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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1965

Tables of elliptic integrals

Elliptic integral tables for evaluation of integrals with algebraic or trigonometric integrands

ELLIPTIC INTEGRAL↗
NASA NTRS1976

Elliptic integral solutions to a class of space flight optimization problems

This paper is initially concerned with the minimum-time, exoatmospheric flight of a rocket with constant thrust acceleration magnitude, as in the cases of nuclear and solar electric propulsion. Gravitational acceleration is assumed to be a constant scalar multiple of the radius vector, plus a correction term which is a given function of time. The solution to the state equations is obtained in terms of elliptic integrals. A method is presented for the solution of the two-point boundary-condition problem associated with orbital transfer. At most, the latter method requires iteration upon final time, angle of injection, and two other parameters which are bounded. An example problem is provided which involves a rocket with very low thrust and a spiraling trajectory of many revolutions, but an altitude change of only several hundred miles above the earth. Finally, the original elliptic integral solution is extended to a larger class of low and intermediate thrust problems with constant thrust magnitude, mass decreasing with time, and an inverse square gravitational force.

Andrus, J. F.↗
NASA NTRS1986

Improved Numerical Evaluation Method for Elliptic Integrals

Two modifications to Bartky's method for numerical evaluation of complete elliptic integrals increase rate of convergence and eliminate loss of accuracy due to roundoff errors. Other integrals (nonelliptic) evaluated by manipulating integrand into form F(R)/R required for evaluation by this method. Improved method used to map upper half of complex plane conformally onto interior or exterior of round-nosed wedges of various angles.

Rossow, V. J.↗
NASA NTRS1992

Transverse Mercator Projection Via Elliptic Integrals

Improved method of construction of U.S. Army's universal transverse Mercator grid system based on Gauss-Kruger transverse Mercator projection and on use of elliptic integrals of second kind. Method can be used to map entire northern or southern hemisphere with respect to single principal meridian.

Wallis, David E.↗
DOE OSTI2026

Analysis of the elliptic integrable non-linear system in IOTA using tracking of a single electron

Integrable nonlinear lattices that can be realized in practical accelerators are of great interest, as they offer the potential to support high-intensity beams via Landau damping of collective instabilities. One such system, based on an elliptic potential, has been extensively studied at the IOTA storage ring at Fermilab. The analysis of strongly nonlinear dynamics with multi-particle bunches is challenging due to the rapid decoherence of kicked beams. IOTA has the capability to track single electrons using linear multi-anode photomultiplier tubes for simultaneously measuring transverse coordinates and arrival times of synchrotron-radiation pulses. This technology enables the full reconstruction of turn-by-turn positions and momenta in all three planes for a single particle. Using this apparatus, we measured the dependence of small-amplitude tunes on the strength of the nonlinear magnet, as well as tunes dependence on oscillations amplitudes.

Romanov, A. [Fermilab]↗
DOE OSTI2025

Analysis of the Elliptic Integrable Non-Linear System in IOTA Using Tracking of a Single Electron

Integrable nonlinear lattices that can be realized in practical accelerators are of great interest, as they offer the potential to support high-intensity beams via Landau damping of collective instabilities. One such system, based on an elliptic potential, has been extensively studied at the IOTA storage ring at Fermilab. The analysis of strongly nonlinear dynamics with multi-particle bunches is challenging due to the rapid decoherence of kicked beams. IOTA has the capability to track single electrons using linear multi-anode photomultiplier tubes for simultaneously measuring transverse coordinates and arrival times of synchrotron-radiation pulses. This technology enables the full reconstruction of turn-by-turn positions and momenta in all three planes for a single particle. Using this apparatus, we measured the dependence of small-amplitude tunes on the strength of the nonlinear magnet, as well as tunes dependence on oscillations amplitudes.

Romanov, Aleksandr Leonidovich [Fermilab] (ORCID:0↗
NASA NTRS1986

Vortex conception of rotor and mutual effect of screw/propellers

A vortex theory of screw/propellers with variable circulation according to the blade and its azimuth is proposed, the problem is formulated and circulation is expanded in a Fourier series. Equations are given for inductive velocities in space for crews, including those with an infinitely large number of blades and expansion of the inductive velocity by blade azimuth of a second screw. Multiparameter improper integrals are given as a combination of elliptical integrals and elementary functions, and it is shown how to reduce elliptical integrals of the third kind with a complex parameter to integrals with a real parameter.

Lepilkin, A. M.↗
NASA NTRS1985

On Bartky's method for evaluation of integrals of elliptic type with application to round-nosed wedges

Bartky's method for the numerical evluation of integrals of the complete elliptic type is modified to improve its accuracy. The resulting modified method is then applied to integrals involving complex arithmetic which map the upper half of one plane onto either the interior or exterior of round-nosed wedges. These solutions have engineering applications to such problems as the design of magnets and the flow of fluids in and around corners.

Rossow, V. J.↗
NASA NTRS1958

Elliptic Functions and Integrals with Real Modulus in Fluid Mechanics

Advantage of the elliptic functions and of the more general functions of Schwarz for fluid mechanics. Flows outside and inside polygons. Application to the calculation of an elbow diffuser for a wind tunnel. Properties of the elliptic integrals of the first kind and of the elliptic functions. Properties of the theta functions and decomposition of the elliptic functions into products of theta functions. Properties of the zeta functions. Decomposition of the elliptic functions into sums of zeta functions and calculations of the elliptic integrals. Applications to the calculation of wing profiles, of compressor profiles, and to the study of the vibrations of airplane wings and of compressor vanes. The manuscript of the present paper was checked by Mr. Eichelbrenner who corrected several imperfections and suggested numerous improvements to make reading of the paper easier. However, the limited subject does not permit filling in more than an incomplete knowledge of the properties of analytic functions.

Legendre, Robert↗
NASA NTRS1926

Inertia Factors of Ellipsoids for Use in Airship Design

This report is based on a study made by the writer as a member of the Special Committee on Design of Army Semirigid Airship RS-1 appointed by the National Advisory Committee for Aeronautics. The increasing interest in airships has made the problem of the potential flow of a fluid about an ellipsoid of considerable practical importance. In 1833 George Green, in discussing the effect of the surrounding medium upon the period of a pendulum, derived three elliptic integrals, in terms of which practically all the characteristics of this type of motion can be expressed. The theory of this type of motion is very fully given by Horace Lamb in his "Hydrodynamics," and applications to the theory of airships by many other writers. Tables of the inertia coefficients derived from these integrals are available for the most important special cases. These tables are adequate for most purposes, but occasionally it is desirable to know the values of these integrals in other cases where tabulated values are not available. For this reason it seems worth while to assemble a collection of formulae which would enable them to be computed directly from standard tables of elliptic integrals, circular and hyperbolic functions and logarithms without the need of intermediate transformations. Some of the formulae for special cases (elliptic cylinder, prolate spheroid, oblate spheroid, etc.) have been published before, but the general forms and some special cases have not been found in previous publications. (author)

Tuckerman, L. B.↗
NASA NTRS1977

Simplified solution for elliptical-contact deformation between two elastic solids

A linear regression by the method of least squares is made on the geometric variables that occur in the equation for elliptical-contact deformation. The ellipticity and the complete elliptic integrals of the first and second kind are expressed as a function of the x,y-plane principal radii. The ellipticity was varied from 1 (circular contact) to 10 (a configuration approaching line contact). The procedure for solving these variables without the use of charts or a high-speed computer would be quite tedious. These simplified equations enable one to calculate easily the elliptical-contact deformation to within 3 percent accuracy without resorting to charts or numerical methods.

Brewe, D. E.↗