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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 NTRS1983

Separation of time scales in aircraft trajectory optimization

Two methods for analyzing the time-scale properties of aircraft trajectory optimization problems are presented. Time-scale properties must be identified before solutions can be obtained by using singular perturbation methods. Both methods only require a knowledge of the state equations, the aircraft characteristics, and the bounds on the state and control variables. Although these methods give only rough estimates of time-scale separation, they do not require that an 'exact' optimal trajectory be known, as do the more rigorous methods, and they are an improvement on the ad hoc methods currently in use. The two methods are applied to an example problem for a high performance aircraft.

Ardema, M. D.↗
NASA NTRS1982

Nonlinear zero-sum differential game analysis by singular perturbation methods

A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane.

Sinar, J.↗
NASA NTRS1979

Aircraft trajectory optimization using singular perturbation methods

Singular perturbation methods are used to derive nonlinear feedback control laws for aircraft minimum time long range interception under the assumption of complete time scale separation. The resulting algorithms are in feedback form and can be implemented on a microcomputer for on-line trajectory optimization.

Mehra, R. K.↗
NASA NTRS1984

Selection of Slow and Fast Variables in the Three-Dimensional Flight Dynamics

A transformation from the altitude and velocity state variables of three-dimensional flight mechanics to a new set of more desirable variables is found. The new variables provide a greater time-scale separation, decrease system coupling, and give better estimates of the fast-variable values along the reduced solution. One of the new variables is the often-used specific energy, whereas the other variable changes along a given trajectory, depending on the nature of the local reduced solution. Numerical examples are included.

Ardema, M.↗
NASA NTRS1981

Computing aerodynamic sound using advanced statistical turbulence theories

It is noted that the calculation of turbulence-generated aerodynamic sound requires knowledge of the spatial and temporal variation of Q sub ij (xi sub k, tau), the two-point, two-time turbulent velocity correlations. A technique is presented to obtain an approximate form of these correlations based on closure of the Reynolds stress equations by modeling of higher order terms. The governing equations for Q sub ij are first developed for a general flow. The case of homogeneous, stationary turbulence in a unidirectional constant shear mean flow is then assumed. The required closure form for Q sub ij is selected which is capable of qualitatively reproducing experimentally observed behavior. This form contains separation time dependent scale factors as parameters and depends explicitly on spatial separation. The approximate forms of Q sub ij are used in the differential equations and integral moments are taken over the spatial domain. The velocity correlations are used in the Lighthill theory of aerodynamic sound by assuming normal joint probability.

Hecht, A. M.↗
NASA NTRS1976

Linear regulator design for stochastic systems by a multiple time scales method

A hierarchically-structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems is considered. The controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite. The methodology is illustrated by design of a controller to suppress the phugoid and short period modes of the longitudinal dynamics of the F-8 aircraft.

Teneketzis, D.↗
NASA NTRS1977

Linear regulator design for stochastic systems by a multiple time-scales method

This short paper develops a hierarchically structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems. It is proved that the controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite. The methodology is illustrated by design of a controller to suppress the phugoid and short-period modes of the longitudinal dynamics of the F-8 aircraft.

Teneketzis, D.↗
NASA NTRS1976

Linear regulator design for stochastic systems by a multiple time scales method

This paper develops a hierarchically-structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems. It is proved that the controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite. The methodology is illustrated by design of a controller to suppress the phugoid and short period modes of the longitudinal dynamics of the F-8 aircraft.

Teneketzis, D.↗
NASA NTRS1984

Intercomparison of planetary-scale diagnostics derived from separate satellite and radiosonde time-mean temperature fields

The planetary-scale components of the extratropical Northern Hemisphere troposphere-stratosphere 1973-74 winter circulation are diagnosed using separate time-mean temperature fields based on radiosonde and satellite observations. Meridional cross-sections of zonal wind together with, for zonal wavenumbers 1, 2 and 3, the streamfunction amplitude, phase and Eliassen-Palm flux are displayed, with the relative accuracy of the satellite-derived diagnostics assessed through comparison with the 'ground-truth' radiosonde information. The satellite and radiosonde diagnostics compare most favourably in terms of zonal wind speed and shear, direction of wave propagation and meridional wave structure - all of which are closely related to the differential properties of the atmospheric temperature field. The intensity of the satellite-derived patterns of tropospheric wave propagation is underestimated due to the effects of spatial smoothing and residual cloud contamination present in the satellite radiance measurements.

Miles, T.↗
NASA NTRS1984

Mechanisms of interannual ocean-atmosphere interactions

Results of an investigation to study the interaction between ocean and atmosphere on the annual to decadal time scale are reported. Separate studies of the ocean response to atmospheric forcing, and of atmospheric response to ocean forcing were also conducted. The main findings are the dynamics of sea surface temperature anomalies, the role of short time scale weather fluctuations in the seasonal cycle of the upper ocean variability, and the planetary wave response to sea surface temperature anomalies. A numerical model of the ocean atmosphere continent system and a two layer quasi-geostropic ocean model is discussed.

Frankignoul, C.↗
NASA NTRS1981

Predicting aerodynamic sound utilizing a two-point, two-time turbulence theory

The feasibility of determining two-point, two-time turbulent velocity correlations based on extending closure models for one-point, one-time turbulence correlations is demonstrated. The procedure used is based on a spatial moment integral formulation of the governing equations using approximate, parameterized trial functions for the two-point, two-time velocity correlations. Solution of the equations is shown to give a set of anisotropic length scales and the separation-time-dependent decorrelation of the ensemble averaged turbulent velocities. The analysis is simplified using the assumption of homogeneous stationary turbulence and a constant shear, unidirectional mean flow. It is shown that the anisotropic behavior of measured turbulence correlations can be characterized through this technique.

Hecht, A. M.↗
NASA NTRS1981

Analysis of the tensile stress-strain behavior of elastomers at constant strain rates. I - Criteria for separability of the time and strain effects

A theoretical analysis of the tensile stress-strain relation of elastomers at constant strain rate is presented which shows that the time and the stress effect are separable if the experimental time scale coincides with a segment of the relaxation modulus that can be described by a single power law. It is also shown that time-strain separability is valid if the strain function is linearly proportional to the Cauchy strain, and that when time-strain separability holds, two strain-dependent quantities can be obtained experimentally. In the case where time and strain effect are not separable, superposition can be achieved only by using temperature and strain-dependent shift factors.

Hong, S. D.↗
NASA NTRS1975

Satellite attitude prediction by multiple time scales method

An investigation is made of the problem of predicting the attitude of satellites under the influence of external disturbing torques. The attitude dynamics are first expressed in a perturbation formulation which is then solved by the multiple scales approach. The independent variable, time, is extended into new scales, fast, slow, etc., and the integration is carried out separately in the new variables. The theory is applied to two different satellite configurations, rigid body and dual spin, each of which may have an asymmetric mass distribution. The disturbing torques considered are gravity gradient and geomagnetic. Finally, as multiple time scales approach separates slow and fast behaviors of satellite attitude motion, this property is used for the design of an attitude control device. A nutation damping control loop, using the geomagnetic torque for an earth pointing dual spin satellite, is designed in terms of the slow equation.

Tao, Y. C.↗
NASA NTRS1974

A catalogue of solar cosmic ray events: IMPS 4 and 5, May 1967 - December 1972

This catalogue of solar cosmic ray events has been prepared for the use of solar physicists and other interested scientists. It contains some 185 solar particle events detected by the Goddard Space Flight Center Cosmic Ray Experiments on IMP's IV and V (Explorer 34 and 41) for the period May 1967 - December 1972. The data is presented in the form of hourly averages for three proton energy intervals - 0.9 - 1.6 MeV; 6 - 20 MeV and 20 - 80 MeV. In addition the time histories of .5 - 1.1 MeV electrons are shown on a separate scale. To assist in the identification of related solar events, the onset time of the electron event is indicated. The details of the instrumentation and detector techniques are described. Further descriptions of data reduction procedure and on the time-history plots are given.

Vanhollebeke, M. A.↗
NASA NTRS1973

Development of a global cloud model for simulating earth-viewing space missions.

Existing global cloud models are improved and expanded so that they might be more effectively used in planning and evaluating potential earth-viewing space missions. A relationship is developed between the ground and satellite-derived cloud-amount frequency distributions. This relationship is used to improve internal consistency between the ground-observed unconditional statistics and the satellite-derived conditional statistics as tabulated in previous models. A statistical technique is developed which permits the scaling of the conditional statistics to time and distance separations other than those for which the data base is tabulated. A new technique to increase or decrease the representative area size of the statistical data base is developed. Both the scaling and area adjustment techniques are shown to represent significant improvements over the techniques previously employed.

Greaves, J. R.↗
NASA NTRS1984

Operating systems

A counter operating system creates a hierarchy of levels of abstraction, so that at a given level all details concerning lower levels can be ignored. This hierarchical structure separates functions according to their complexity, characteristic time scale, and level of abstraction. The lowest levels include the system's hardware; concepts associated explicitly with the coordination of multiple tasks appear at intermediate levels, which conduct 'primitive processes'. Software semaphore is the mechanism controlling primitive processes that must be synchronized. At higher levels lie, in rising order, the access to the secondary storage devices of a particular machine, a 'virtual memory' scheme for managing the main and secondary memories, communication between processes by way of a mechanism called a 'pipe', access to external input and output devices, and a hierarchy of directories cataloguing the hardware and software objects to which access must be controlled.

Denning, P. J.↗
NASA NTRS1973

A new approach to the design of time varying control systems with application to the space shuttle booster

A general approach toward the analysis and design of closed loop control for slowly time-varying linear systems was investigated. The approach is by the method of generalized multiple scales, in which slow and fast dynamics are systematically separated by employing different clocks which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, so that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock functions are shown to satisfy an algebraic characteristic equation and can be determined in general in terms of the coefficients.

Ramnath, R. V.↗