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Efforts are continued to develop digital filter compensation schemes for the correction of momentum gains observed in the closed loop simulation of the docking of two satellites using the 6 DOF motion system. Several filters that work well for small delays ( .100ms) and a non-preloaded probe are discussed.
The reduction of the O(cu epsilon) integro differential equations to ordinary differential equations using a set of orthogonal functions is described. Attention was focused on the hover flight condition. The set of Galerkin integrals that appear in the reduced equations was evaluated by making use of nonrotating beam modes. Although a large amount of computer time was needed to accomplish this task, the Galerkin integrals so evaluated were stored on tape on a permanent basis. Several of the coefficients were also obtained in closed form in order to check the accuracy of the numerical computations. The equilibrium solution to the set of 3n equations obtained was determined as the solution to a minimization problem.
Short-risetime pulses contain frequency components above flat-response region of typical instrumentation amplifiers.
Small blade-to-blade property differences are investigated to determine their effects on the behavior of a simple rotor-body system. An analytical approach is used which emphasizes the significance of these effects from the experimental point of view. It is found that the primary effect of blade-to-blade dissimilarities is the appearance of additional peaks in the frequency spectrum which are separated from the convention response modes by multiples of the rotor speed. These additional responses are potential experimental problems because when they occur near a mode of interest they act as contaminant frequencies which can make damping measurements difficult. The effects of increased rotor-body coupling and a rotor shaft degree of freedom act to improve the situation by altering the frequency separation of the modes.
A perturbation/numerical methodology to analyze the flap-lead/lag motion of a centrally hinged spring restrained rotor blade that is valid for both hover and for forward flight was developed. The derivation of the nonlinear differential equations of motion and the analysis of the stability of the steady state response of the blade were conducted entirely in a Symbolics 3670 Machine using MACSYMA to perform all the lengthy symbolic manipulations. It also includes generation of the fortran codes and plots of the results. The Floquet theory was also applied to the differential equations of motion in order to compare results with those obtained from the perturbation analysis. The results obtained from the perturbation methodology and from Floquet theory were found to be very close to each other, which demonstrates the usefullness of the perturbation methodology. Another problem under study consisted in the analysis of the influence of higher order terms in the response and stability of a flexible rotor blade in forward flight using Computerized Symbolic Manipulation and a perturbation technique to bypass the Floquet theory. The derivation of the partial differential equations of motion is presented.
Two Van der Pol oscillators with reciprocal linear velocity coupling are utilized to model the response of the human circadian timing system to abrupt displacements of the environmental time cues (zeitgebers). The core temperature rhythm and sleep-wake cycle simulated by the model are examined. The relationship between the masking of circadian rhythms by environmental variables and behavioral and physiological events and the rates of resynchronization is studied. The effects of zeitgeber phase shifts and zeitgeber strength on the resynchronization rates are analyzed. The influence of intrinsic pacemakers periods and coupling strength on resynchronization are investigated. The simulated data reveal that: resynchronization after a time zone shift depends on the magnitude of the shift; the time of day of the shift has little influence on resynchronization; the strength of zeitgebers affects the rate and direction of the resynchronization; the intrinsic pacemaker periods have a significant effect on resynchronization; and increasing the coupling between the oscillators results in an increase in the rate of resynchronization. The model data are compared to transmeridian flight studies data and similar resynchronization patterns are observed.
A numerical filter for transforming measured temperature signals into a close approximation of the actual temperature signal is described. The filter is derived by minimizing the mean-square error of the system, and assuming a knowledge of the characteristics of the sensing element and its housing. The equation representing the frequency-response function of the numerical filter is given. Input and output spectra for a filter applied to a case with negligible noise and a noise level of 1.5 percent of the total power in the input spectrum are analyzed, and the numerical weights for these two cases are calculated. Phase angle and gain for the entire system are examined. It is noted that the filter can enhance spectral components as high as 8 Hz with little phase and gain degradation over the bandwidth.
Small blade-to-blade property differences are investigated to determine their effects on the behavior of a simple rotor-body system. An analytical approach is used which emphasizes the significance of these effects from the experimental point of view. It is found that the primary effect of blade-to-blade dissimilarities is the appearance of additional peaks in the frequency spectrum which are separated from the conventional response modes by multiples of the rotor speed. These additional responses are potential experimental problems because when they occur near a mode of interest they act as contaminant frequencies which can make damping measurements difficult. The effects of increased rotor-body coupling and a rotor shaft degree of freedom act to improve the situation by altering the frequency separation of the modes.
In view of the recent publication of Eviatar and Richardson (1986), who have calculated the Pedersen conductance of Saturn's ionosphere to be much smaller than previous estimates, the Pedersen conductance is recalculated using the same neutral atmosphere model as these authors. The results confirm the earlier estimates that the ionospheric Pedersen conductance of Saturn's ionosphere ranges from 0.3 to 17 mho near the terminator as a function of latitude. The source of discrepancy appears to be the inclusion by Eviatar and Richardson of ion density into the ion-neutral collision frequency term, which is incorrect. Contrary to the conclusion of Eviatar and Richardson, Saturn's ionospheric Pedersen conductance is high enough to impose nearly perfect corotation between the ionosphere and the magnetosphere.
Examples are presented of applications of a fast Fourier transform algorithm to analyze time series of images of Normalized Difference Vegetation Index values. The results obtained for a case study on Zambia indicated that differences in vegetation development among map units of an existing agroclimatic map were not significant, while reliable differences were observed among the map units obtained using the Fourier analysis.
The problem of the distribution of normal stress across a wide corrugated sheet used as the chord of a box-beam-like structure is investigated theoretically and experimentally. Expressions are developed giving the stress distribution in beams, symmetrical or unsymmetrical, about a plane passed spanwise through the center of the sheet. The experiments were arranged to insure bending without torsion and surveys of the normal stresses were made by means of mechanical and electrical strain gages. The experimental data showed very good agreement with the new b of the theoretical curves, especially at the highly stressed sections, for both the symmetrical and unsymmetrical beams. Several suggestions for future research are included.
Theoretical and experimental investigations were made of the distribution of strains in a plywood sheet-stringer combination used as the chord member of a box beam acted upon by bending loads. The theoretical solution was obtained with the help of the principle of minimum potential energy and certain simplifying assumptions. Strain measurements were made on a build-up box beam by means of electrical-resistance strain gages connected with strain indicators. A very satisfactory agreement between the theoretical and experimental strains was obtained.
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