First-occurrence time of high-level crossings in a continuous random process
Statistical probability distribution of first occurrence and first recurrence times of given level crossing in continuous random process
STATISTICAL PROBABILITY↗
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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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A recursive formulation for computing the coefficients of the time-dependent f and g series solution to the two-body problem.
Recursive generation of expansion coefficients of time-dependent f and g series in two-body problem, using algebraic recurrence formulas
SERIES EXPANSION↗
First-occurrence time of high-level crossings in a continuous random process.
Statistical distribution of first occurrence and recurrence of crossing of given level in continuous random process determined, using approximate forms and exponential distribution
RANDOM PROCESS↗
Liapunov criteria for weak stochastic stability.
Sufficient conditions for recurrence and positivity of diffusion process defined by stochastic differential equation, using Liapunov function
DIFFERENTIAL EQUATION↗
Combinatorial communications - Enumeration of a special class of permutations
Enumeration of special class class of permutations - generating function expression and asymtotic expansion for recurrence relation - combinatorial communications
COMMUNICATION SYSTEM↗
Research in stability of periodic motions Quarterly progress report, 5 Aug. - 4 Nov. 1966
Stability of periodic and equilibrium solutions of restricted three-body problems - measure preserving mappings, normal form of Hamiltonian, and Poincare recurrence theorem
HAMILTONIAN↗
Theoretical Study of Natural Convection Flows in Closed-End Cylindrical Vessels Final Report
This study is concerned with the analytical solutions of natural convection flows in closed-end cylindrical vessels to obtain exact solutions of temperature and velocity distribution in the laminar flow region under steady state condition. The temperature and velocity distributions, in general power series of displacements, are substituted into the three basic equations of continuity, momentum and energy. The relationships between coefficients of all powers are obtained through initial and boundary conditions and recurrence formulae. For constant wall temperature conditions the general solution of temperature and velocity may be expressed as a function of displacement, geometry ratio and Rayleigh number. Prandtl number does not enter as an independent parameter.
Convective flow↗
Energetic particles from the sun.
Solar cosmic rays, discussing flare association, solar particle acceleration, recurrence and low energy solar particle events
Fichtel, C. E.↗
Interplanetary sector structure, 1962-1966.
Interplanetary magnetic field sector structure, noting Archimedes spiral directivity and 27 day recurrence period for pattern
Ness, N. F.↗
A second-order variational method for discrete-time optimal control problems.
Discrete time optimal control problems solved by second order variational algorithm, developing recurrence relations for perturbation equations
Koivo, A. J.↗
Interplanetary sector structure in the rising portion of the sunspot cycle.
Interplanetary sector structure during rising portion of 1966-1967 sunspot cycle, giving recurrence period of interplanetary field
Colburn, D. S.↗
An algorithm for computing spherical partials
Algorithm for computing acceleration and partial derivatives in satellite equations of motion, using recurrences in spherical coordinates
Borchers, R. V.↗
An algorithm for integrating stepwise the restricted problem in Thiele's coordinates
Planar restricted three body problem in Thiele coordinates, developing recurrence formulas for coefficients in Taylor series expansions of solution
Estes, R. H.↗
Satellite observations of solar cosmic rays
Solar cosmic rays satellite observation, considering flare associated, recurrent and storm particle events and active center associated energetic particles
Mcdonald, F. B.↗
Perturbation method in the theory of nonlinear oscillations
Perturbation method in nonlinear oscillations theory, using asymptotic recurrence formulas based on Lie transform
Kamel, A. A.↗
The OGO attitude control subsystem redesign as a result of OGO 3 experience. Volume 1: System analysis and design studies
An oscillation in the OGO-3 roll control channel, resulting from the EP-5 and EP-6 boom motion coupling into the control channel and causing loss of attitude control, is investigated. The study includes (1) an analysis of the OGO-3 and OGO-2 flight data to determine the nature and extent of the roll oscillation phenomena, (2) design analysis of the complete attitude control subsystem (ACS) to evolve changes which would prevent recurrences of the coupled ACS boom oscillation observed on OGO-3, and (3) analog simulations to verify the performance of the design changes selected. Portions of OGO-3 and OGO-2 flight data are illustrated and the major flexible body oscillation are identified. A model of the major flexible appendage dynamics is developed and is shown analytically and through analog simulations to reproduce the OGO-3 oscillation phenomena. The design changes which were found necessary are: a reversal delay logic for the roll reaction wheels, widening of the solar array dead zone from 0.5 to 1.0 deg, and modification of the OPEP control loop to include a filter and stabilizing feedback loops.
Mckenna, K. J.↗
Energetic ion bursts on the nightside of the moon.
Recurrent bursts of positive ions are a persistent feature of the data from the Apollo 12 and Apollo 14 Alsep suprathermal ion detectors. Most remarkable is the occasional occurrence of these events when the Alsep is deep in the lunar night. One such series of bursts seen during December 1969 starting approximately 4.7 days before sunrise at the Apollo 12 Alsep site is reported. These bursts have durations ranging up to 14 min and recur with a highly variable frequency. The ions have differential energy spectra with narrow peaks. The peak energies range from 10 to 1250 eV but are found most frequently in the vicinity of 250 to 500 eV. They can be seen when the field of view of the detector looks as close as 16 deg to the antisolar direction. Data from the ion-mass analyzer indicate that, unlike some similar events seen on other occasions, these ions have mass per unit charge less than 10 amu/q, and hence, are probably of solar-wind origin.
Freeman, J. W., Jr.↗
Power series representation of partial derivatives required in orbit determination.
A program to integrate the equations of motion by series in powers of the time step can be easily modified to furnish the elements of the matrizant in power series of the time step. In particular, if the series representing the motion are obtained recursively, differentiation of the recurrence relations will provide immediately a recursive scheme for computing the coefficient in the power series for the elements of the matrizant.
Schanzle, A. F.↗