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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Ephemeris of a highly eccentric orbit - Explorer 28.

An ephemeris has been obtained for Explorer 28 (IMP 3) which agrees well with 2 years of radio observations and with SAO observations a year later. This ephemeris is generated over the 3 year lifetime by a numerical integration method utilizing a set of initial conditions at launch and without requiring further differential correction. Because highly eccentric orbits are difficult to compute with acceptable accuracy and because a long continuous arc has been obtained which compares with actual data to a known precision, this ephemeris may be used as a standard for computing highly eccentric orbits in the earth-moon system. Orbit improvement was used to obtain the initial conditions which generated the ephemeris. This improvement was based on correcting the energy by adjusting the semimajor axis to match computed times of perigee passage with the observed. This procedure may generate errors in semimajor axis to compensate for model errors in the energy; however, this compensation error is also implicit in orbit determination itself.

Lowrey, B. E.↗
NASA NTRS1972

The optimal control of merging aircraft - Implementation of the hybrid air traffic controller.

The control of merging aircraft is formulated as a finite-time, quadratic optimal control problem of a linear system with state and control constraints. The purpose of this paper is to demonstrate that the Hybrid Air Traffic Controller (HAC), which has been previously developed as a solution to this problem, may be easily implemented. Use is made of both the properties of the algebraic solution to the matrix Riccati equation and the structure of the linear model. This approach results in a real-time synthesis procedure for the HAC which does not rely on iterative numerical integration techniques.

Schatz, J. G.↗
NASA NTRS1972

Simplified analysis and optimization of space base and space shuttle heat rejection systems

A simplified radiator system analysis was performed to predict steady state radiator system performance. The system performance was found to be describable in terms of five non-dimensional system parameters. The governing differential equations are integrated numerically to yield the enthalpy rejection for the coolant fluid. The simplified analysis was extended to produce the derivatives of the coolant exit temperature with respect to the governing system parameters. A procedure was developed to find the optimum set of system parameters which yields the lowest possible coolant exit temperature for either a given projected area or a given total mass. The process can be inverted to yield either the minimum area or the minimum mass, together with the optimum geometry, for a specified heat rejection rate.

Wulff, W.↗
NASA NTRS1973

A new method to compute lunisolar perturbations in satellite motions

A new method to compute lunisolar perturbations in satellite motion is proposed. The disturbing function is expressed by the orbital elements of the satellite and the geocentric polar coordinates of the moon and the sun. The secular and long periodic perturbations are derived by numerical integrations, and the short periodic perturbations are derived analytically. The perturbations due to the tides can be included in the same way. In the Appendix, the motion of the orbital plane for a synchronous satellite is discussed; it is concluded that the inclination cannot stay below 7 deg.

Kozai, Y.↗
NASA NTRS1973

Computer simulation of space station computer steered high gain antenna

The mathematical modeling and programming of a complete simulation program for a space station computer-steered high gain antenna are described. The program provides for reading input data cards, numerically integrating up to 50 first order differential equations, and monitoring up to 48 variables on printed output and on plots. The program system consists of a high gain antenna, an antenna gimbal control system, an on board computer, and the environment in which all are to operate.

Beach, S. W.↗
NASA NTRS1973

Quarantine constraints as applied to satellites

Plans for unmanned missions to planets beyond Mars in the 1970s include satellite encounters. Recently published observations of data for Titan, a satellite of Saturn, indicate that conditions may be hospitable for the growth of microorganisms. Therefore, the problem of satisfying possible quarantine constraints for outer planet satellites was investigated. This involved determining the probability of impacting a satellite of Jupiter or Saturn by a spacecraft for a planned satellite encounter during an outer planet mission. Mathematical procedures were formulated which determine the areas in the aim-plane that would result in trajectories that impact the satellite and provide a technique for numerically integrating the navigation error function over the impact area to obtain impact probabilities. The results indicate which of the planned spacecraft trajectory correction maneuvers are most critical in terms of satellite quarantine violation.

Hoffman, A. R.↗
NASA NTRS1973

An improved method for the aerodynamic analysis of wing-body-tail configurations in subsonic and supersonic flow. Part 1: Theory and application

A new method has been developed for calculating the pressure distribution and aerodynamic characteristics of wing-body-tail combinations in subsonic and supersonic potential flow. A computer program has been developed to perform the numerical calculations. The configuration surface is subdivided into a large number of panels, each of which contains an aerodynamic singularity distribution. A constant source distribution is used on the body panels, and a vortex distribution having a linear variation in the streamwise direction is used on the wing and tail panels. The normal components of velocity induced at specified control points by each singularity distribution are calculated and make up the coefficients of a system of linear equations relating the strengths of the singularities to the magnitude of the normal velocities. The singularity strengths which satisfy the boundary condition of tangential flow at the control points for a given Mach number and angle of attack are determined by solving this system of equations using an interactive procedure. Once the singularity strengths are known, the pressure coefficients are calculated, and the forces and moments acting on the configuration determined by numerical integration.

Woodward, F. A.↗
NASA NTRS1973

Tables for Supersonic Flow of Helium Around Right Circular Cones at Zero Angle of Attack

The results of the calculation of supersonic flow of helium about right circular cones at zero angle of attack are presented in tabular form. The calculations were performed using the Taylor-Maccoll theory. Numerical integrations were performed using a Runge-Kutta method for second-order differential equations. Results were obtained for cone angles from 2.5 to 30 degrees in regular increments of 2.5 degrees. In all calculations the desired free-stream Mach number was obtained to five or more significant figures.

Sims, J. L.↗
NASA NTRS1973

Analysis of free turbulent shear flows by numerical methods

Studies are described in which the effort was essentially directed to classes of problems where the phenomenologically interpreted effective transport coefficients could be absorbed by, and subsequently extracted from (by comparison with experimental data), appropriate coordinate transformations. The transformed system of differential equations could then be solved without further specifications or assumptions by numerical integration procedures. An attempt was made to delineate different regimes for which specific eddy viscosity models could be formulated. In particular, this would account for the carryover of turbulence from attached boundary layers, the transitory adjustment, and the asymptotic behavior of initially disturbed mixing regions. Such models were subsequently used in seeking solutions for the prescribed two-dimensional test cases, yielding a better insight into overall aspects of the exchange mechanisms.

Korst, H. H.↗
NASA NTRS1973

The numerical solution of ordinary differential equations by the Taylor series method

A programming implementation of the Taylor series method is presented for solving ordinary differential equations. The compiler is written in PL/1, and the target language is FORTRAN IV. The reduction of a differential system to rational form is described along with the procedures required for automatic numerical integration. The Taylor method is compared with two other methods for a number of differential equations. Algorithms using the Taylor method to find the zeroes of a given differential equation and to evaluate partial derivatives are presented. An annotated listing of the PL/1 program which performs the reduction and code generation is given. Listings of the FORTRAN routines used by the Taylor series method are included along with a compilation of all the recurrence formulas used to generate the Taylor coefficients for non-rational functions.

Silver, A. H.↗
NASA NTRS1973

Resonances and librations of some Apollo and Amor asteroids with the Earth.

The orbital evolution of the Apollo asteroids 1620 Geographos and 1685 Toro and Amor asteroids 433 Eros, 1221 Amor, and 1627 Ivar are investigated by numerical integration. All these asteroids, with the exception of Geographos, exhibit systematic orbital couplings with the Earth during the time interval studied (1600-2350 A.D.). 1685 Toro is captured into libration once with Venus due to the 13.5 resonance, and once with the Earth due to the 8:5 resonance. Both librations are unstable because of the effect of the 13:8 near commensurability of the Venus-Earth system. 433 Eros exhibits no libration pattern; the regular variation of its orbital period is due to the beat-effect of the 4:7 resonance with the Earth.

Ip, W.-H.↗
NASA NTRS1971

Numerical analysis of shells of revolution.

Summary of some of the major computer programs in existence for the analysis of shells of revolution based on numerical integration and finite-difference procedures. Selected results obtained with several of these programs are presented. A number of significant points is made on the basis of these results.

Fulton, R. E.↗
NASA NTRS1972

Static geometric and material nonlinear analysis.

This paper presents a survey of four aspects of nonlinear analysis - basic formulation, plasticity relations, computational procedures, and methods of solution. This survey is for the most part limited to static geometric and material nonlinear analysis under the assumption of small strains. The two formulations covered are the total Lagrangian and the incremental moving coordinate formulations. A comparison of the two formulations is presented and an attempt is made to clarify the underlying basis of each formulation. The survey of computational procedures reveals that most researchers are now using some form of numerical integration to evaluate nonlinear contributions.

Stricklin, J. A.↗
NASA NTRS1973

An adaptive precision gradient method for optimal control.

This paper presents a gradient algorithm for unconstrained optimal control problems. The algorithm is stated in terms of numerical integration formulas, the precision of which is controlled adaptively by a test that ensures convergence. Empirical results show that this algorithm is considerably faster than its fixed precision counterpart.-

Klessig, R.↗
NASA NTRS1972

Comments on lunar origin.

Consideration of the tidal evolution of the earth-moon system in the light of recent published studies of lunar origin. The subjects include the factors of orbital evolution, the auxiliary Model Zero, orbital evolution along the outgoing branch, capture models, capture probability, capture with break-up, the tidal evolution of circular and elliptical fragmented rings, and precession and collisions in a ring of fragments. A numerical integration of precessions is performed for the actual nonzero mass of the moon and for a lunar distance of about 22 earth radii. A simplified Model Zero is found to compare well with Goldreich's solution (1968). It is concluded that the moon must have become freely yielding to tidal deformation at distances less than about 8 earth radii. Arguments are given in favor of the capture theory as a basis for the genesis of the moon.

Opik, E. J.↗
NASA NTRS1973

Laminar film condensation on the inside of slender, rotating truncated cones.

A solution for film condensation on the inside of slender rotating truncated cones is established in the region where the half cone angle phi is close to zero and where the equation of Dhir and Lienhard (1971) is no longer valid. All the familiar assumptions used in Nusselt's theory of laminar film condensation are assumed valid, including negligible sub-cooling and momentum changes in the condensate film, no interfacial shear between the condensate and the vapor, and pure conduction within the condensate film. A Runge-Kutta numerical integration method using a digital computer was used. Results for a specific geometry are given for water condensing at 212 F on a condenser wall maintained at 70 F.

Marto, P. J.↗
NASA NTRS1973

Computational considerations in application of the finite element method for analysis of unsteady flow around airfoils.

Difficulties related to the application of the finite element method for numerical solution of the Navier-Stokes equation are discussed. The unsteady flow around a stationary and oscillating NACA 0012 airfoil was analyzed. In an effort to establish the range of applicability of the developed numerical method, the accuracy and stability problems in representing unsteady flow patterns and determining pressure distribution around the airfoil were investigated. Error involved in determining the velocity field and in the numerical integration of the discretized equations were analyzed in terms of geometry of the finite element gridwork, boundary conditions for stationary and oscillating airfoils, angles of attack and flow conditions.

Bratanow, T.↗