SEARCH · Engineering Papers
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Numerical integration for continuously thrusting spacecraft optimal trajectory, considering rectangular Cartesian and polar cylindrical coordinates characteristics
Generalized relaxation methods application to transonic flow problems, combining with numerical integration theory for ordinary differential equations
Weakly singular integrals numerical compound quadrature error bound and convergence rate estimate by applying Peano theorem with modification for avoiding singularity
Numerical integration of Schroedinger equation for spontaneous ionization of hydrogen atom in electric field
Glauber scattering amplitudes for atomic hydrogen excitation by electrons or protons, presenting closed form expressions requiring no numerical integration
Analytical model of eclipsing binary star systems, testing validity through numerical integration error analysis
Method is described for reduction of error components in numerical integration, sampling with zero hold order, and execution time delay.
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.
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.
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.
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.
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.
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.
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.
The accuracy of five mathematical models in computing a nominal orbit for the Vanguard 2 satellite by using a position velocity vector is considered. Either numerical integration or analytical theories are used in all models as well as the same force model that corresponds to a potential with the zonal harmonics to order four. The amounts of spread in the values of the total energy and the z-component of the angular momentum for a set of times are considered as measures of accuracy.
A computer program is described which performs a numerical integration of the equations of motion for a compressible two-dimensional boundary layer. Boundary layer calculations may be carried out for both laminar and turbulent flow for arbitrary Reynolds number and free stream Mach number distribution on planar or axisymmetric bodies with wall heating or cooling, longitudinal wall curvature, wall suction or blowing, and a rough or a smooth wall. A variety of options are available as initial conditions. The program can generate laminar initial conditions such as Falkner-Skan similarity solutions (so that initial wedge flows can be simulated including Blasius or stagnation point flow) or approximate equilibrium turbulent profiles. Alternatively, initial profile input data can be utilized.
A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.
The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.