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Results for “rectangular coordinates”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Time elements in rectangular coordinates

In a paper by the second author (Nacozy, 1981), various time elements are presented for use with the Sundman time transformation. In that paper, the time elements are given in terms of Keplerian orbital elements. We give here the corresponding time elements in terms of rectangular coordinates. Extensive references are given in the previous paper and will be omitted here. We present additional numerical experiments comparing the use of time elements and time transformations together with the use of time transformations alone. The results indicate a reduction in computational error when time elements are used.

Kwok, J. H.↗
NASA NTRS1986

Supersonic flow computations using a rectangular-coordinate finite-volume method

A numerical procedure has been developed for the computation of supersonic flows over complex conical geometries. The full potential equation is solved using a finite-volume method with a non-body-fitted rectangular grid. The only mapping done is the transformation of the spherical cross-flow plane to a flat surface using a stereographic projection. A new procedure for very thin fins is described which does not require the resolution of the fin thickness. Applications for simple cones, conical wing-bodies, wave riders and finned geometries compare favorably with existing solutions with body-fitted grids and available experimental data.

Grossman, B.↗
NASA NTRS1975

Accurate integration of geostationary orbits with Burdet's focal elements

The theory of Burdet's focal elements (1969) is outlined. The differential equations are presented, and the initial value problem is described together with the transformation to rectangular coordinates and classical elements. The focal elements are well defined for zero eccentricity and inclination and can be adopted for the computation of elliptic, parabolic, and hyperbolic motion. For the numerical integration of near-geostationary orbits, a comparison of the efficiency is made between focal elements, Kustaanheimo-Stiefel (1971) theory, and rectangular coordinates. For this class of orbits, a higher accuracy has been obtained by integrating elements than integrating rectangular coordinates.

Flury, W.↗
NASA NTRS1974

Computation of solar perturbations with Poisson series

Description of a project for computing first-order perturbations of natural or artificial satellites by integrating the equations of motion on a computer with automatic Poisson series expansions. A basic feature of the method of solution is that the classical variation-of-parameters formulation is used rather than rectangular coordinates. However, the variation-of-parameters formulation uses the three rectangular components of the disturbing force rather than the classical disturbing function, so that there is no problem in expanding the disturbing function in series. Another characteristic of the variation-of-parameters formulation employed is that six rather unusual variables are used in order to avoid singularities at the zero eccentricity and zero (or 90 deg) inclination. The integration process starts by assuming that all the orbit elements present on the right-hand sides of the equations of motion are constants. These right-hand sides are then simple Poisson series which can be obtained with the use of the Bessel expansions of the two-body problem in conjunction with certain interation methods. These Poisson series can then be integrated term by term, and a first-order solution is obtained.

Broucke, R.↗
NASA NTRS1981

Transformation formulas relating geodetic coordinates to a tangent to Earth, plane coordinate system

Formulas and their approximation were developed to map geodetic position to an Earth tangent plane with an airport centered rectangular coordinate system. The transformations were developed for use in a terminal area air traffic model with deterministic aircraft traffic. The exact configured vehicle's approximation equations used in their precision microwave landing system navigation experiments.

Credeur, L.↗