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  • 1
    facet.materialart.
    Unknown
    In:  Other Sources
    Publication Date: 2011-08-24
    Description: Scientific data often contains random errors that make plotting and curve-fitting difficult. The Rational-Spline Approximation with Automatic Tension Adjustment algorithm lead to a flexible, smooth representation of experimental data. The user sets the conditions for each consecutive pair of knots:(knots are user-defined divisions in the data set) to apply no tension; to apply fixed tension; or to determine tension with a tension adjustment algorithm. The user also selects the number of knots, the knot abscissas, and the allowed maximum deviations from line segments. The selection of these quantities depends on the actual data and on the requirements of a particular application. This program differs from the usual spline under tension in that it allows the user to specify different tension values between each adjacent pair of knots rather than a constant tension over the entire data range. The subroutines use an automatic adjustment scheme that varies the tension parameter for each interval until the maximum deviation of the spline from the line joining the knots is less than or equal to a user-specified amount. This procedure frees the user from the drudgery of adjusting individual tension parameters while still giving control over the local behavior of the spline The Rational Spline program was written completely in FORTRAN for implementation on a CYBER 850 operating under NOS. It has a central memory requirement of approximately 1500 words. The program was released in 1988.
    Keywords: NUMERICAL ANALYSIS
    Type: LAR-13694
    Format: text
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  • 2
    Publication Date: 2006-02-14
    Description: The performance and aerodynamic characteristics of the Space Shuttle Columbia are analyzed over the speed range from Mach 2 to 26 using flight data taken from the first five Space Transportation System flights. These data are used to reconstruct the entry trajectory, calculate vehicle performance, and estimate lateral stability and control derivatives including those assocated with the onboard Reaction Control System. The trajectory reconstruction process is discussed in its relationship to the determination of the vehicle flight characteristics. Vehicle performance results are presented which show that lift and drag were generally overpredicted by 3 percent and that the life-to-drag ratio was underpredicted by 1 percent. Anomalies in pitching-moment trim characteristics are shown and noted to be due to real-gas and Mach-number effects. Lateral stability and control derivatives estimated using programmed test input maneuvers are corrected with preflight predictions and are usually within the uncertainties associated with the predictions. The lateral reaction-control system effectiveness is evaluated.
    Keywords: SPACE TRANSPORTATION
    Type: Shuttle Performance: Lessons Learned, Pt. 1; p 473-508
    Format: text
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  • 3
    Publication Date: 2006-02-14
    Description: The first five flights of the Space Transportation System (STS) have exhibited unexpected lateral oscillations in the Mach Number = 1.7 to Mach Number = 1.0 region of the descent trajectory. These oscillations can be split into two parts: a predominantly rolling oscillation referred to as the quarter hertz motion and a long-priod, large-amplitude oscillation in sideslips, roll rate, and yaw rate. These motions are analyzed in this paper in order to determine their source and the mechanism driving them. They will first be examined to determine how much of the motion can be explained using the set of equations that contain linear aerodynamic parameters. Then differences between measured moments and those calculated using linear aerodynamics which are considered to be due to unmodeled moments will be exained. Possible error sources such as not inluding nonlinear aerodynamics in the vehicle model, measurement errors, and the effect of pressure gradients will be considered. Based on these analyses, conclusions as to the nature and cause of the Shuttle lateral oscillations will be drawn.
    Keywords: SPACE TRANSPORTATION
    Type: Shuttle Performance: Lessons Learned, Part 1; p 397-412
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  • 4
    Publication Date: 2011-08-19
    Description: An overview of several multivariate image processing techniques is presented, with emphasis on techniques based upon the principal component transformation (PCT). Multiimages in various formats have a multivariate pixel value, associated with each pixel location, which has been scaled and quantized into a gray level vector, and the bivariate of the extent to which two images are correlated. The PCT of a multiimage decorrelates the multiimage to reduce its dimensionality and reveal its intercomponent dependencies if some off-diagonal elements are not small, and for the purposes of display the principal component images must be postprocessed into multiimage format. The principal component analysis of a multiimage is a statistical analysis based upon the PCT whose primary application is to determine the intrinsic component dimensionality of the multiimage. Computational considerations are also discussed.
    Keywords: EARTH RESOURCES AND REMOTE SENSING
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  • 5
    Publication Date: 2011-08-18
    Description: Measurements taken in 1976 from the St. Louis Regional Air Pollution Study (RAPS) data base, conducted by EPA, were analyzed to determine an optimum set of air-quality and meteorological variables for predicting maximum ozone levels for each day in 1976. A 'leaps and bounds' regression analysis was used to identify the best subset of variables. Three particular variables, the 9 a.m. ozone level, the forecasted maximum temperature, and the 6-9 a.m. averaged wind speed, have useful forecasting utility. The trajectory history of air masses entering St. Louis was studied, and it was concluded that transport-related variables contribute to the appearance of very high ozone levels. The final empirical forecast model predicts the daily maximum ozone over 341 days with a standard deviation of 11 ppb, which approaches the estimated error.
    Keywords: ENVIRONMENT POLLUTION
    Type: Environmental Science and Technology; 15; Apr. 198
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  • 6
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    Unknown
    In:  Other Sources
    Publication Date: 2011-08-19
    Keywords: RESEARCH AND SUPPORT FACILITIES (AIR)
    Type: Journal of Aircraft (ISSN 0021-8669); 23; 131-135
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  • 7
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    In:  Other Sources
    Publication Date: 2018-12-01
    Description: The study reported here explored the development and utility of a spline representation of the sample quantile function of a continuous probability distribution in providing a functional description of a random sample and a method of generating random variables. With a spline representation, the random samples are generated by transforming a sample of uniform random variables to the interval of interest. This is useful, for example, in simulation studies in which a random sample represents the only known information about the distribution. The spline formulation considered here consists of a linear combination of cubic basis splines (B-splines) fit in a least squares sense to the sample quantile function using equally spaced knots. The following discussion is presented in five parts. The first section highlights major results realized from the study. The second section further details the results obtained. The methodology used is described in the third section, followed by a brief discussion of previous research on quantile functions. Finally, the results of the study are evaluated.
    Keywords: NUMERICAL ANALYSIS
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  • 8
    Publication Date: 2019-06-28
    Description: Two algorithms for interpolating surfaces with spline functions containing tension parameters are discussed. Both algorithms are based on the tensor products of univariate rational spline functions. The simpler algorithm uses a single tension parameter for the entire surface. This algorithm is generalized to use separate tension parameters for each rectangular subregion. The new algorithm allows for local control of tension on the interpolating surface. Both algorithms are illustrated and the results are compared with the results of bicubic spline and bilinear interpolation of terrain elevation data.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TP-2536 , L-16045 , NAS 1.60:2536
    Format: application/pdf
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  • 9
    Publication Date: 2019-06-28
    Description: Flight data taken from the first five flights (STS-2, 3, 4, 5 and 9) of the Space Transportation System Shuttle Columbia during entry are analyzed to determine the Shuttle lateral aerodynamic characteristics. Maximum likelihood estimation is applied to data derived from accelerometer and rate gyro measurements and trajectory, meteorological and control surface data to estimate lateral-directional stability and control derivatives. The estimated parameters are compared across the five flights and to preflight predicted values.
    Keywords: SPACE TRANSPORTATION
    Type: NASA-TM-88994 , NAS 1.15:88994
    Format: application/pdf
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  • 10
    Publication Date: 2019-06-28
    Description: An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TP-2366 , L-15826 , NAS 1.60:2366
    Format: application/pdf
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