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Walden, H.

Publications and source records attributed to Walden, H..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Airborne Lidar measurements of the atmospheric pressure profile with tunable Alexandrite lasers

The first remote measurements of the atmospheric pressure profile made from an airborne platform are described. The measurements utilize a differential absorption lidar and tunable solid state Alexandrite lasers. The pressure measurement technique uses a high resolution oxygen A band where the absorption is highly pressure sensitive due to collision broadening. Absorption troughs and regions of minimum absorption were used between pairs of stongly absorption lines for these measurements. The trough technique allows the measurement to be greatly desensitized to the effects of laser frequency instabilities. The lidar system was set up to measure pressure with the on-line laser tuned to the absorption trough at 13147.3/cm and with the reference laser tuned to a nonabsorbing frequency near 13170.0/cm. The lidar signal returns were sampled with a 200 range gate (30 vertical resoltion) and averaged over 100 shots.

Korb, C. L.↗
NASA NTRS1986

Real-time atmospheric absorption spectra for in-flight tuning of an airborne dial system

Real-time measurements of atmospheric absorption spectra are displayed and used to precisely calibrate and fix the frequency of an Alexandrite laser to specific oxygen absorption features for airborne Differential Absorption Lidar (DIAL) measurements of atmospheric pressure and temperature. The DIAL system used contains two narrowband tunable Alexandrite lasers: one is electronically scanned to tune to oxygen absorption features for on-line signals while the second is used to obtain off-line (nonabsorbed) atmospheric return signals. The lidar operator may select the number of shots to be averaged, the altitude, and altitude interval over which the signals are averaged using single key stroke commands. The operator also determines exactly which oxygen absorption lines are scanned by comparing the line spacings and relative strengths with known line parameters, thus calibrating the laser wavelength readout. The system was used successfully to measure the atmospheric pressure profile on the first flights of this lidar, November 20, and December 9, 1985, aboard the NASA Wallops Electra aircraft.

Dombrowski, M.↗
NASA NTRS1982

Numerical computation of exponential matrices using the Cayley-Hamilton theorem

A method for computing exponential matrices, which often arise naturally in the solution of systems of linear differential equations, is developed. An exponential matrix is generated as a linear combination of a finite number (equal to the matrix order) of matrices, the coefficients of which are scalar infinite sums. The method can be generalized to apply to any formal power series of matrices. Attention is focused upon the exponential function, and the matrix exponent is assumed tri-diagonal in form. In such cases, the terms in the coefficient infinite sums can be extracted, as recursion relations, from the characteristic polynomial of the matrix exponent. Two numerical examples are presented in some detail: (1) the three dimensional infinitesimal rotation rate matrix, which is skew symmetric, and (2) an N-dimensional tri-diagonal and symmetric finite difference matrix which arises in the numerical solution of the heat conduction partial differential equation. In the second example, the known eigenvalues and eigenvectors of the finite difference matrix permit an analytical solution for the exponential matrix, through the theory of diagonalization and similarity transformations, which is used for independent verification. The convergence properties of the scalar infinite summations are investigated for finite difference matrices of various orders up to ten, and it is found that the number of terms required for convergence increases slowly with the order of the matrix.

Walden, H.↗
NASA NTRS1977

Calibration analysis for a multi-channel infrared scanning radiometer

A procedure for calibrating an infrared scanning spectroradiometer by a computerized parametric error analysis technique was developed. The uncertainties in the radiometric measurements of scene radiance and (for the case of a blackbody scene) temperature due to possible uncertainties in the calibration target temperature, calibration target emissivity, and instrument temperature were calculated for a range of uncertainty levels in the parameters, as well as for a gamut of scent temperatures corresponding to a given spectral channel. This technique is applicable to the radiometric calibration of any infrared radiometer. It was applied specifically to the Cloud-Top Scanning (C.T.S) Radiometer, a three-channel instrument designed for aircraftborne cloud radiance measurements in the 6.75 and 11.5 micron thermal emission spectral regions.

Walden, H.↗
NASA NTRS1977

Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (i.e., the membrane eignevalue problem for the vibration equation) on the unit spherical surface are developed. Two types of spherical surface domains are considered: the interior of a spherical triangle, and the exterior of a great circle arc extending for less than pi radians (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is employed. The fundamental eigenvalue is approximated by iteration utilizing the power method and point successive overrelaxation. Some numerical results are given and compared, in certain special cases, with analytical solutions to the eigenvalue problem. The significance of the numerical eigenvalue results is discussed in terms of the singularities in the solution of three-dimensional boundary-value problems near a polyhedral corner of the domain.

Walden, H.↗
NASA NTRS1974

Post-flight differential correction analysis using Vinti's spheroidal method for the small astronomy satellite orbit

The results of an intensive analysis of a differential orbit improvement method utilizing observational data for a 550-kilometer altitude, near-circular, near-equatorial satellite orbit are presented. Observations of the Small Astronomy Satellite (SAS-1) are in the form of direction cosines as measured at two ground interferometer tracking stations near the Equator during the first 22 orbital revolutions (approximately 37 hours) after launch of the spacecraft. Numerical results, in both tabular and graphical form, are displayed for numerous iterated fittings of various observational arcs by differential correction of the orbital elements. Parameters varied in these comparative cases include the time duration of the observational data block, the number of pairs of direction cosine data and the number of tracking station passes included in the solution, the distribution of such passes between the two available tracking stations, and the acceptance criterion for the observational residuals in the least squares fitting procedure. It was found that three observational pairs of direction cosine data, the minimum number possible for a uniquely determined solution in theory, are sufficient to promote covergence to an accurate solution, if properly selected.

Walden, H.↗
NASA NTRS1974

Solution of an eigenvalue problem for the Laplace operator on a spherical surface

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

Walden, H.↗
NASA NTRS1973

Proposed gravity-gradient dynamics experiments in lunar orbit using the RAE-B spacecraft

A series of seven gravity-gradient dynamics experiments is proposed utilizing the Radio Astronomy Explorer (RAE-B) spacecraft in lunar orbit. It is believed that none of the experiments will impair the spacecraft structure or adversely affect the continuation of the scientific mission of the satellite. The first experiment is designed to investigate the spacecraft dynamical behavior in the absence of libration damper action and inertia. It requires stable gravity-gradient capture of the spacecraft in lunar orbit with small amplitude attitude librations as a prerequisite. Four subsequent experiments involve partial retraction, ultimately followed by full redeployment, of one or two of the 230-meter booms forming the lunar-directed Vee-antenna. These boom length change operations will induce moderate amplitude angular librations of the spacecraft.

Blanchard, D. L.↗
NASA NTRS1973

Gravity-gradient dynamics experiments performed in orbit utilizing the Radio Astronomy Explorer (RAE-1) spacecraft

Six dynamic experiments were performed in earth orbit utilizing the RAE spacecraft in order to test the accuracy of the mathematical model of RAE dynamics. The spacecraft consisted of four flexible antenna booms, mounted on a rigid cylindrical spacecraft hub at center, for measuring radio emissions from extraterrestrial sources. Attitude control of the gravity stabilized spacecraft was tested by using damper clamping, single lower leading boom operations, and double lower boom operations. Results and conclusions of the in-orbit dynamic experiments proved the accuracy of the analytic techniques used to model RAE dynamical behavior.

Walden, H.↗
NASA NTRS1972

Dynamical in-orbit behavior of the Radio Astronomy Explorer satellite

Onboard sensors and associated ground based processing systems are used to maintain a well stabilized attitude for the RAE 1 in its near circular earth orbit despite the satellite's four extremely long and flexible antenna booms. Boom tip deflection pictures and central hub orientation measurements show that large boom vibrations and major attitude stability problems anticipated prior to launch have not materialized.

Walden, H.↗