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At least 793 records · Page 44

Space shuttle visual simulation system design study

The current and near-future state-of-the-art in visual simulation equipment technology is related to the requirements of the space shuttle visual system. Image source, image sensing, and displays are analyzed on a subsystem basis, and the principal conclusions are used in the formulation of a recommended baseline visual system. Perceptibility and visibility are also analyzed.

Source record↗

Capabilities and applications of a computer program system for dynamic loads analyses of flexible airplanes with active controls /DYLOFLEX/

This paper describes and illustrates the capabilities of the DYLOFLEX Computer Program System. DYLOFLEX is an integrated system of computer programs for calculating dynamic loads of flexible airplanes with active control systems. A brief discussion of the engineering formulation for each of the nine DYLOFLEX programs is described. The capabilities of the system are illustrated by the analyses of two example configurations.

Perry, B., III↗

On the symmetric form of systems of conservation laws with entropy

The present investigation has the objective to review the general structure of system of conservation laws with entropy, giving particular attention to a presentation of symmetric formulations of the equations of gas dynamics. Systems of hyperbolic conservation laws are considered, taking into account the case in which a system of equations is symmetric hyperbolic, questions of symmetrization, and entropy functions. The Euler equations for a polytropic gas in conservation form are considered. The symmetric form retains the conservation properties of the equations. Weak solutions remain, therefore, unchanged. Of particular computational interest is the possibility of using the symmetric form.

Harten, A.↗

Automation of vibroacoustic data bank for random vibration criteria development

A computerized data bank system was developed for utilization of large amounts of vibration and acoustic data to formulate component random vibration design and test criteria. This system consists of a computer, graphics tablet, and a dry-silver hard copier which are all desk-top type hardware and occupy minimal space. The data bank contains data from the Saturn V and Titan III flight and static test programs. The vibration and acoustic data are stored in the form of power spectral density and one-third octave band plots over the frequency range from 20 to 2000 Hz. The data was stored by digitizing each spectral plot by tracing with the graphics tablet. The digitized data was statistically analyzed and the resulting 97.5% probability levels were stored on tape along with the appropriate structural parameters. Standard extrapolation procedures were programmed for prediction of component random vibration test criteria for new launch vehicle and payload configurations. This automated vibroacoustic data bank system greatly enhances the speed and accuracy of formulating vibration test criteria. In the future, the data bank will be expanded to include all data acquired from the space shuttle flight test program.

Ferebee, R. C.↗

Dynamics formulations for the real-time simulation of constrained motion

The Space Shuttle program has relied heavily on simulation throughout all phases of development and operation. Real-time, man-in-the-loop simulation has served the NASA manned space flight program by providing the means to evaluate systems design and integrated systems performance in a simulated flight environment as well as provide a means to train flight crews. New challenges are presented by the development and operation of a permanently manned space station. The assembly of the space station, the transferral of payloads and the use of the space station manipulator to berth the Orbiter are operations critical to the success of the space station. All these operations are examples of constrained motion among the bodies associated with the Orbiter and space station system. The state of the art of formulating the governing dynamical equations of motion for constrained systems are described. The uses of the two basic problems in multibody dynamics are discussed. The most efficient formulations of the equations of motion are addressed from the point of view of completeness. The issues surrounding incorporating the constraints into the equation of motion are presented.

Kelly, Frederick A.↗

Discrete versus continuous: Enhancing battery optimization in capacity expansion models

This study compares two battery modeling approaches for capacity expansion models: discrete-duration and continuous-duration formulations. In the discrete approach, battery duration is fixed, and power capacity is optimized. In the continuous approach, both power and energy capacities are decision variables, allowing storage duration to be optimized endogenously. Although both discrete-duration and continuous-duration battery formulations are used in long-term power system planning models, the literature has provided limited direct, systematic comparisons of their implications within a common modeling framework. To address this gap, this study implements both approaches in the Regional Energy Deployment System (ReEDS TM ) capacity expansion model using two resource adequacy methods, across a range of future system conditions, and with varying battery cost projections. Results show continuous-duration and high-resolution discrete approaches produce similar capacity expansion outcomes. The continuous formulation achieves faster runtimes compared to discrete-duration runs with many discrete-duration options. However, the discrete-duration approach allows users to choose to have limited fidelity for storage duration options, which in some cases can outperform the continuous formulation. The continuous formulation has the lowest overall system costs, indicating its ability to fine-tune storage duration to better meet specific system needs. This study's findings provide a side-by-side evaluation of discrete and continuous battery modeling approaches and offer guidance for improving the representation of real-world systems, flexibility, and computational efficiency for representing energy storage in long-term power system planning models.

25 ENERGY STORAGE↗

A Scenario-Based Process for Requirements Development: Application to Mission Operations Systems

The notion of using operational scenarios as part of requirements development during mission formulation (Phases A & B) is widely accepted as good system engineering practice. In the context of developing a Mission Operations System (MOS), there are numerous practical challenges to translating that notion into the cost-effective development of a useful set of requirements. These challenges can include such issues as a lack of Project-level focus on operations issues, insufficient or improper flowdown of requirements, flowdown of immature or poor-quality requirements from Project level, and MOS resource constraints (personnel expertise and/or dollars). System engineering theory must be translated into a practice that provides enough structure and standards to serve as guidance, but that retains sufficient flexibility to be tailored to the needs and constraints of a particular MOS or Project. We describe a detailed, scenario-based process for requirements development. Identifying a set of attributes for high quality requirements, we show how the portions of the process address many of those attributes. We also find that the basic process steps are robust, and can be effective even in challenging Project environments.

MOS↗

Numerical Evaluation of the "Dual-Kernel Counter-flow" Matric Convolution Integral that Arises in Discrete/Continuous (D/C) Control Theory

Discrete/Continuous (D/C) control theory is a new generalized theory of discrete-time control that expands the concept of conventional (exact) discrete-time control to create a framework for design and implementation of discretetime control systems that include a continuous-time command function generator so that actuator commands need not be constant between control decisions, but can be more generally defined and implemented as functions that vary with time across sample period. Because the plant/control system construct contains two linear subsystems arranged in tandem, a novel dual-kernel counter-flow convolution integral appears in the formulation. As part of the D/C system design and implementation process, numerical evaluation of that integral over the sample period is required. Three fundamentally different evaluation methods and associated algorithms are derived for the constant-coefficient case. Numerical results are matched against three available examples that have closed-form solutions.

Nixon, Douglas D.↗

Adaptive Stress Testing: Finding Likely Failure Events with Reinforcement Learning

Finding the most likely path to a set of failure states is important to the analysis of safety-critical systems that operate over a sequence of time steps, such as aircraft collision avoidance systems and autonomous cars. In many applications such as autonomous driving, failures cannot be completely eliminated due to the complex stochastic environment in which the system operates.As a result, safety validation is not only concerned about whether a failure can occur, but also discovering which failures are most likely to occur. This article presents adaptive stress testing (AST), a framework for finding the most likely path to a failure event in simulation. We consider a general black box setting for partially observable and continuous-valued systems operating in an environment with stochastic disturbances. We formulate the problem as a Markov decision process and use reinforcement learning to optimize it. The approach is simulation-based and does not require internal knowledge of the system, making it suitable for black-box testing of large systems. We present different formulations depending on whether the state is fully observable or partially observable. In the latter case, we present a modified Monte Carlo tree search algorithm that only requires access to the pseudorandom number generator of the simulator to overcome partial observability. We also present an extension of the framework, called differential adaptive stress testing (DAST), that can find failures that occur in one system but not in another. This type of differential analysis is useful in applications such as regression testing, where we are concerned with finding areas of relative weakness compared to a baseline. We demonstrate the effectiveness of the approach on an aircraft collision avoidance application, where a prototype aircraft collision avoidance system is stress tested to find the most likely scenarios of near mid-air collision.

Verification and Validation↗

Synthesis Methods for Robust Passification and Control

The research effort under this cooperative agreement has been essentially the continuation of the work from previous grants. The ongoing work has primarily focused on developing passivity-based control techniques for Linear Time-Invariant (LTI) systems. During this period, there has been a significant progress made in the area of passivity-based control of LTI systems and some preliminary results have also been obtained for nonlinear systems, as well. The prior work has addressed optimal control design for inherently passive as well as non- passive linear systems. For exploiting the robustness characteristics of passivity-based controllers the passification methodology was developed for LTI systems that are not inherently passive. Various methods of passification were first proposed in and further developed. The robustness of passification was addressed for multi-input multi-output (MIMO) systems for certain classes of uncertainties using frequency-domain methods. For MIMO systems, a state-space approach using Linear Matrix Inequality (LMI)-based formulation was presented, for passification of non-passive LTI systems. An LMI-based robust passification technique was presented for systems with redundant actuators and sensors. The redundancy in actuators and sensors was used effectively for robust passification using the LMI formulation. The passification was designed to be robust to an interval-type uncertainties in system parameters. The passification techniques were used to design a robust controller for Benchmark Active Control Technology wing under parametric uncertainties. The results on passive nonlinear systems, however, are very limited to date. Our recent work in this area was presented, wherein some stability results were obtained for passive nonlinear systems that are affine in control.

Kelkar, Atul G.↗

Enigma Version 12

Enigma Version 12 software combines model building, animation, and engineering visualization into one concise software package. Enigma employs a versatile user interface to allow average users access to even the most complex pieces of the application. Using Enigma eliminates the need to buy and learn several software packages to create an engineering visualization. Models can be created and/or modified within Enigma down to the polygon level. Textures and materials can be applied for additional realism. Within Enigma, these models can be combined to create systems of models that have a hierarchical relationship to one another, such as a robotic arm. Then these systems can be animated within the program or controlled by an external application programming interface (API). In addition, Enigma provides the ability to use plug-ins. Plugins allow the user to create custom code for a specific application and access the Enigma model and system data, but still use the Enigma drawing functionality. CAD files can be imported into Enigma and combined to create systems of computer graphics models that can be manipulated with constraints. An API is available so that an engineer can write a simulation and drive the computer graphics models with no knowledge of computer graphics. An animation editor allows an engineer to set up sequences of animations generated by simulations or by conceptual trajectories in order to record these to highquality media for presentation. Enigma Version 12 Lyndon B. Johnson Space Center, Houston, Texas 28 NASA Tech Briefs, September 2013 Planetary Protection Bioburden Analysis Program NASA's Jet Propulsion Laboratory, Pasadena, California This program is a Microsoft Access program that performed statistical analysis of the colony counts from assays performed on the Mars Science Laboratory (MSL) spacecraft to determine the bioburden density, 3-sigma biodensity, and the total bioburdens required for the MSL prelaunch reports. It also contains numerous tools that report the data in various ways to simplify the reports required. The program performs all the calculations directly in the MS Access program. Prior to this development, the data was exported to large Excel files that had to be cut and pasted to provide the desired results. The program contains a main menu and a number of submenus. Analyses can be performed by using either all the assays, or only the accountable assays that will be used in the final analysis. There are three options on the first menu: either calculate using (1) the old MER (Mars Exploration Rover) statistics, (2) the MSL statistics for all the assays, or This software implements penetration limit equations for common micrometeoroid and orbital debris (MMOD) shield configurations, windows, and thermal protection systems. Allowable MMOD risk is formulated in terms of the probability of penetration (PNP) of the spacecraft pressure hull. For calculating the risk, spacecraft geometry models, mission profiles, debris environment models, and penetration limit equations for installed shielding configurations are required. Risk assessment software such as NASA's BUMPERII is used to calculate mission PNP; however, they are unsuitable for use in shield design and preliminary analysis studies. The software defines a single equation for the design and performance evaluation of common MMOD shielding configurations, windows, and thermal protection systems, along with a description of their validity range and guidelines for their application. Recommendations are based on preliminary reviews of fundamental assumptions, and accuracy in predicting experimental impact test results. The software is programmed in Visual Basic for Applications for installation as a simple add-in for Microsoft Excel. The user is directed to a graphical user interface (GUI) that requires user inputs and provides solutions directly in Microsoft Excel workbooks. This work was done by Shannon Ryan of the USRA Lunar and Planetary Institute for Johnson Space Center. Further information is contained in a TSP (see page 1). MSC- 24582-1 Micrometeoroid and Orbital Debris (MMOD) Shield Ballistic Limit Analysis Program Lyndon B. Johnson Space Center, Houston, Texas Commercially, because it is so generic, Enigma can be used for almost any project that requires engineering visualization, model building, or animation. Models in Enigma can be exported to many other formats for use in other applications as well. Educationally, Enigma is being used to allow university students to visualize robotic algorithms in a simulation mode before using them with actual hardware.

Shores, David↗

Micrometeoroid and Orbital Debris (MMOD) Shield Ballistic Limit Analysis Program

This software implements penetration limit equations for common micrometeoroid and orbital debris (MMOD) shield configurations, windows, and thermal protection systems. Allowable MMOD risk is formulated in terms of the probability of penetration (PNP) of the spacecraft pressure hull. For calculating the risk, spacecraft geometry models, mission profiles, debris environment models, and penetration limit equations for installed shielding configurations are required. Risk assessment software such as NASA's BUMPERII is used to calculate mission PNP; however, they are unsuitable for use in shield design and preliminary analysis studies. The software defines a single equation for the design and performance evaluation of common MMOD shielding configurations, windows, and thermal protection systems, along with a description of their validity range and guidelines for their application. Recommendations are based on preliminary reviews of fundamental assumptions, and accuracy in predicting experimental impact test results. The software is programmed in Visual Basic for Applications for installation as a simple add-in for Microsoft Excel. The user is directed to a graphical user interface (GUI) that requires user inputs and provides solutions directly in Microsoft Excel workbooks.

Ryan, Shannon↗

Planetary Protection Bioburden Analysis Program

This program is a Microsoft Access program that performed statistical analysis of the colony counts from assays performed on the Mars Science Laboratory (MSL) spacecraft to determine the bioburden density, 3-sigma biodensity, and the total bioburdens required for the MSL prelaunch reports. It also contains numerous tools that report the data in various ways to simplify the reports required. The program performs all the calculations directly in the MS Access program. Prior to this development, the data was exported to large Excel files that had to be cut and pasted to provide the desired results. The program contains a main menu and a number of submenus. Analyses can be performed by using either all the assays, or only the accountable assays that will be used in the final analysis. There are three options on the first menu: either calculate using (1) the old MER (Mars Exploration Rover) statistics, (2) the MSL statistics for all the assays, or This software implements penetration limit equations for common micrometeoroid and orbital debris (MMOD) shield configurations, windows, and thermal protection systems. Allowable MMOD risk is formulated in terms of the probability of penetration (PNP) of the spacecraft pressure hull. For calculating the risk, spacecraft geometry models, mission profiles, debris environment models, and penetration limit equations for installed shielding configurations are required. Risk assessment software such as NASA's BUMPERII is used to calculate mission PNP; however, they are unsuitable for use in shield design and preliminary analysis studies. The software defines a single equation for the design and performance evaluation of common MMOD shielding configurations, windows, and thermal protection systems, along with a description of their validity range and guidelines for their application. Recommendations are based on preliminary reviews of fundamental assumptions, and accuracy in predicting experimental impact test results. The software is programmed in Visual Basic for Applications for installation as a simple add-in for Microsoft Excel. The user is directed to a graphical user interface (GUI) that requires user inputs and provides solutions directly in Microsoft Excel workbooks. This work was done by Shannon Ryan of the USRA Lunar and Planetary Institute for Johnson Space Center. Further information is contained in a TSP (see page 1). MSC- 24582-1 Micrometeoroid and Orbital Debris (MMOD) Shield Ballistic Limit Analysis Program Lyndon B. Johnson Space Center, Houston, Texas Commercially, because it is so generic, Enigma can be used for almost any project that requires engineering visualization, model building, or animation. Models in Enigma can be exported to many other formats for use in other applications as well. Educationally, Enigma is being used to allow university students to visualize robotic algorithms in a simulation mode before using them with actual hardware. This work was done by David Shores and Sharon P. Goza of Johnson Space Center; Cheyenne McKeegan, Rick Easley, Janet Way, and Shonn Everett of MEI Technologies; Mark Manning of PTI; and Mark Guerra, Ray Kraesig, and William Leu of Tietronix Software, Inc. For further information, contact the JSC Innovation Partnerships Office at (281) 483-3809. MSC-24211-1 Spitzer Telemetry Processing System NASA's Jet Propulsion Laboratory, Pasadena, California The Spitzer Telemetry Processing System (SirtfTlmProc) was designed to address objectives of JPL's Multi-mission Image Processing Lab (MIPL) in processing spacecraft telemetry and distributing the resulting data to the science community. To minimize costs and maximize operability, the software design focused on automated error recovery, performance, and information management. The system processes telemetry from the Spitzer spacecraft and delivers Level 0 products to the Spitzer Science Center. SirtfTlmProc is a unique system with automated error notification and recovery, with a real-time continuous service that can go quiescent after periods of inactivity. The software can process 2 GB of telemetry and deliver Level 0 science products to the end user in four hours. It provides analysis tools so the operator can manage the system and troubleshoot problems. It automates telemetry processing in order to reduce staffing costs. This work was done by Alice Stanboli, Elmain M. Martinez, and James M. McAuley of Caltech for NASA's Jet Propulsion Laboratory. For more information, contact iaoffice @jpl.nasa.gov. This software is available for commercial licensing. Please contact Dan Broderick at Daniel.F. Broderick@jpl.nasa.gov. Refer to NPO-47803. NASA Tech Briefs, September 2013 29 This rapid response computer program predicts Orbiter Wing Leading Edge (WLE) damage caused by ice or foam impact during a Space Shuttle launch (Program "IMPACT2"). The program was developed after the Columbia accident in order to assess quickly WLE damage due to ice, foam, or metal impact (if any) during a Shuttle launch. IMPACT2 simulates an impact event in a few minutes for foam impactors, and in seconds for ice and metal impactors. The damage criterion is derived from results obtained from one sophisticated commercial program, which requires hours to carry out simulations of the same impact events. The program was designed to run much faster than the commercial program with prediction of projectile threshold velocities within 10 to 15% of commercial-program values. The mathematical model involves coupling of Orbiter wing normal modes of vibration to nonlinear or linear springmass models. IMPACT2 solves nonlinear or linear impact problems using classical normal modes of vibration of a target, and nonlinear/ linear time-domain equations for the projectile. Impact loads and stresses developed in the target are computed as functions of time. This model is novel because of its speed of execution. A typical model of foam, or other projectile characterized by material nonlinearities, impacting an RCC panel is executed in minutes instead of hours needed by the commercial programs. Target damage due to impact can be assessed quickly, provided that target vibration modes and allowable stress are known. This work was done by Robert Clark, Jr., Paul Cotter, and Constantine Michalopoulos of The Boeing Company for Johnson Space Center. For further information, contact the JSC Innovation Partnerships Office at (281) 483-3809. MSC-24988-1 Wing Leading Edge RCC Rapid Response Damage Prediction Tool (IMPACT2) Lyndon B. Johnson Space Center, Houston, Texas (3) the MSL statistics for only the accountable assays. Other options on the main menu include a data editing form and utility programs that produce various reports requested by the microbiologists and the project, and tools to generate the groupings for the final analyses. The analyses can be carried out in three ways: Each assay can be treated separately, the assays can be collectively treated for the whole zone as a group, or the assays can be collected in groups designated by the JPL Planetary Protection Manager. The latter approach was used to generate the final report because assays on the same equipment or similar equipment can be assumed to have been exposed to the same environment and cleaning. Thus, the statistics are improved by having a larger population, thereby reducing the standard deviation by the square root of N. For each method mentioned above, three reports are available. The first is a detailed report including all the data. This version was very useful in verifying the calculations. The second is a brief report that is similar to the full detailed report, but does not print out the data. The third is a grand total and summary report in which each assay requires only one line. For the first and second reports, most of the calculations are performed in the report section itself. For the third, all the calculations are performed directly in the query bound to the report. All the numerical results were verified by comparing them with Excel templates, then exporting the data from the Planetary Protection Analysis program to Excel.

Beaudet, Robert A.↗

Reliable Bonding of Composite Laminates Using Reflowable Epoxy Resins

Epoxy matrix composites assembled with adhesives maximize the performance of aerospace structures, but the possibility of forming weak bonds requires the installation of redundant fasteners, which add weight and manufacturing cost. Co-cured joints (e.g. unitized composite structures) are immune to weak bonds because the uncured resin undergoes diffusion and mixing through the joint. A means of co-curing complex structures may reduce the need for redundant fasteners in bondlines. To this end, NASA started the AERoBOND project to develop novel joining materials to enable a “secondary-co-cure” assembly process. Aerospace epoxy resin systems reformulated with offset stoichiometry prevented the resin from advancing beyond the gel point during a conventional autoclave cure cycle up to 180 °C. The offset resins were applied to the joining surfaces of laminate preforms as prepreg. Two surfaces with complimentary offset resins were joined using conventional secondary bonding techniques. Preliminary efforts have indicated that the resulting joint has no discernable interface and appears as a conventional co-cured laminate under optical magnification. This report will discuss the initial work performed regarding formulation of the epoxy resin system using calorimetry, rheology, and mechanical testing.

Palmieri, Frank L.↗

Advanced Computational Methods for Security Constrained Financial Transmission Rights

Financial Transmission Rights (FTRs) are financial insurance tools to help power market participants reduce price risks associated with transmission congestion. FTRs are issued based on a process of solving a constrained optimization problem with the objective to maximize the FTR social welfare under power flow security constraints. Security constraints for different FTR categories (monthly, seasonal or annual) are usually coupled and the number of constraints increases exponentially with the number of categories. Commercial software for FTR calculation can only provide limited categories of FTRs due to the inherent computational challenges mentioned above. In this paper, first an innovative mathematical reformulation of the FTR problem is presented which dramatically improves the computational efficiency of optimization problem. After having re-formulated the problem, a novel non-linear dynamic system (NDS) approach is proposed to solve the optimization problem. The new formulation and performance of the NDS solver is benchmarked against widely used linear programming (LP) solvers like CPLEX™ and tested on both standard IEEE test systems and large-scale systems using data from the Western Electricity Coordinating Council (WECC). The performance of the NDS is demonstrated to be comparable and in some cases is shown to outperform the widely used CPLEX algorithms. The proposed formulation and NDS based solver is also easily parallelizable enabling further computational improvement.

Environmental Molecular Sciences Laboratory↗

Evaluating an Exterior Insulation and Finish System for Deep Energy Retrofits

Exterior insulation and finish systems (EIFS) are proprietary synthetic formulations that are applied to the exterior walls of buildings to serve as insulation and exterior cladding. The insulation thickness can vary from less than one inch to a foot or more. In this project the applicability of EIFS for residential deep energy retrofits was investigated through modeling and a case study home. The home was retrofitted using a site-applied four-inch-thick EIFS. Site-specific details were developed as required for the residential retrofit application. Site work and the costs of the EIFS system were documented. The demonstration home was modeled using Building Energy Optimization energy and cost analysis software to explore cost effectiveness of various EIFS insulation thicknesses in two climate locations.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evaluating an Exterior Insulation and Finish System for Deep Energy Retrofits

Exterior insulation and finish systems (EIFS) are proprietary synthetic formulations that are applied to the exterior walls of buildings to serve as insulation and exterior cladding. The insulation thickness can vary from less than one inch to a foot or more. In this project the applicability of EIFS for residential deep energy retrofits was investigated through modeling and a case study home. The home was retrofitted using a site-applied four-inch-thick EIFS. Site-specific details were developed as required for the residential retrofit application. Site work and the costs of the EIFS system were documented. The demonstration home was modeled using Building Energy Optimization energy and cost analysis software to explore cost effectiveness of various EIFS insulation thicknesses in two climate locations.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Analog and symbolic computation through the Koopman framework

We develop a Koopman operator framework for studying the computational structure of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ‘Koopman halting problem’ that is recursively enumerable in general. For symbolic systems, such as those defined on Cantor space, this operator formulation captures reachability between clopen sets, while for equicontinuous systems we prove that the Koopman halting problem is decidable. Our framework demonstrates that absorbing (halting) states in coarse-grained finite automata correspond to Koopman eigenfunctions with eigenvalue one, while cycles in the transition graph impose spectral constraints associated with periodic dynamics. These results provide a unifying perspective on computation in symbolic and analog systems, showing how computational universality is reflected in operator spectra, invariant subspaces, and algebraic structures. Beyond symbolic dynamics, this operator-theoretic lens opens pathways to analyze the computational properties of a broader class of dynamical systems, including polynomial and analog models, and suggests that computational hardness may admit dynamical signatures in terms of Koopman spectral structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗