A system of equations for optimized powered flight trajectories
Motion equations for optimized power flight trajectories in earth fixed polar coordinate system
COORDINATE SYSTEM↗
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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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On the Theory of Thin Shallow Shells
This report is concerned with the theory of thin shallow shells. It does not employ the lines of curvature as the coordinate system, but employs "almost cartesian coordinates" or the coordinates obtained by cutting the surface into two mutually orthogonal systems of parallel planes.
Nazarov, A. A.↗
Astrodynamics Convention and Modeling Reference for Lunar, Cislunar, and Libration Point Orbits
The purpose and direction of this document is to provide U.S. government agencies, specifically National Aeronautics and Space Administration (NASA) and Department of Defense (DoD) space related centers, with a foundational summary of astrodynamics concepts for trajectory design, navigation, and operations in the cislunar, lunar, and libration point regions. This document is provided in response to an Interagency Agreement (IAA) between NASA and the National Geospatial-Intelligence Agency (NGA). With applications to these regions of the Earth-Moon system, this document summarizes: the definitions of standard and unique coordinate systems for Positioning, Navigation, Timing and targeting (PNT), transformations between those coordinate frames, definitions of common time systems, a description of numerical integration, description of a widely-used and approximate dynamical model of a three-body system for preliminary analysis and nomenclature definition, description of higher-fidelity models of cislunar space, and the application of these concepts to sample scenarios with a focus on common steps in trajectory and maneuver design for a spacecraft in cislunar space. This information is critical to mission design and navigation far above the geosynchronous orbit region, where lunar perturbations are required to be modeled accurately and consistently but render trajectory design and analysis a complex procedure. Software tools such as the Goddard Space Flight Center (GSFC) open source General Mission Analysis Tool (GMAT) is used as a reference, along with a wide variety of resources constructed by NASA and other government agencies, academia, and industry, for mathematical specifications and practical considerations. This document has been prepared by and under the auspices of NASA. The GSFC Mission Engineering and Systems Analysis (MESA) Division (Code 590) and the Navigation and Mission Design Branch (Code 595) are part of NASA. Their engineers and scientists have expertise in lunar, cislunar, and libration point region trajectory guidance and navigation and timing. NASA GSFC has supported many successful lunar and cislunar missions over the past several decades. These missions include the Lunar Reconnaissance Orbiter (LRO), the two Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon’s Interaction with the Sun (ARTEMIS) spacecraft, Transiting Exoplanet Survey Satellite (TESS), Lunar Prospector, Lunar Crater Observation and Sensing Satellite (LCROSS), Clementine, and several Sun-Earth libration point missions such as WIND and Deep Space Climate Observatory (DSCOVR), dating back four decades. NASA GSFC also supports the upcoming Gateway lunar mission, the Artemis Lunar Program and Human Landing Systems, and leads both the Lunar IceCube low thrust mission and concept design for the Lunar Communication Relay and Navigation System (LCRNS).
Lunar, CisLunar, Libration, trajectory dynamics, p↗
Formulation of static boundary value problems for shallow shells for multiply connected regions
Static boundary value problem for multiply connected shallow shell considered arbitrary orthogonal coordinate system
COORDINATE SYSTEM↗
The axisymmetric thermoelastic problem in bispherical coordinates.
Steady state axisymmetric thermoelastic problems in bispherical coordinate system
COORDINATE SYSTEM↗
Problems of astrometry
Construction of reliable inertial coordinate system - star catalogs from Ukrainian observatories, ILS materials analysis and increasing accuracy of astrometric observations
STELLAR MOTION↗
Elliptic grid generation
Various types of generating systems for boundary-conforming coordinate systems based on the numerical solution of systems of elliptic partial differential equations are discussed. Particular emphasis is given to the determination of functions in these equations which control the distribution of the curvilinear coordinate lines in the field.
Thompson, J. F.↗
Lie series solutions of partial differential equations Administrative report no. 1, 1 Jul. - 31 Dec. 1965
Lie series solutions for 33 partial differential equations resulting from separation of Helmholtz equation into 11 coordinate systems
PARTIAL DIFFERENTIAL EQUATION↗
Analytic platform simulation
Analytic platform simulation program to calculate vehicle velocities and positions in space-fixed coordinate system
ANGULAR VELOCITY↗
Optimal mitigation and control over power system dynamics for stochastic grid resilience
Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the western system coordinating council 9-bus test system using synthetic multi-device outage scenarios.
30 DIRECT ENERGY CONVERSION↗
Cause identification of electromagnetic transient events using spatiotemporal feature learning
This paper presents a spatiotemporal feature learning method for cause identification of electromagnetic transient events in power grids. The proposed method is formulated based on the availability of time-synchronized high-frequency measurements and using the convolutional neural network as the spatiotemporal feature representation along with softmax function for the classification. Despite the existing threshold-based, or energy-based events analysis methods, such as support vector machine autoencoder, and tapered multi-layer perceptron neural network, the proposed feature learning is carried out with respect to both time and space. The effectiveness of the proposed feature learning and the subsequent cause identification is validated through the Electromagnetic Transients Program (EMTP) simulation of different events such as line energization, capacitor bank energization, lightning, fault, and high-impedance fault in the IEEE 30-bus, and the real-time digital simulation of the Western System Coordinating Council (WSCC) 9-bus system.
42 ENGINEERING↗
A graph embedding‐based approach for automatic cyber‐physical power system risk assessment to prevent and mitigate threats at scale
Abstract Power systems are facing an increasing number of cyber incidents, potentially leading to damaging consequences to both physical and cyber aspects. However, the development of analytical methods for the study of large‐scale power infrastructures as cyber‐physical systems is still in its early stages. Drawing inspiration from machine‐learning techniques, the authors introduce a method inspired by the principles of graph embedding that is tailored for quantitative risk assessment and the exploration of possible mitigation strategies of large‐scale cyber‐physical power systems. The primary advantage of the graph embedding approach lies in its ability to generate numerous random walks on a graph, simulating potential access paths. Meanwhile, it enables capturing high‐dimensional structures in low‐dimensional spaces, facilitating advanced machine‐learning applications, and ensuring scalability and adaptability for comprehensive network analysis. By employing this graph embedding‐based approach, the authors present a structured and methodical framework for risk assessment in cyber‐physical systems. The proposed graph embedding‐based risk analysis framework aims to provide a more insightful perspective on cyber‐physical risk assessment and situation awareness for power systems. To validate and demonstrate its applicability, the method has been tested on two cyber‐physical power system models: the Western System Coordinating Council (WSCC) 9‐Bus System and the Illinois 200‐Bus System , thereby showing its advantages in enhancing the accuracy of risk analysis and comprehensiveness of situational awareness.
Sun, Shining↗
Multidate Landsat lake quality monitoring program
A unified package of files and programs has been developed to automate the multidate Landsat-derived analyses of water quality for about 3000 inland lakes throughout Wisconsin. A master lakes file which stores geographic information on the lakes, a file giving the latitudes and longitudes of control points for scene navigation, and a program to estimate control point locations and produce microfiche character maps for scene navigation are among the files and programs of the system. The use of ground coordinate systems to isolate irregular shaped areas which can be accessed at will appears to provide an economical means of restricting the size of the data set.
Fisher, L. T.↗
Boundary-layer equations in generalized curvilinear coordinates
A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.
Panaras, Argyris G.↗
Post-Flight Estimation of Motion of Space Structures: Part 2
A computer program related to the one described in the immediately preceding article estimates the relative position of two space structures that are hinged to each other. The input to the program consists of time-series data on distances, measured by two range finders at different positions on one structure, to a corner-cube retroreflector on the other structure. Given a Cartesian (x,y,z) coordinate system and the known x coordinate of the retroreflector relative to the y,z plane that contains the range finders, the program estimates the y and z coordinates of the retroreflector. The estimation process involves solving for the y,z coordinates of the intersection between (1) the y,z plane that contains the retroreflector and (2) spheres, centered on the range finders, having radii equal to the measured distances. In general, there are two such solutions and the program chooses the one consistent with the design of the structures. The program implements a Kalman filter. The output of the program is a time series of estimates of the relative position of the structures.
Brugarolas, Paul↗
Kamodo’s Model-Agnostic Satellite Flythrough: Lowering the Utilization Barrier for Heliophysics Model Outputs
Heliophysics model outputs are increasingly accessible, but typically are not usable by the majority of the community unless directly collaborating with the relevant model developers. Prohibitive factors include complex file output formats, cryptic metadata, unspecified and often customized coordinate systems, and non-linear coordinate grids. Some pockets of progress exist, giving interfaces to various simulation outputs, but only for a small set of outputs and typically not with open-source, freely available packages. Additionally, the increasing array of tools built upon these sporadic interfaces are typically model-specific. We present Kamodo’s model-agnostic satellite flythrough capabilities as the solution to the utilization barrier for heliophysics model outputs. Developed at the Community Coordinated Modeling Center, these flythrough capabilities are built in Python upon a network of model-agnostic interfaces developed in collaboration with model developers, providing interpolation results the community can trust. Kamodo’s flythrough capabilities present the user with a growing variety of flythrough tools based upon a rapidly expanding library of heliophysics model outputs in several domains, currently including a variety of Ionosphere-Thermosphere-Mesosphere and global magnetosphere model outputs. Each capability is designed to be easily accessible via simplistic model-agnostic syntax, with the entire package freely available in the cloud on Github. Here, we describe the tools developed, include several sample applications for common science questions, demonstrate interoperability with selected packages, and summarize ongoing developments.
Software↗
Development of an orbit determination program to regress for lunar potential constants
Orbit calculation program modified to provide corrected state vectors for lunar potential constants in moon centered coordinate system
STATE VECTOR↗