A method for computation of meteoroid impact distribution over spacecraft
Computer program using numerical integration techniques for computation of meteoroid impact and angular distributions over complex geometric spacecraft configurations
Fu, T.↗
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Results for “numerical integration”
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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Design and implementation of models for the double precision trajectory program /DPTRAJ/
Development and numerical integration of differential equations of spacecraft motion used in Double Precision Trajectory Program
Spier, G. W.↗
Virtual mass technique for computing N-body solutions
Virtual mass technique for numerically integrating n-body solution like spacecraft trajectories
Novak, D. H.↗
A preliminary special perturbation theory for the lunar motion
Lunar ephemeris for nanosecond resolution laser ranging systems by literal and numerical integration techniques
Garthwaite, K.↗
Coordinate system influence on the regularized trajectory optimization problem
Numerical integration for continuously thrusting spacecraft optimal trajectory, considering rectangular Cartesian and polar cylindrical coordinates characteristics
Lewallen, J. M.↗
Generalized relaxation methods applied to problems in transonic flow
Generalized relaxation methods application to transonic flow problems, combining with numerical integration theory for ordinary differential equations
Lomax, H.↗
Error bounds for compound quadrature of weakly singular integrals
Weakly singular integrals numerical compound quadrature error bound and convergence rate estimate by applying Peano theorem with modification for avoiding singularity
Feldstein, A.↗
Spontaneous ionization of a hydrogen atom in an electric field. I
Numerical integration of Schroedinger equation for spontaneous ionization of hydrogen atom in electric field
Curtiss, L. A.↗
Glauber amplitudes in charged particle hydrogen atom collisions
Glauber scattering amplitudes for atomic hydrogen excitation by electrons or protons, presenting closed form expressions requiring no numerical integration
Gerjuoy, E.↗
An analytic model of eclipsing binary star systems
Analytical model of eclipsing binary star systems, testing validity through numerical integration error analysis
Wood, D. B.↗
Errors in hybrid computers
Method is described for reduction of error components in numerical integration, sampling with zero hold order, and execution time delay.
Alford, C. O.↗
Computational investigations of low-discrepancy point sets
The quasi-Monte Carlo method of integration offers an attractive solution to the problem of evaluating integrals in a large number of dimensions; however, the associated error bounds are difficult to obtain theoretically. Since these bounds are associated with the L2 discrepancy of the set of points used in the integration. Numerical calculations of the L2 discrepancy for several types of quasi-Monte Carlo formulae are presented.
Warnock, T. T.↗
A study of the Nordsieck-type predictor-corrector methods
Predictor-corrector schemes are discussed for the numerical integration of initial value problems by computer. Descloux formulas, which are considered modified Nordsieck formulas are studied because of their desirable stability and truncation properties along with the standard Nordsieck formulas. The stability of Nordsieck and modified Nordsieck algorithms are computed, and the results are graphed. Test problems are included as examples for comparing the efficiency of the algorithms.
Eiserike, H. M.↗
The lunar laser ranging experiment
With data from two or more well-located observing stations, the lunar range can be corrected accurately for the effects of polar motion and fluctuations in the earth's rotation rate. Very accurate corrections can be made for the earth tides at each station. It appears that the use of lasers giving roughly 0.1-msec pulse lengths is highly desirable. With them, single-shot ranging accuracies of about 3 cm are expected. The actual lunar range results will be analyzed by fitting a numerical integration for the lunar motion to the data. A mathematical model for lunar range is given. Tests of the theory of gravitation are considered.
Bender, P. L.↗
On Lashinsky's equation y'' plus alpha y' minus ay plus by cubed equals o
A differential equation proposed by H. Lashinsky to describe the nonlinear solution of aperiodic instabilities is investigated. Oscillatory and nonoscillatory solutions are discussed and a numerical integration is presented.
Cap, F. F.↗
Evaluation of massless-spring modeling of suspension-line elasticity during the parachute unfurling process
A general theory on mathematical modeling of elastic parachute suspension lines during the unfurling process was developed. Massless-spring modeling of suspension-line elasticity was evaluated in detail. For this simple model, equations which govern the motion were developed and numerically integrated. The results were compared with flight test data. In most regions, agreement was satisfactory. However, poor agreement was obtained during periods of rapid fluctuations in line tension.
Poole, L. R.↗
Apollo experience report: Onboard navigational and alignment software
The onboard navigational and alignment routines used during the nonthrusting phases of an Apollo mission are discussed as to their limitations, and alternate approaches that have more desirable capabilities are presented. A more efficient procedure for solving Kepler's equation, which is used in the calculation of Kepler's problem and Lambert's problem is included, and a sixth-order predictor scheme with a Runge-Kutta starter is recommended for numerical integration. The extension of the rendezvous navigation state to include angle biases and the use of a fixed coordinate system is also evaluated.
Savely, R. T.↗
Generation of the invariant coefficients of the characteristic polynomial for an nxn matrix
In theories of numerical stability, roots to a characteristic polynomial are sought, which, in the case of the predictor with iterative correction method of numerical integration, are eigenvalues of a matrix whose elements depend on the coefficients used in the integration process. The characteristic polynomial is displayed explicitly in terms of the elements of the characteristic matrix.
Beaudet, P. R.↗