Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytical mathematics”

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 361 records · Page 20

An information driven strategy to support multidisciplinary design

The design of complex engineering systems such as aircraft, automobiles, and computers is primarily a cooperative multidisciplinary design process involving interactions between several design agents. The common thread underlying this multidisciplinary design activity is the information exchange between the various groups and disciplines. The integrating component in such environments is the common data and the dependencies that exist between such data. This may be contrasted to classical multidisciplinary analyses problems where there is coupling between distinct design parameters. For example, they may be expressed as mathematically coupled relationships between aerodynamic and structural interactions in aircraft structures, between thermal and structural interactions in nuclear plants, and between control considerations and structural interactions in flexible robots. These relationships provide analytical based frameworks leading to optimization problem formulations. However, in multidisciplinary design problems, information based interactions become more critical. Many times, the relationships between different design parameters are not amenable to analytical characterization. Under such circumstances, information based interactions will provide the best integration paradigm, i.e., there is a need to model the data entities and their dependencies between design parameters originating from different design agents. The modeling of such data interactions and dependencies forms the basis for integrating the various design agents.

Rangan, Ravi M.↗

Fuzzy logic based robotic controller

Existing Proportional-Integral-Derivative (PID) robotic controllers rely on an inverse kinematic model to convert user-specified cartesian trajectory coordinates to joint variables. These joints experience friction, stiction, and gear backlash effects. Due to lack of proper linearization of these effects, modern control theory based on state space methods cannot provide adequate control for robotic systems. In the presence of loads, the dynamic behavior of robotic systems is complex and nonlinear, especially where mathematical modeling is evaluated for real-time operators. Fuzzy Logic Control is a fast emerging alternative to conventional control systems in situations where it may not be feasible to formulate an analytical model of the complex system. Fuzzy logic techniques track a user-defined trajectory without having the host computer to explicitly solve the nonlinear inverse kinematic equations. The goal is to provide a rule-based approach, which is closer to human reasoning. The approach used expresses end-point error, location of manipulator joints, and proximity to obstacles as fuzzy variables. The resulting decisions are based upon linguistic and non-numerical information. This paper presents a solution to the conventional robot controller which is independent of computationally intensive kinematic equations. Computer simulation results of this approach as obtained from software implementation are also discussed.

Attia, F.↗

Investigation of finite element: ABC methods for electromagnetic field simulation

The mechanics of wave propagation in the presence of obstacles is of great interest in many branches of engineering and applied mathematics like electromagnetics, fluid dynamics, geophysics, seismology, etc. Such problems can be broadly classified into two categories: the bounded domain or the closed problem and the unbounded domain or the open problem. Analytical techniques have been derived for the simpler problems; however, the need to model complicated geometrical features, complex material coatings and fillings, and to adapt the model to changing design parameters have inevitably tilted the balance in favor of numerical techniques. The modeling of closed problems presents difficulties primarily in proper meshing of the interior region. However, problems in unbounded domains pose a unique challenge to computation, since the exterior region is inappropriate for direct implementation of numerical techniques. A large number of solutions have been proposed but only a few have stood the test of time and experiment. The goal of this thesis is to develop an efficient and reliable partial differential equation technique to model large three dimensional scattering problems in electromagnetics.

Chatterjee, A.↗

Ascent Aborts 2 Flight, Reconstruction of Structural Dynamics (Couple Loads Transients)

- This work describes the elements of AA2 post-flight data analysis, couple loads analysis, and comparisons of the flight data with the results of analytical methods transiently. - The measured transient responses ranged from rigid body frequencies (zero Hz) to 150 Hz. - The analytical methods consisted of defining and determining all forcing functions, i.e., buffet, aerodynamics, thrusts from the abort motor and the carrier lunch vehicle motor, and the initial conditions at pre-separation. - Mathematical models representing the mechanics of Orion abort is relatively complex because 1) two motors (carrier’s and LAS’s) are operating at the same time at pre-separation, and 2) the separation occurs in atmosphere. - Other challenges consist of determining the aerodynamics with plume-on condition at every millisecond of the flight ranging from transonic to supersonic (i.e., Mach 1.1 to Mach 1.6), and defining the mechanics of separation of LAS from the launch vehicle.

Launch Vehicle↗

Tropospheric Delay Effects in Radio Interferometry

A new tropospheric mapping function is derived which is more accurate than previous mapping functions above elevations of 4 degrees. The error due to the given analytic approximation is estimated to be less than 0.02% for elevation angles larger than 6 degrees, (less than 0.4 cm at 6 degrees, and approximately 0.004% or 0.03 cm at 20 degrees). The mathematical expansion used in the derivation is valid for any laterally homogeneous atmospheric model of refractivity. The new mapping function, computer generated ray tracing tables and other mapping functions are compared. The results can be used in correcting for tropospheric delays of radio signals.

Lanyi, G.↗

Analysis of temperature distribution in liquid-cooled turbine blades

The temperature distribution in liquid-cooled turbine blades determines the amount of cooling required to reduce the blade temperature to permissible values at specified locations. This report presents analytical methods for computing temperature distributions in liquid-cooled turbine blades, or in simplified shapes used to approximate sections of the blade. The individual analyses are first presented in terms of their mathematical development. By means of numerical examples, comparisons are made between simplified and more complete solutions and the effects of several variables are examined. Nondimensional charts to simplify some temperature-distribution calculations are also given.

Livingood, John N B↗

A Log Logistic Survival Model Applied to Hypobaric Decompression Sickness

Decompression sickness (DCS) is a complex, multivariable problem. A mathematical description or model of the likelihood of DCS requires a large amount of quality research data, ideas on how to define a decompression dose using physical and physiological variables, and an appropriate analytical approach. It also requires a high-performance computer with specialized software. I have used published DCS data to develop my decompression doses, which are variants of equilibrium expressions for evolved gas plus other explanatory variables. My analytical approach is survival analysis, where the time of DCS occurrence is modeled. My conclusions can be applied to simple hypobaric decompressions - ascents lasting from 5 to 30 minutes - and, after minutes to hours, to denitrogenation (prebreathing). They are also applicable to long or short exposures, and can be used whether the sufferer of DCS is at rest or exercising at altitude. Ultimately I would like my models to be applied to astronauts to reduce the risk of DCS during spacewalks, as well as to future spaceflight crews on the Moon and Mars.

Conkin, Johnny↗

Distorted-Toroidal Flux Rope Model

The 3D characterization of magnetic flux ropes observed in the heliosphere has been a challenging task for decades. This is mainly due to the limitations on inferring the 3D global topology and physical properties from the 1D time series from any spacecraft. To advance our understanding of magnetic flux ropes whose configuration departs from the typical stiff geometries, here we present an analytical solution for a 3D flux rope model with an arbitrary cross section and a toroidal global shape. This constitutes the next level of complexity following the elliptic-cylindrical (EC) geometry. The mathematical framework was established by Nieves-Chinchilla et al. with the EC flux rope model, which describes a magnetic topology with an elliptical cross section as a first approach to changes in the cross section. In the distorted-toroidal flux rope model, the cross section is described by a general function. The model is completely described by a nonorthogonal geometry and the Maxwell equations can be consistently solved to obtain the magnetic field and relevant physical quantities. As a proof of concept, this model is generalized in terms of the radial dependence of current density components. The last part of this paper is dedicated to a specific function, F (φ) = δ (1 - λ cosφ), to illustrate possibilities of the model. This model paves the way toward the investigation of complex distortions of magnetic structures in the solar wind. Future investigations will explore these distortions in depth by analyzing specific events; studying implications for physical quantities, such as magnetic fluxes, helicity, or energy; and evaluating the force balance with the ambient solar wind that allows such distortions.

Solar wind↗

Analytical evaluation of ILM sensors. Volume 2: Appendices

The applicability of various sensing concepts to independent landing monitor systems was analyzed. Microwave landing system MLS accuracy requirements are presented along with a description of MLS airborne equipment. Computer programs developed during the analysis are described and include: a mathematical computer model for use in the performance assessment of reconnaissance sensor systems; a theoretical formulation of electromagnetic scattering to generate data at high incidence angles; atmospheric attenuation of microwaves; and microwave radiometry, programs

Kirk, R. J.↗

Improved dynamic modeling of a Space-Shuttle Turbo-Pump

The dynamic response of turbo-pumps has traditionally been modeled mathematically using electrical networks. A recently developed computer program is used herein to adjust the model parameters (L - inductance, R - resistance, C - capacitance, etc.) of the electrical network in an attempt to bring the analytical response of the network into closer agreement with newly-available experimental results. Results are presented for a fully-wetted (noncavitating) test of a Space-Shuttle Turbo-Pump and a significant improvement in the dynamic model is achieved.

Evensen, D. A.↗

Simplified Modeling of Tetrahedral Trusses

Tetrahedral-lattice structure exhibits great complexity in mathematical analysis, and complexity quickly increases with number of elements. Solutions for static and dynamic behavior of structure obtained with model consisting of analogous structure with fewer repeating elements. Advantage of continuum models is analytic solutions can be obtained, either in closed form or in relatively-tractable Taylor series.

Leondis, A.↗

Attitude Determination Error Analysis System (ADEAS) mathematical specifications document

The mathematical specifications of Release 4.0 of the Attitude Determination Error Analysis System (ADEAS), which provides a general-purpose linear error analysis capability for various spacecraft attitude geometries and determination processes, are presented. The analytical basis of the system is presented. The analytical basis of the system is presented, and detailed equations are provided for both three-axis-stabilized and spin-stabilized attitude sensor models.

Nicholson, Mark↗

Research on the structural dynamics verification of flexible spacecraft

Langley spacecraft structural dynamics research based on a broad range of experimental and analytical studies, which contributed to the technology base for designing and building advanced spacecraft structures, is reviewed. It is concluded that considerable progress has been made toward developing the scale model technology for validating mathematical models used to predict the on-orbit dynamic behavior of spacecraft structures. Advanced suspension systems for testing models of spacecraft as well as feasibility of using modal data to detect damage in truss-type structures were demonstrated.

Kvaternik, Raymond G.↗

Direct Linearization and Adjoint Approaches to Evaluation of Atmospheric Weighting Functions and Surface Partial Derivatives: General Principles, Synergy and Areas of Application

This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches

remote sensing↗

PASCO: Structural panel analysis and sizing code, capability and analytical foundations

A computer code denoted PASCO which can be used for analyzing and sizing uniaxially-stiffened composite panels is described. Buckling and vibration analyses are carried out with a linked-plate analysis computer code denoted VIPASA, which is incorporated in PASCO. Sizing is based on nonlinear mathematical programming techniques and employs a computer code denoted CONMIN, also incorporated in PASCO. Design requirements considered are initial buckling, material strength, stiffness, and vibration frequency. The capability of the PASCO computer code and the approach used in the structural analysis and sizing are described.

Stroud, W. J.↗

The Viking X ray fluorescence experiment - Analytical methods and early results

Ten samples of the Martian regolith have been analyzed by the Viking lander X ray fluorescence spectrometers. Because of high-stability electronics, inclusion of calibration targets, and special data encoding within the instruments the quality of the analyses performed on Mars is closely equivalent to that attainable with the same instruments operated in the laboratory. Determination of absolute elemental concentrations requires gain drift adjustments, subtraction of background components, and use of a mathematical response model with adjustable parameters set by prelaunch measurements on selected rock standards. Bulk fines at both Viking landing sites are quite similar in composition, implying that a chemically and mineralogically homogeneous regolith covers much of the surface of the planet. Important differences between samples include a higher sulfur content in what appear to be duricrust fragments than in fines and a lower iron content in fines taken from beneath large rocks than those taken from unprotected surface material. Further extensive reduction of these data will allow more precise and more accurate analytical numbers to be determined and thus a more comprehensive understanding of elemental trends between samples.

Clark, B. C., III↗

Minimum-mass design of filamentary composite panels under combined loads: Design procedure based on simplified buckling equations

An analytical procedure is presented for designing hat stiffened and corrugated panels made of composite material and subjected to longitudinal (in the direction of the stiffeners) compression and shear loadings. The procedure is based on nonlinear mathematical programming techniques and a simplified set of buckling equations. Design requirements considered are buckling, strength, and extensional and shear stiffness. The effects of specified thickness, variation of cross-section dimensions, stiffness requirements, local buckling boundary conditions, and the effect of combined compression and shear loadings are shown.

Stroud, W. J.↗