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NASA NTRS1971

A note on 'The main problem of satellite theory for small eccentricities, by A. Deprit and A. Rom, 1970.'

Criticism of Deprit and Rom's (1970) extension of Brouwer's (1959) first-order satellite theory to the third order in J sub 2. It is noted that Deprit and Rom's theory suffers from the drawback that the perturbations of all orders are expressed as infinite power series in the eccentricity e. It is demonstrated that Deprit and Rom's reported failure to extend Brouwer's theory to the second order in a closed form by means of Lie transforms is due to an oversight and is not caused by difficulties inherent in the problem or in the particular perturbation method used.

Aksnes, K.↗

NASA NTRS1974

A note on velocity-related series expansions in the two-body problem

The present note describes a few important series expansions in the two-body problem. They are related to the magnitude v of the velocity vector and are important for the treatment of atmospheric drag by the method of general perturbations. These series have been obtained with computerized Poisson series manipulations. The results are given to order seven in the eccentricity, for both the mean anomaly and the true anomaly.

Broucke, R.↗

NASA NTRS1975

A note on optimal filtering in the presence of unknown biases

This note considers some aspects of the optimal filtering problem for linear processes in the presence of unknown biases in the input and the observations. It is proved via duality that the optimal filtering problem in the presence of an input bias is equivalent to a certain optimal regulator problem incorporating integral feedback. The question of observability of the augmented system used in the state and bias estimation is answered by deriving necessary and sufficient conditions when bias is present (1) in the input, (2) in the observations and (3) both in the input and the observations.

Joshi, S. M.↗

NASA NTRS1975

A note on the consistency of maximum likelihood estimates for finite families of stochastic processes

The note considers families of stochastic processes indexed by a finite number of alternative parameter values. For general classes of stochastic processes, it is shown that maximum-likelihood estimates converge almost surely to the correct parameter value. This is established by use of a submartingale property of the sequence of maximized-likelihood ratios together with a technique first employed by Wald (1949) in the case of independent identically distributed random variables.

Caines, P. E.↗

NASA NTRS1976

A note on Hansen's coefficients in satellite theory

General formulas for Hansen's coefficients in satellite theory are derived along with expressions for the eccentricity functions G and H. Recurrence relations for the eccentricity functions and their derivatives are obtained which are valid for all values of the parameter p. It is noted that the recurrence relations obtained by Challe and Laclaverie (1969) as well as by Balmino (1973) do not satisfy certain parity conditions and therefore involve coefficients outside the range of usage.

Giacaglia, G. E. O.↗

NASA NTRS1978

A note on the problem of jet stream formation

It is noted that the formation of 'jet streams', or narrow ringlike structures of small particles, in early planetary and satellite systems cannot result solely from inelastic collisions among the small particles. The possibility is considered that gravitational encounters between the particles will perturb them into more eccentric orbits and thus maintain the orbital coupling between particles (or jet streams) in neighboring orbits. It is found that when the gravitational effect of the particles is taken into account, the average eccentricity of the particles increases as agglomeration due to inelastic collisions proceeds. With respect to jet-stream formation, it is suggested that the ever-increasing orbital eccentricity of the particles will aid in coupling together the different 'sub-jet streams', so that large-scale orbital focusing toward the center of the whole system can continue. Alternative mechanisms leading to planetary accretion are briefly discussed.

Ip, W.-H.↗

NASA NTRS1979

Brief note for consideration of active seismic exploration on Mars

Considerable controversy has arisen regarding the existence of water and water ice below the surface of Mars. Results of laboratory internal friction measurements on strongly outgassed rocks, recently made as part of an effort to interpret the high seismic Q values observed in the lunar crust, show that moisture absorbed in pores and cracks causes the low Q values. Unfortunately, the Viking seismology investigation found a surprisingly inactive planet. This note makes the case for active seismic exploration in order to ascertain the existence of liquid water in the crust from Q determinations.

Tittmann, B. R.↗

NASA NTRS1980

Hand-held radiometry: A set of notes developed for use at the Workshop of Hand-held radiometry

A set of notes was developed to aid the beginner in hand-held radiometry. The electromagnetic spectrum is reviewed, and pertinent terms are defined. View areas of multiband radiometers are developed to show the areas of coincidence of adjacent bands. The amounts of plant cover seen by radiometers having different fields of view are described. Vegetation indices are derived and discussed. Response functions of several radiometers are shown and applied to spectrometer data taken over 12 wheat plots, to provide a comparison of instruments and bands within and among instruments. The calculation of solar time is reviewed and applied to the calculation of the local time of LANDSAT satellite overpasses for any particular location in the Northern Hemisphere. The use and misuse of hand-held infrared thermometers are discussed, and a procedure for photographic determination of plant cover is described. Some suggestions are offered concerning procedures to be followed when collecting hand-held spectral and thermal data. A list of references pertinent to hand-held radiometry is included.

Jackson, R. D.↗

NASA NTRS1981

A note on the statistics of early-type close binaries

A degree of contact index (I sub c) is defined, and its frequency diagram is given for 16 early-type close binaries. The objective is to determine whether the numbers of such systems are continuous or discontinuous across marginal contact. Data for four of the systems (TU Mus, V499 Sco, Delta Pic, and SZ Cam) derive from new photometric analyses, the results of which are also given. Present results indicate that there is continuity in frequency across marginal contact, although it would be desirable to include more binaries as further observations become available. It is noted that the only two systems in the bin of largest I sub c are known to be in the rapid phase of mass transfer.

Wilson, R. E.↗

NASA NTRS1981

Notes for Brazil sampling frame evaluation trip

Field notes describing a trip conducted in Brazil are presented. This trip was conducted for the purpose of evaluating a sample frame developed using LANDSAT full frame images by the USDA Economic and Statistics Service for the eventual purpose of cropland production estimation with LANDSAT by the Foreign Commodity Production Forecasting Project of the AgRISTARS program. Six areas were analyzed on the basis of land use, crop land in corn and soybean, field size and soil type. The analysis indicated generally successful use of LANDSAT images for purposes of remote large area land use stratification.

Horvath, R.↗

NASA NTRS1985

A note on the Charleston Gyre

The deflection of the Gulf Stream caused by a topographic feature - the Charleston Bump, located offshore of Savannah, Georgia - results in a quasi-stationary cyclonic eddy - the Charleston Gyre which is situated over the continental slope east of Charleston and Cape Romain. Occasionally, the upwelling associated with this eddy produces an enhancement in the surface layer primary production that is great enough to be detected by the Nimbus 7 coastal zone color scanner (CZCS). In this note a CZCS image with simultaneous hydrography, current, and wind observations is presented that documents an unusual manifestation of the gyre. In addition to the CZCS image a Seasat synthetic aperture radar (SAR) image is included that clearly indicates the presence of the eddy adjacent to the Gulf Stream front.

Mcclain, C. R.↗

NASA NTRS1985

A note on the finite differencing of the linearized primitive equations' lower boundary condition

This note examines the accuracy of finite difference solutions of the midlatitude primitive equations and the quasi-geostrophic equation. First order accurate forward differencing of the equations' lower boundary condition is shown to poorly simulate the radiating wave response to midlatitude heating. Forward differencing always exaggerates the magnitude of the radiating response. For a realistic heating height scale and for a reasonable mesh size this exaggeration is on the order of 50 percent. Central differencing of the lower boundary condition gives an error of only about 3 percent.

Jacqmin, D.↗

NASA NTRS1985

A note on finite-dimensional estimators for infinite-dimensional systems

In this note two theorems are proved regarding finite-dimensional estimators for infinite-dimensional systems. The first concerns the finite dimensionality of the model and the second concerns the finite dimensionality of the observation space. The analysis applies to very general systems, but appears to be most useful for the estimation of static systems from point sensing.

Milman, M. H.↗

NASA NTRS1987

A note on the generation of Tollmien-Schlichting waves by sudden surface-curvature change

This note is primarily concerned with the generation of spatially growing Tollmien-Schlichting waves by the interaction of very long-wavelength free-stream disturbances with a discontinuity in the curvature of a bounding surface (whose slope may or may not be continuous). The theory is combined with a numerical solution of the local Orr-Sommerfeld equation, and the result is used to predict the Tollmien-Schlichting amplitude in a relevant experiment carried out by Leehey and Shapiro (1980). The calculated results are in satisfactory agreement with their observations.

Goldstein, M. E.↗

NASA NTRS1988

Some notes on applying the one-step multiconic method of trajectory propagation

The one-step multiconic method (also called the pseudostate method) has been known for years to offer up to an order of magnitude of improvement over the patched-conic method for propagating trajectories under the gravitational influence of two bodies. In these notes, the method and some of its variations are described. Then, a crucial parameter of this method, the sweepback duration, is examined, and it is shown that the traditional wisdom concerning this parameter should be replaced by an algorithm which relates it to the trajectory characteristics. Remarkably, this algorithm is independent of the masses of the primary and secondary bodies.

Sweetser, Theodore H., III↗

NASA NTRS1989

A note concerning the onset of three dimensionality and time dependence in Goertler vortices

Recently Hall and Seddougui (1989) considered the secondary instability of large amplitude Goertler vortices in a growing boundary layer evolving into a three-dimensional flow with wavy vortex boundaries. They obtained a pair of coupled, linear ordinary differential equations for this instability which constituted an eigenproblem for the wavelength and frequency of this wavy mode. Investigations into the nonlinear version of this problem by Seddougui and Bassom have revealed several omissions in the numerical work of Hall and Seddougui. These issues are addressed in this note. In particular, it is found that many neutrally stable modes are possible. The properties of such modes are derived in a high wavenumber limit and it is shown that the combination of the results of Hall and Seddougui and the modifications made here lead to conclusions which are consistent with the available experimental observations.

Bassom, Andrew P.↗

NASA NTRS1991

Collected Notes on the Workshop for Pattern Discovery in Large Databases

These collected notes are a record of material presented at the Workshop. The core data analysis is addressed that have traditionally required statistical or pattern recognition techniques. Some of the core tasks include classification, discrimination, clustering, supervised and unsupervised learning, discovery and diagnosis, i.e., general pattern discovery.

Buntine, Wray↗

NASA NTRS1991

Implementation notes on bdes(1)

This note describes the implementation of bdes, the file encryption program being distributed in the 4.4 release of the Berkeley Software Distribution. It implements all modes of the Data Encryption Standard program.

Bishop, Matt↗