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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 NTRS1976

The development of the Poincare-similar elements with eccentric anomaly as the independent variable

A new set of element differential equations for the perturbed two-body motion is derived. The elements are canonical and are similar to the classical canonical Poincare elements, which have time as the independent variable. The phase space is extended by introducing the total energy and time as canonically conjugated variables. The new independent variable is, to within an additive constant, the eccentric anomaly. These elements are compared to the Kustaanheimo-Stiefel (KS) element differential equations, which also have the eccentric anomaly as the independent variable. For several numerical examples, the accuracy and stability of the new set are equal to those of the KS solution. This comparable accuracy result can probably be attributed to the fact that both sets have the same time element and very similar energy elements. The new set has only 8 elements, compared to 10 elements for the KS set. Both sets are free from singularities due to vanishing eccentricity and inclination.

Bond, V. R.↗
NASA NTRS1977

Assessment of Relative Velocity as Independent Variable for Space Shuttle First Stage Guidance Attitude Command Tables

The selection of relative velocity as the independent variable for the space shuttle first stage guidance attitude command tables was assessed to support the first stage guidance point design. The criterion for selecting the independent variable for first stage open loop guidance is to reduce or minimize performance dispersions, primarily those affecting structural loads. The products of angle of attack and angle of sideslip times dynamic pressure are used as load indicators, and minimizing their dispersions will indicate a minimum loads dispersion. Relative velocity is shown to be an acceptable steering independent variable.

Kimbrough, M.↗
NASA NTRS1971

A note on independent variables for restricted three-body problems.

In studies of the elliptic restricted three-body problem, the true anomaly of the motion of the primaries is often used as the independent variable. The equations of motion then show invariancy in form from the circular case. It is of interest whether other independent variables exist, such that the invariant form of the equations is maintained. It is found that true anomaly is the only such variable.

Heppenheimer, T. A.↗
NASA NTRS2011

Iterative Strain-Gage Balance Calibration Data Analysis for Extended Independent Variable Sets

A new method was developed that makes it possible to use an extended set of independent calibration variables for an iterative analysis of wind tunnel strain gage balance calibration data. The new method permits the application of the iterative analysis method whenever the total number of balance loads and other independent calibration variables is greater than the total number of measured strain gage outputs. Iteration equations used by the iterative analysis method have the limitation that the number of independent and dependent variables must match. The new method circumvents this limitation. It simply adds a missing dependent variable to the original data set by using an additional independent variable also as an additional dependent variable. Then, the desired solution of the regression analysis problem can be obtained that fits each gage output as a function of both the original and additional independent calibration variables. The final regression coefficients can be converted to data reduction matrix coefficients because the missing dependent variables were added to the data set without changing the regression analysis result for each gage output. Therefore, the new method still supports the application of the two load iteration equation choices that the iterative method traditionally uses for the prediction of balance loads during a wind tunnel test. An example is discussed in the paper that illustrates the application of the new method to a realistic simulation of temperature dependent calibration data set of a six component balance.

Ulbrich, Norbert Manfred↗
NASA NTRS1976

The development of the Poincare-similar elements with true anomaly as the independent variable

In reference 1, the Hamiltonian of the unperturbed two-body problem in extended phase space is established. Depending on the type of time transformation, eight canonical elements were developed with the true anomaly or the eccentric anomaly as the independent variable. These two new sets, DS(phi) and DS(u), however contain singularities for small eccentricities and inclinations. In reference 2, these singularities are removed by a transformation from DS(u) to eight canonical PS(u) elements. In reference 3, the DS(phi) variables are transformed to the PS(phi) elements to remove the singularities. However, no direct relation was established between the eight canonical PS(phi) elements and the Cartesian coordinates. It is the purpose of this report to establish those relations and to develop the perturbed equations of motion in the PS(phi) space. This report also demonstrates the accuracy of this new set when it is applied to numerical orbit prediction problems.

Mueller, A.↗
NASA NTRS1985

FIT: Computer Program that Interactively Determines Polynomial Equations for Data which are a Function of Two Independent Variables

A computer program for interactively developing least-squares polynomial equations to fit user-supplied data is described. The program is characterized by the ability to compute the polynomial equations of a surface fit through data that are a function of two independent variables. The program utilizes the Langley Research Center graphics packages to display polynomial equation curves and data points, facilitating a qualitative evaluation of the effectiveness of the fit. An explanation of the fundamental principles and features of the program, as well as sample input and corresponding output, are included.

Arbuckle, P. D.↗
NASA NTRS1992

Dark focus of accommodation as dependent and independent variables in visual display technology

When independent stimuli are available for accommodation, as in the dark or under low contrast conditions, the lens seeks its resting position. Individual differences in resting positions are reliable, under autonomic control, and can change with visual task demands. We hypothesized that motion sickness in a flight simulator might result in dark focus changes. Method: Subjects received training flights in three different Navy flight simulators. Two were helicopter simulators entailed CRT presentation using infinity optics, one involved a dome presentation of a computer graphic visual projection system. Results: In all three experiments there were significant differences between dark focus activity before and after simulator exposure when comparisons were made between sick and not-sick pilot subjects. In two of these experiments, the average shift in dark focus for the sick subjects was toward increased myopia when each subject was compared to his own baseline. In the third experiment, the group showed an average shift outward of small amount and the subjects who were sick showed significantly less outward movement than those who were symptom free. Conclusions: Although the relationship is not a simple one, dark focus changes in simulator sickness imply parasympathetic activity. Because changes can occur in relation to endogenous and exogenous events, such measurement may have useful applications as dependent measures in studies of visually coupled systems, virtual reality systems, and space adaptation syndrome.

Jones, Sherrie↗