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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Sines and Cosines. Part 1 of 3

Applying the concept of similarities, the mathematical principles of circular motion and sine and cosine waves are presented utilizing both film footage and computer animation in this 'Project Mathematics' series video. Concepts presented include: the symmetry of sine waves; the cosine (complementary sine) and cosine waves; the use of sines and cosines on coordinate systems; the relationship they have to each other; the definitions and uses of periodic waves, square waves, sawtooth waves; the Gibbs phenomena; the use of sines and cosines as ratios; and the terminology related to sines and cosines (frequency, overtone, octave, intensity, and amplitude).

Apostol, Tom M.↗
NASA NTRS1997

Microgravity: A Teacher's Guide with Activities in Science, Mathematics, and Technology

Microgravity is the subject of this teacher's guide. This publication identifies the underlying mathematics, physics, and technology principles that apply to microgravity. The topics included in this publication are: 1) Microgravity Science Primer; 2) The Microgravity Environment of Orbiting Spacecraft; 3) Biotechnology; 4) Combustion Science; 5) Fluid Physics; 6) Fundamental Physics; and 7) Materials Science; 8) Microgravity Research and Exploration; and 9) Microgravity Science Space Flights. This publication also contains a glossary of selected terms.

Rogers, Melissa J.B.↗
NASA NTRS2006

Spatiotemporal Filtering Using Principal Component Analysis and Karhunen-Loeve Expansion Approaches for Regional GPS Network Analysis

Spatial filtering is an effective way to improve the precision of coordinate time series for regional GPS networks by reducing so-called common mode errors, thereby providing better resolution for detecting weak or transient deformation signals. The commonly used approach to regional filtering assumes that the common mode error is spatially uniform, which is a good approximation for networks of hundreds of kilometers extent, but breaks down as the spatial extent increases. A more rigorous approach should remove the assumption of spatially uniform distribution and let the data themselves reveal the spatial distribution of the common mode error. The principal component analysis (PCA) and the Karhunen-Loeve expansion (KLE) both decompose network time series into a set of temporally varying modes and their spatial responses. Therefore they provide a mathematical framework to perform spatiotemporal filtering.We apply the combination of PCA and KLE to daily station coordinate time series of the Southern California Integrated GPS Network (SCIGN) for the period 2000 to 2004. We demonstrate that spatially and temporally correlated common mode errors are the dominant error source in daily GPS solutions. The spatial characteristics of the common mode errors are close to uniform for all east, north, and vertical components, which implies a very long wavelength source for the common mode errors, compared to the spatial extent of the GPS network in southern California. Furthermore, the common mode errors exhibit temporally nonrandom patterns.

displacement↗
NASA NTRS1973

Computer programs: Operational and mathematical, a compilation

Several computer programs which are available through the NASA Technology Utilization Program are outlined. Presented are: (1) Computer operational programs which can be applied to resolve procedural problems swiftly and accurately. (2) Mathematical applications for the resolution of problems encountered in numerous industries. Although the functions which these programs perform are not new and similar programs are available in many large computer center libraries, this collection may be of use to centers with limited systems libraries and for instructional purposes for new computer operators.

Source record↗
NASA NTRS1998

Shielding from Space Radiations

This Final Progress Report for NCC-1-178 presents the details of the engineering development of an analytical/computational solution to the heavy ion transport equation in terms of a multi-layer Green's function formalism as applied to the Small Spacecraft Technology Initiative (SSTI) program. The mathematical developments are recasted into a series of efficient computer codes for space applications. The efficiency of applied algorithms is accomplished by a nonperturbative technique of extending the Green's function over the solution domain. The codes may also be applied to the accelerator boundary conditions to allow code validation in laboratory experiments. Correlations with experiments for the isotopic version of the code with 59 and 80 isotopes present for a two layers target material in water has been verified.

Chang, C. Ken↗
NASA NTRS1991

Planning and executing motions for multibody systems in free-fall

The purpose of this research is to develop an end-to-end system that can be applied to a multibody system in free-fall to analyze its possible motions, save those motions in a database, and design a controller that can execute those motions. A goal is for the process to be highly automated and involve little human intervention. Ideally, the output of the system would be data and algorithms that could be put in ROM to control the multibody system in free-fall. The research applies to more than just robots in space. It applies to any multibody system in free-fall. Mathematical techniques from nonlinear control theory were used to study the nature of the system dynamics and its possible motions. Optimization techniques were applied to plan motions. Image compression techniques were proposed to compress the precomputed motion data for storage. A linearized controller was derived to control the system while it executes preplanned trajectories.

Cameron, Jonathan M.↗
DOE OSTI2025

Boundary Corrections for Kernel Approximation to Differential Operators

The kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same computational cost as an explicit finite difference scheme but can exhibit order reduction at boundaries. In previous work on periodic domains, order reduction was addressed, yielding high-order accuracy. The issue addressed in this work is the elimination of order reduction of the kernel-based approach for a more general set of boundary conditions. Further, we consider the case of both first and second order operators. To demonstrate the theory, we provide not only the mathematical proofs but also experimental results by applying various boundary conditions to different types of equations. The results agree with the theory, demonstrating a systematic path to high order for kernel-based methods on bounded domains.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Aero-Propulsive Damping Characterization for eVTOL Aircraft Using Free Motion Wind-Tunnel Testing

This paper describes an electric vertical takeoff and landing (eVTOL) aircraft system identification method applied using three degree-of-freedom (3DOF) free motion wind-tunnel testing. The approach, similar to flight-test system identification, allows for efficient mathematical model development of the aero-propulsive moments applied on an eVTOL vehicle, including aerodynamic damping effects. The approach is demonstrated using a subscale tiltrotor eVTOL aircraft mounted on a new 3DOF wind-tunnel apparatus. To execute the test, a model-based 3DOF control system is designed to track attitude commands and transition the aircraft based on the freestream dynamic pressure. While the flight controller is active, orthogonal phase-optimized multisine inputs are injected into the attitude command and control effector command signals to enable collection of informative data for model identification. Aero-propulsive models are then identified at several reference conditions in the transition flight envelope using the equation-error method in the frequency domain. The identified models are shown to have a good fit to the modeling data and good prediction capability of data not used for model identification. The method yields aerodynamic damping estimates using less wind-tunnel test time compared to traditional forced oscillation experiments and supplements static wind-tunnel testing to produce a comprehensive transition aero-propulsive model suitable for use in flight dynamics simulations.

RAVEN↗
NASA NTRS1991

Characterization of Asymmetry in Magnetoacoustic Emission Burst by Numerical Processes

It has been well known that the pattern of the magnetoacoustic emission (MAE) burst observed during the sweep over one half-cycle of the hysteresis loop becomes asymmetric depending on the strength of the magnetic domain wall-defect interaction and the state of residual stresses in a ferromagnet. The ascending asymmetry due to the former has been observed at a very low frequency (.7 Hz) of applied AC magnetic field at a given amplitude. The descending asymmetry due to uniaxial compressive stress has been typically observed at the AC applied magnetic field frequency of 20 Hz. The physical interpretation of both types of asymmetry has been well established. It is, however, necessary to perform investigations of the dependence of asymmetry on externally controlled parameters such as the amplitude and frequency of the AC applied magnetic fields. The purpose of the present study is therefore to devise a mathematical means that describes the degree of asymmetry of the MAE burst and apply this scheme to investigate the AC magnetic field amplitude dependence of the asymmetry.

Namkung, M.↗
DOE OSTI2025

Solving sparse finite element problems on neuromorphic hardware

The finite element method (FEM) is one of the most important and ubiquitous numerical methods for solving partial differential equations (PDEs) on computers for scientific and engineering discovery. Applying the FEM to larger and more detailed scientific models has driven advances in high-performance computing for decades. Here we demonstrate that scalable spiking neuromorphic hardware can directly implement the FEM by constructing a spiking neural network that solves the large, sparse, linear systems of equations at the core of the FEM. We show that for the Poisson equation, a fundamental PDE in science and engineering, our neural circuit achieves meaningful levels of numerical accuracy and close to ideal scaling on modern, inherently parallel and energy-efficient neuromorphic hardware, specifically Intel’s Loihi 2 neuromorphic platform. We illustrate extensions to irregular mesh geometries in both two and three dimensions as well as other PDEs such as linear elasticity. Our spiking neural network is constructed from a recurrent network model of the brain’s motor cortex and, in contrast to black-box deep artificial neural network-based methods for PDEs, directly translates the well-understood and trusted mathematics of the FEM to a natively spiking neuromorphic algorithm.

Applied mathematics↗
DOE OSTI2025

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗
NASA NTRS1976

The human operator in manual preview tracking /an experiment and its modeling via optimal control/

A manual preview tracking experiment and its results are presented. The preview drastically improves the tracking performance compared to zero-preview tracking. Optimal discrete finite preview control is applied to determine the structure of a mathematical model of the manual preview tracking experiment. Variable parameters in the model are adjusted to values which are consistent to the published data in manual control. The model with the adjusted parameters is found to be well correlated to the experimental results.

Tomizuka, M.↗
NASA NTRS1977

Study of the application of an implicit model-following flight controller to lift-fan VTOL aircraft

An implicit model-following flight controller is proposed. This controller is relatively simple in concept: it provides an input/output relationship that is approximately that of any selected second order system; it provides good gust alleviation; and it is self-trimming. The flight controller was applied to all axes of a comprehensive mathematical model of a lift-fan V/STOL transport. Power management controls and displays were designed to match the various modes of control provided by the flight controller. A piloted simulation was performed using a six degree of freedom simulator. The fixed-operating-point handling qualities throughout the powered lift flight envelope received pilot ratings of 3-1/2 or better. Approaches and vertical landings in IFR zero-zero conditions received pilot ratings varying from 2-1/2 to 4 depending on the type of approach and weather conditions.

Merrick, V. K.↗
NASA NTRS1986

Three-dimensional vibrations of twisted cantilevered parallelepipeds

A large number of references dealing with the vibrations of twisted, cantilevered beams and plates exist in the literature. These works show considerable disagreement concerning the effect of twist angle upon frequencies. The present work is the first three-dimensional study of the problem. Displacement components are assumed in the form of algebraic polynomials which satisfy the fixed face conditions exactly, and which are mathematically complete. The Ritz method is then applied. Accurate frequencies are calculated for twisted thick plates and are compared with ones obtained recently by others using beam, shell, and finite element theory.

Leissa, A.↗