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Results for “TRIGONOMETRIC FUNCTION”

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
DOE OSTI2014

Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials

New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak. Bibliography: 27 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

The properties of Q-deformed hyperbolic and trigonometric functions in quantum deformation

Quantum deformation has been studied due to its relation with applications in nuclear physics, conformal field theory, and statistical-quantum theory. The q-deformation of hyperbolic function was introduced by Arai. The application of q-deformed functions has been widely used in quantum mechanics. The properties of this two kinds of system explained in this paper including their derivative. The graph of q-deformed functions presented using Matlab. The special case is given for modified Poschl-Teller plus q-deformed Scarf II trigonometry potentials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2014

Automated Testcase Generation for Numerical Support Functions in Embedded Systems

We present a tool for the automatic generation of test stimuli for small numerical support functions, e.g., code for trigonometric functions, quaternions, filters, or table lookup. Our tool is based on KLEE to produce a set of test stimuli for full path coverage. We use a method of iterative deepening over abstractions to deal with floating-point values. During actual testing the stimuli exercise the code against a reference implementation. We illustrate our approach with results of experiments with low-level trigonometric functions, interpolation routines, and mathematical support functions from an open source UAS autopilot.

Metrics↗
NASA NTRS1971

A table of integrals of the error function. II - Additions and corrections.

Integrals of products of error functions with other functions are presented, taking into account a combination of the error function with powers, a combination of the error function with exponentials and powers, a combination of the error function with exponentials of more complicated arguments, definite integrals from Laplace transforms, and a combination of the error function with trigonometric functions. Other integrals considered include a combination of the error function with logarithms and powers, a combination of two error functions, and a combination of the error function with other special functions.

Geller, M.↗
NASA NTRS1978

A method of weighted residuals with trigonometric basis functions for sound transmission in circular ducts

The method of weighted residuals (MWR) in the form of a modified Galerkin method with trigonometric basis functions is used to compute the transmission of sound in an axisymmetric duct. The method is used to generate the axial wave number for uniform ducts. These are compared with exact solutions generated by a formal eigenvalue routine in the hard-wall case and a Runge-Kutta integration eigenvalue scheme in the soft-wall case. The method is applicable to both flow and no-flow cases.

Vo, P. T.↗
DOE OSTI2020

Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. Next, we introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Energy spectra and wave function of trigonometric Rosen-Morse potential as an effective quantum chromodynamics potential in D-dimensions

The Energy Spectra and Wave Function of Schrodinger equation in D-Dimensions for trigonometric Rosen-Morse potential were investigated analytically using Nikiforov-Uvarov method. This potential captures the essential traits of the quark-gluon dynamics of Quantum Chromodynamics. The approximate energy spectra are given in the close form and the corresponding approximate wave function for arbitrary l-state (l ≠ 0) in D-dimensions are formulated in the form of differential polynomials. The wave function of this potential unnormalizable for general case. The wave function of this potential unnormalizable for general case. The existence of extra dimensions (centrifugal factor) and this potential increase the energy spectra of system.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1984

An analytic solution for the orbital perturbations of the Venus Radar Mapper due to gravitational harmonics

Hill's variational equations are solved analytically for the orbital perturbations of a spacecraft nominally in an elliptic orbit around a non-spherical body. The rotation of the central planet about its spin-axis is not considered in the analysis. The perturbations are restricted to the planetary gravitational harmonics only. An extremely simple algorithm is derived to transform the spherical harmonic potentials to the orbital coordinate system, and the resulting accelerations are shown to be simply trigonometric functions of the true anomaly. With the principal matrix solution for the differential equations of the adjoint system given in closed form, the orthogonality of the trigonometric functions makes it possible to obtain an analytic solution for the non-homogeneous problem, at intervals of 2 pi in true anomaly. The solution for orbital perturbations can be extended over several revolutions by applying well-known results from Floquet's theory. The technique is demonstrated with results presented on the spacecraft periapsis altitude for the forthcoming Venus Radar Mapper Mission.

Vijayaraghavan, A.↗
DOE OSTI2015

PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1971

Sunspot analysis and prediction

An attempt is made to develop an accurate functional representation, using common trigonometric functions, of all existing sunspot data, both quantitative and qualitative, ancient and modern. It is concluded that the three periods of high sunspot activity (1935 to 1970, 1835 to 1870, and 1755 to 1790) are independent populations. It is also concluded that these populations have long periods of approximately 400, 500, and 610 years, respectively. The difficulties in assuming a periodicity of seven 11-year cycles of approximately 80 years are discussed.

Steyer, C. C.↗
NASA NTRS1994

Adaptation of a Control Center Development Environment for Industrial Process Control

In the control center, raw telemetry data is received for storage, display, and analysis. This raw data must be combined and manipulated in various ways by mathematical computations to facilitate analysis, provide diversified fault detection mechanisms, and enhance display readability. A development tool called the Graphical Computation Builder (GCB) has been implemented which provides flight controllers with the capability to implement computations for use in the control center. The GCB provides a language that contains both general programming constructs and language elements specifically tailored for the control center environment. The GCB concept allows staff who are not skilled in computer programming to author and maintain computer programs. The GCB user is isolated from the details of external subsystem interfaces and has access to high-level functions such as matrix operators, trigonometric functions, and unit conversion macros. The GCB provides a high level of feedback during computation development that improves upon the often cryptic errors produced by computer language compilers. An equivalent need can be identified in the industrial data acquisition and process control domain: that of an integrated graphical development tool tailored to the application to hide the operating system, computer language, and data acquisition interface details. The GCB features a modular design which makes it suitable for technology transfer without significant rework. Control center-specific language elements can be replaced by elements specific to industrial process control.

Killough, Ronnie L.↗
NASA NTRS2008

Expressions Module for the Satellite Orbit Analysis Program

The Expressions Module is a software module that has been incorporated into the Satellite Orbit Analysis Program (SOAP). The module includes an expressions- parser submodule built on top of an analytical system, enabling the user to define logical and numerical variables and constants. The variables can capture output from SOAP orbital-prediction and geometric-engine computations. The module can combine variables and constants with built-in logical operators (such as Boolean AND, OR, and NOT), relational operators (such as >, <, or =), and mathematical operators (such as addition, subtraction, multiplication, division, modulus, exponentiation, differentiation, and integration). Parentheses can be used to specify precedence of operations. The module contains a library of mathematical functions and operations, including logarithms, trigonometric functions, Bessel functions, minimum/ maximum operations, and floating- point-to-integer conversions. The module supports combinations of time, distance, and angular units and has a dimensional- analysis component that checks for correct usage of units. A parser based on the Flex language and the Bison program looks for and indicates errors in syntax. SOAP expressions can be built using other expressions as arguments, thus enabling the user to build analytical trees. A graphical user interface facilitates use.

Edmonds, Karina↗