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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1967

Self-starting procedure simplifies numerical integration

A self-starting, multistep procedure for the numerical integration of ordinary differential equations is devised to produce all the required backward differences directly from the initial equations. The self-starting element eliminates nonessential tallying to determine starting values.

Source record↗
NASA NTRS1975

Special Perturbations Using Back-Correction Methods of Numerical Integration

A new class of linear multistep methods for numerical integration of differential equations is reported that permits satellite computation solutions to be corrected at certain points in the past as the integration advances in time. Algorithms have been developed for the solution of both first- and second-order differential equations. The back correction method appears to be more efficient than classical methods when dominant and perturbing forces can be separated.

Feagin, T.↗
NASA NTRS1976

Orientation of the earth by numerical integration

A fundamental problem is the determination of the orientation of the earth in the celestial coordinate system. Classical reductions for precession and nutation can be expected to be consistent with the present-day observations, however, corrections to the classical theory are difficult to model because of the large number of coefficients involved. Consequently, a portion of the research has been devoted to numerically integrating the Eulerian equations of motion for a rigid earth and considering the six initial conditions of the integration as unknowns. Comparison of the three adjusted Eulerian angles from the numerical integration over 1000 days indicates agreement with classical theory to within 0.003 seconds of arc.

Fajemirokun, F. A.↗
NASA NTRS1981

Numerical integration of the satellites of the outer planets

The formulation of a numerical integration program, used to construct ephemerides for satellites of the outer planets, is described. The equations of motion are derived, including (1) n massive integrated satellites, (2) m massive perturbing planets, (3) J2, J4 oblateness coefficients of the primary and each satellite, and (4) a barycentric coordinate system. Variational equations are also found: (1) 6n initial states and n masses of the integrated satellites, (2) J2, J4 of the primary planet, (3) the mass of the system, and (4) right ascension and declination of the pole. The formulation was used to construct the satellite ephemerides of Saturn for the Voyager mission.

Peters, C. F.↗
NASA NTRS1971

The application of generalized, cyclic, and modified numerical integration algorithms to problems of satellite orbit computation

Generalized, cyclic, and modified multistep numerical integration methods are developed and evaluated for application to problems of satellite orbit computation. Generalized methods are compared with the presently utilized Cowell methods; new cyclic methods are developed for special second-order differential equations; and several modified methods are developed and applied to orbit computation problems. Special computer programs were written to generate coefficients for these methods, and subroutines were written which allow use of these methods with NASA's GEOSTAR computer program.

Chesler, L.↗
NASA NTRS1973

Orientation of the moon by numerical integration

The differential equations of rotational motion of the moon are solved by numerical integration methods. Euler's dynamical equations transformed to a convenient form are treated by techniques analogous to ordinary orbit determination procedures. The proposed method is fully consistent with the ephemeris of the moon and can utilize a variety of observational material for the solution of the selected parameters. Examples are given of comparison between the proposed method and Eckhardt's 1970 model of the physical librations of the moon. The merits of the new method are discussed in the light of conventional data sources like earth-based or satellite-based photography as well as newly available data types like laser ranging to retroreflectors on the moon.

Papo, H. B.↗
NASA NTRS1990

An efficient numerical integral in three-dimensional electromagnetic field computations

An improved algorithm for efficiently computing a sinusoid and an exponential integral commonly encountered in method-of-moments solutions is presented. The new algorithm has been tested for accuracy and computer execution time against both numerical integration and other existing numerical algorithms, and has outperformed them. Typical execution time comparisons on several computers are given.

Whetten, Frank L.↗
NASA NTRS1993

Numerically Integrated Orbits of the Major Saturnian Satellites fit to Earthbased Observations

We have fit numerically integrated orbits of the eight major satellites of Saturn to all available astrometric and meridian circle observations for the period of 1971 to 1992. The integration was carried out in cartesian coordinates in the J2000 system. The force model included the gravitational effects of the oblate primary, the mutual perturbations of the satellites, and perturbations due to Jupiter and the Sun. Values of the gravitational parameters of the Saturnian system, e.g. planet and satellite masses, were taken from Campbell, et. al., 1989, only the epoch state vectors of the satellites were adjusted to obtain orbits which fit the observations. All astrometric data was processed in the form of satellite relative positions which were weighted according to observer and opposition to reflect the varying data quality...

Jacobson, R. A.↗