where directly imaged planet(s) and debris disks coexist.

gas content↗