Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “POWER SERIES”

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.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

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.↗
NASA NTRS1976

Phase modulating with odd and even finite power series of a modulating signal

Method and apparatus is presented for producing a phase-modulated waveform having a high degree of linearity between the modulating signal and the phase of the modulated carrier signal. Two signals representing finite odd and even power series transformations of the modulating signal are produced and multiplied with two quadrature components of the input carrier signal, respectively. One of the multiplied signals is subtracted from the other and the resulting signal is hard-limited to produce a phase-modulated output signal. The means for producing the two signals representing the odd and even power series of the modulating signal includes means for varying the coefficients of the two power series. By means of an existing computer program, the coefficients of the two power series are selected such that there is an extremely high degree of linearity between the modulating signal and the phase of the modulated carrier signal.

Hearn, C. P.↗
NASA NTRS1945

Method of expanding noise autocorrelation function in a power series

Under certain conditions the normalized autocorrelation function ρ(τ) of stationary random noise may be expanded as a power series about the point τ = 0. This paper indicates that the coefficients of the expansion are rather simply related to the average rate of occurrence of zeros in the noise function and its derivatives. The expansion of academic interest in providing another perspective of the relationships among the noise function, its power spectrum, and its autocorrelation function. It may also be of practical interest in providing a quick means of estimating the normalized autocorrelation function from a noise record over the range of τ in which the power series converges rapidly. The class of noise spectrum for which convergent series expansion is not possible is of interest in pointing up necessary physical characteristics of noise signals which have such spectra.

F W Lehan↗
NASA NTRS1972

Power series evaluation of transition and covariance matrices.

Reexamination power series solutions to the matrix covariance differential equation and the transition differential equation. Truncation error bounds are derived which are computationally attractive and which extend previous results. Polynomial approximations are obtained by exploiting the functional equations satisfied by the transition and covariance matrices. The series-functional equation propagation technique represents a fast and accurate alternative to the numerical integration of the time-invariant transition and covariance equations.

Bierman, G. J.↗
NASA NTRS1993

Flexure-torsion behavior of prismatic beams. I - Section properties via power series

The behavior of a tip-loaded cantilever beam with an arbitrary cross section is studied using Saint-Venant's semi-inverse method along with a power series solution for the out-of-plane flexure and torsion warping functions. The power series coefficients are determined by solving a set of variationally derived linear algebraic equations. For complex cross sections, the calculated coefficients represented a 'best-fit approximation' to the exact warping function. The resulting warping functions are used to determine the cross-sectional properties (torsion constant, shear correction factors, shear deformation coefficients, and shear center location). A new linear relation is developed for locating the shear center, where the twist rate is zero about the line of shear centers. Moreover, the kinematic relations for a new fully compatible one-dimensional beam theory are developed. Numerical results are presented first to verify the approach and second to provide section data on NACA four-series airfoils not currently found in the literature.

Kosmatka, J. B.↗