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NASA NTRS2019

Vestibulo-Spinal Pathways in Tetrapods: Chapter - 6.26

The vestibulospinal system provides the spinal motor circuits controlling head/neck and limb movements and body posture with rapid reflex adjustments to maintain equilibrium and stability and with a continuous essential excitatory drive, called tonus, to enhance reactive responses to perturbations that force the animal off normal posture. The sensory signals to these reflex circuits originate from hair cells in the inner ear of otolith structures, namely the utricle and saccule, that transduce inertial acceleration and orientation of the head with respect to gravity and in the three orthogonally arranged semicircular canals that transduce angular head rotation. The principal vestibulospinal pathways are 1) the medial vestibulospinal tract that descends in the ventromedial funiculus and innervates inter- and motoneurons located mainly in lamina VII, VIII, and dorsomedial IX throughout the cervical segments; and 2) the lateral vestibulospinal tracts that course in the lateral to ventrolateral funiculi and are distinguished by two divisions: i) a cervical-projecting tract that overlaps many of the targets of medial vestibulospinal tract neurons including the motoneurons in ventromedial IX and also contributes to reflex control of shoulder and forelimb (arm) muscles; and ii) a lumbosacral-projecting tract that provides a rapid input to maintain stable posture and reflex control of the lower body. A striking observation in understanding the functional organization of this sensory-motor system is both that the driving sensory input can be dynamically modified by the behavioral context in which the sensation is made and that it remains able to quickly respond to an external force during self-generated head movements. The structural basis for vestibulospinal inputs to spinal motor control circuits in quadrupeds and bipeds rely in part on the animal's need for coordination between fore- and hind-limb reflex movements. Understanding the sensory-to-motor transformations in the diverse species rely on the correlations of the conserved and unique species behavior, morphology and physiologic function.

Spinal Cord↗
NASA NTRSDate not supplied

Initial Development and Integration of a Vertiport Automation System for Advanced Air Mobility Operations

The High Density Vertiplex Sub-Project, as part of NASA’s Advanced Air Mobility (AAM) Project, has been developing a reference Vertiport Automation System (VAS) to support the management of arrival and departure operations in the terminal area of a vertiport or network of inter-connected vertiports known as a vertiplex. The VAS is potentially a key element of an integrated AAM architecture that will enable greater levels of coordination and predictability for vertiport users through its integration and sharing of information, and greater control of vertiport resources for managing operators. This paper provides an overview of the VAS and a description of an initial implementation that has been integrated into a broader reference architecture as part of ongoing research. Examples from recent simulations are presented with an outline for next steps and considerations.

vertiport↗
NASA NTRS2024

High Precision and Spatial Resolution Chemical Interrogation of Planetary Materials Using fs-LA/LIBS in Tandem With Multi-Collector ICP-MS

Combining femtosecond laser ablation (fs-LA) with laser-induced breakdown spectroscopy (LIBS), together with multi-collector inductively coupled plasma mass spectrometry (MC-ICPMS), can provide remarkable insights into the composition, structure, and therefore geologic history of planetary materials and their terrestrial analogs. Using the Applied Spectra iX-fs-Tandem LA-LIBS Instrument and the Nu SP1700 MC-ICP-MS housed within the Center for Isotope Cosmochemistry and Geochronology at NASA Johnson Space Center, we present preliminary tandem fs-LA-(MC)-ICP-MS/LIBS measurements of planetary analog materials. The synergistic integration of fs-LA-LIBS offers high spatial resolution elemental mapping, enabling the identification of microscale variations within samples. Simultaneously, the MC-ICP-MS can deliver precise isotopic analyses, and integrating the two datasets yields a wealth of geochemical information for a given sample. LA-based chemical mapping experiment designs are contingent on the information sought (i.e., quantitative, or semi-quantitative) and the preferred or available volume of material removed for the analysis. For example, occasionally, there are significant limitations in the depth of ablation due to the sample value, the amount of material available, or simply the need to coordinate with other in-situ techniques. In these limited sample scenarios, the “depth-controlled” chemical maps allow for precise post-mapping ion-polishing of the sample, while the isotopic and elemental maps can be used for targeting future analyses (e.g., conventional LA analyses, SIMS analyses, and micro milling for solution ICP-MS/TIMS). The emerging methodology will establish a powerful tool for investigation of astromaterials and materials returned by future planetary sample science missions.

Jacob B Setera↗
NASA NTRS1974

On the use of first order rotor dynamics in multiblade coordinates

This paper is directed to the question of how to represent most efficiently rotor/body coupling in a linear flight dynamics analysis. Rigid body pitch, roll and vertical motions are considered for the rotor/body coupling studies. Flapping stability limits, eigenvalues, transient responses to control step inputs, to step gusts and to random gusts are determined for a hypothetical hingeless compound helicopter operating up to .8 advance ratio. Data are obtained for the basic helicopter and for the craft with two simple control feedback systems. While complete periodic system modeling is necessary for determining flapping stability limits and vibrations, constant system modeling using first order dynamics in each of the multiblade rotor coordinates was found to be adequate for rotor-craft stability and response computations.

Hohenemser, K. H.↗
NASA NTRS1980

On-orbit evaluation of the control system/structural mode interactions on OSO-8

The Orbiting Solar Observatory-8 experienced severe structural mode/control loop interaction problems during the spacecraft development. Extensive analytical studies, using the hybrid coordinate modeling approach, and comprehensive ground testing were carried out in order to achieve the system's precision pointing performance requirements. A recent series of flight tests were conducted with the spacecraft in which a wide bandwidth, high resolution telemetry system was utilized to evaluate the on-orbit flexible dynamics characteristics of the vehicle along with the control system performance. This paper describes the results of these tests, reviewing the basic design problem, analytical approach taken, ground test philosophy, and on-orbit testing. Data from the tests was used to determine the primary mode frequency, damping, and servo coupling dynamics for the on-orbit condition. Additionally, the test results have verified analytically predicted differences between the on-orbit and ground test environments. The test results have led to a validation of both the analytical modeling and servo design techniques used during the development of the control system, and also verified the approach taken to vehicle and servo ground testing.

Slafer, L. I.↗
NASA NTRSDate not supplied

Designing for Advanced Aerial Mobility: Human-Autonomy Teaming and In-Time System-Wide Safety Assurance

The continued growth of aviation shall require new innovative technologies and operational concepts to meet the ever-increasing demands on air transportation. The NASA Advanced Air Mobility (AAM) project focuses on emerging aviation markets, such as Urban Air Mobility (UAM). UAM is defined as “...a safe and efficient system for air passenger and cargo transportation within an urban area. It is inclusive of small package delivery and other urban unmanned aerial system services and supports a mix of onboard/ground-piloted and increasingly autonomous operations” ([1]). The AAM project emphasizes technology development and validating system-level concepts and solutions in coordination with other NASA Aeronautics Research Mission Directorate (ARMD) projects to enable UAM metro- and micro-plex vertiport and airspace concepts of operations. The NASA AAM research portfolio includes the concepts of Remote Supervisor-in-Command (RSC) and Fleet and Airspace Manager (FAM) as possible human roles for consumer fleet providers. NASA research in RSC is focused on development of guidelines and standards for remote pilots/operators passively and actively controlling a large fleet of autonomous aircraft. For FAM, flight and ground system concepts and technologies to enable high density homogeneous operations at increased scale from vertiport(s), and coordination with other humans in the systems (e.g., UAM urban airspace manager, Air Traffic Control) are key research areas. The envisioned UAM operations are posited to require autonomous systems to enable functions ranging from fleet and resource management to vehicle control. Although automation has become increasingly sophisticated and ubiquitous in civil aviation, autonomy represents a significant evolution in automation, which has generally been limited in functional scope and capability. As autonomy takes on increasing responsibilities, humans and machines will be required to work together in new and different ways [2], rather than traditional design approaches focused on how machines (i.e., autonomy) can do the work of people. The emerging field of human-autonomy teaming (HAT) represents a comprehensive and prioritized research-driven approach to enable the success of future emerging aviation market applications through capabilities and principles that facilitate humans and machine working and thinking better together. The NASA Transformational Tools and Technologies (TTT) Autonomous System (AS) Sub-project was created to assist with the transition into higher levels of autonomy to enable new modes of air transportation, such as UAM. TTT-AS has identified HAT as a key research need to enable UAM while maintaining today’s ultra-safe aviation system safety levels. The latter challenge has been taken up by the NASA System-Wide Safety (SWS) Project, which recognizes that aviation safety, as it evolves, shall require new ways of thinking about safety to include integration of a wide-range of existing and new safety systems and practices, enhanced tools and technologies, increased access to data and data fusion, improved data analysis capabilities, enhanced in-time risk monitoring and detection, hazard prioritization and mitigation, safety assurance decision-support, and in-time integrated system analytics [3].The operational concept of UAM represents a variety of work that has been termed, “work-as-imagined” to characterize the idea that how people think that work is done and how work is actually done are often not the same [4]. To ensure design success and system safety, looking at “work-as-done” provides a comparative approach toward UAM concept and technology design through examination of corresponding analogs found today in aviation (e.g., on-demand operations) and other transportation domains (e.g., port operations). The paper shall discuss various alternative applications with specific focus on airline operation center (AOC) operations, and unmanned aerial system (UAS) command-and-control to inform scaled-versions of FAM and RSC, respectively, and with consideration of the national airspace system contextual environment. The tenets and principles of the HAT field and current NASA research efforts under the TTT-AS sub-project shall also be described. Finally, the SWS sub-project efforts to develop In-Time System-Wide Safety Assurance (ISSA) and In-Time Safety Management Systems (IASMS) are discussed in terms of how “in-time” safety assurance may be conceptualized for the on-demand mobility air taxi “work-as-imagined” operational concept [5]. As part of this effort, concepts from the emerging field of resilience engineering, are being studied. Traditional approaches to aviation safety have focused on what can go wrong and how to prevent it. Another approach to thinking about system safety should reflect not only “avoiding things that go wrong” (protective safety) but also “ensuring that things go right” (productive safety), that enables a system to exhibit the resilient performance [6] necessary for the success of the future aviation system emerging concepts of operations. The paper shall describe efforts focused on how productive safety and resilience may enable a more complete approach to system safety thinking and design of ISSA and IASMS for UAM. Future directions and research needs shall also be discussed.

resilience↗
NASA NTRS1980

A propulsion and steering control system for the Mars rover

The design of a propulsion and steering control system for the Rensselaer Polytechnic Institute prototype autonomous Mars roving vehicle is presented. The vehicle is propelled and steered by four independent electric motors. The control system must regulate the speeds of the motors so they work in unison during turns and on irregular terrain. An analysis of the motor coordination problem on irregular terrain, where each motor must supply a different torque at a different speed is presented. A procedure was developed to match the output of each motor to the varying load. A design for the control system is given. The controller uses a microprocessor which interprets speed and steering commands from an off-board computer, and produces the appropriate drive voltages for the motors.

Turner, J. M.↗
DOE OSTI2022

CRADA Number NFE-19-07846 with Grid Fruit, LLC (CRADA Final Report)

Cooperative Research and Development Agreement (CRADA) NFE-19-07846 between Oak Ridge National Laboratory (ORNL) and Grid Fruit, LLC (Grid Fruit) focused on simulating, monitoring, and adjusting controls of commercial refrigerator and freezer systems to provide load flexibility and demand response services from these machines. Viewing these medium and low-temp coolers as thermal masses, the volumes of chilled air in these coolers make them time-shiftable loads ripe for deployment at optimal times. Grid Fruit is a startup company developing methods to schedule the chilling cycles (e.g., in “build load” and “shed load” grid events) to provide energy efficiency, peak shifting, and other benefits both to the grid and the broader environment. These benefits can be magnified by coordinating chillers with HVAC, lights, computers, and other loads. Grid Fruit completed simulations and then selected and ordered controls hardware to prove the technology were successful, but the diversity of chiller models in the field without digital controls, as well as limited market demand at present, make further exploration necessary before commercialization.

42 ENGINEERING↗
DOE OSTI2024

Peer-to-peer communication control for resilient operations of networked cyberphysical systems

This report includes two main accomplishments of the peer-to-peer communication control for resilient operation of networked microgrids project in FY24, which include a scheme for cyberattack-aware coordination of networked microgrids for supporting voltages of bulk power systems and a scheme for price signal-based operations of EV-rich networked microgrids with mixed ownership. First, the cyberattack-aware scheme enables networked microgrids to distributedly determine the amount of reactive power injection to support the voltage of bulk power system (BPS) in a fair manner. In this scheme, a risk-informed algorithm is presented to generate the peer-to- peer (P2P) communication graph with minimal risk of attack on communication links. To deal with cyberattacks on MG controllers, the resilient consensus algorithm (CA) is utilized for MG controllers to robustly estimate the total reactive power headroom, from which the MGs can accurately provide the needed amount of reactive power injection for supporting the voltage of BPS. The CA implementation and performance within the P2P communication framework are demonstrated on the IEEE 39-bus system with 6 microgrids contained in the distribution feeder under different cyberattack scenarios. Second, the price-based scheme enables the usage of the real-time price signal for the operations of electric vehicle (EV)-rich networked-microgrids with mixed ownership, in which not all the microgrids can communicate with the distribution system operator (DSO). In this scheme, a max consensus is introduced to enable the real-time price signal to be propagated from the DSO to all the microgrids, from which each microgrid controller will manage the DERs to balance the load demand and the power injection from the EV charging stations within its microgrid. Numerical results over one day with 288 slots of 5-minute intervals on the modified 123-node test feeder including 3 microgrids with high penetration of EV are presented to evaluate how the price signal affects the operations of networked microgrids under different charging strategies of the EV charging stations. The result indicates that our proposed EVCS (dis)charging strategy, which leverages the flexibility of EVs to support the grid through discharging during peak demand, proves to be a cost-effective solution that reduces operational costs while improving the social welfare of EV charging.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2004

Preparing for Themis Controlled Global Mars Mosaics

We have begun work to prepare for producing controlled 2001 Mars Odyssey THEMIS infrared (IR) and visible (VIS) global mosaics of Mars. This effort is being coordinated with colleagues from Arizona State University and on the THEMIS team who plan to address radiometric issues in making such mosaics. We are concentrating on geometric issues. Several areas of investigation are now in progress, including: a) characterizing the absolute pointing accuracy of THEMIS images; b) investigating whether automatic tie point matching algorithms could be used to provide connections between overlapping THEMIS images; c) developing algorithms to allow for the photogrammetric (bundle) adjustment of the THEMIS IR (line scanner) camera images. Our primary goal in this pilot study effort will be to make several test control THEMIS mosaics and better determine which methods could be used, which require development, and what level of effort is required, in order to make large regional or global controlled THEMIS mosaics.

Archinal, B. A.↗
DOE OSTI2026

Laboratory Evaluation of Federated, Hierarchical Controls for Distribution Power System Management: Preprint

The connection of more loads and distributed energy resources (DERs) to the distribution power system brings both challenges and opportunities to system operators. There are opportunities to aggregate flexible loads and DERs to provide transmission grid services, but the coordinated actions of DERs being managed by independent, third-party DER aggregators to support transmission system operations can present challenges. We developed a federated DER management architecture and control framework that aims to manage heterogeneous DERs to deliver reliable transmission grid services while respecting distribution system constraints. The controls include stochastic day-ahead optimization, model predictive control, and a simple real-time management scheme. We present simulation results obtained from a realistic laboratory test bed of federated controls managing DERs within a substation service area to make the substation net power follow the optimal net power determined by the day-ahead optimization based on cost and limiting reverse power flow.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

New-Generation Carbon-Capture Ionic Liquids Regulated by Metal-Ion Coordination

Development of efficient carbon capture-and-release technologies with minimal energy input is a long-term challenge in mitigating CO 2 emissions, especially via CO 2 chemisorption driven by engineered chemical bond construction. Herein, taking advantage of the structural diversity of ionic liquids (ILs) in tuning their physical and chemical properties, precise reaction energy regulation of CO 2 chemisorption was demonstrated deploying metal-ion-amino-based ionic liquids (MAILs) as absorbents. The coordination ability of different metal sites (Cu, Zn, Co, Ni, and Mg) to amines was harnessed to achieve fine-tuning on stability constants of the metal ion-amine complexes, acting as the corresponding cations in the construction of diverse ILs coupled with CO 2 -philic anions. The as-afforded MAILs exhibited efficient and controllable CO 2 release behavior with great reduction in energy input and minimal sacrifice on CO 2 uptake capacity. This coordination-regulated approach offers new prospects for the development of ILs-based systems and beyond towards energy-efficient carbon capture technologies.

36 MATERIALS SCIENCE↗
NASA NTRS2000

Autonomy Architectures for a Constellation of Spacecraft

Until the past few years, missions typically involved fairly large expensive spacecraft. Such missions have primarily favored using older proven technologies over more recently developed ones, and humans controlled spacecraft by manually generating detailed command sequences with low-level tools and then transmitting the sequences for subsequent execution on a spacecraft controller. This approach toward controlling a spacecraft has worked spectacularly on previous missions, but it has limitations deriving from communications restrictions - scheduling time to communicate with a particular spacecraft involves competing with other projects due to the limited number of deep space network antennae. This implies that a spacecraft can spend a long time just waiting whenever a command sequence fails. This is one reason why the New Millennium program has an objective to migrate parts of mission control tasks onboard a spacecraft to reduce wait time by making spacecraft more robust. The migrated software is called a "remote agent" and has 4 components: a mission manager to generate the high level goals, a planner/scheduler to turn goals into activities while reasoning about future expected situations, an executive/diagnostics engine to initiate and maintain activities while interpreting sensed events by reasoning about past and present situations, and a conventional real-time subsystem to interface with the spacecraft to implement an activity's primitive actions. In addition to needing remote planning and execution for isolated spacecraft, a trend toward multiple-spacecraft missions points to the need for remote distributed planning and execution. The past few years have seen missions with growing numbers of probes. Pathfinder has its rover (Sojourner), Cassini has its lander (Huygens), and the New Millenium Deep Space 3 (DS3) proposal involves a constellation of 3 spacecraft for interferometric mapping. This trend is expected to continue to progressively larger fleets. For example, one mission proposed to succeed DS3 would have 18 spacecraft flying in formation in order to detect earth-sized planets orbiting other stars. A proposed magnetospheric constellation would involve 5 to 500 spacecraft in Earth orbit to measure global phenomena within the magnetosphere. This work describes and compares three autonomy architectures for a system that continuously plans to control a fleet of spacecraft using collective mission goals instead of goals or command sequences for each spacecraft. A fleet of self-commanding spacecraft would autonomously coordinate itself to satisfy high level science and engineering goals in a changing partially-understood environment making feasible the operation of tens or even a hundred spacecraft (such as for interferometry or plasma physics missions). The easiest way to adapt autonomous spacecraft research to controlling constellations involves treating the constellation as a single spacecraft. Here one spacecraft directly controls the others as if they were connected. The controlling "master" spacecraft performs all autonomy reasoning, and the slaves only have real-time subsystems to execute the master's commands and transmit local telemetry/observations. The executive/diagnostics module starts actions and the master's real-time subsystem controls the action either locally or remotely through a slave. While the master/slave approach benefits from conceptual simplicity, it relies on an assumption that the master spacecraft's executive can continuously monitor the slaves' real-time subsystems, and this relies on high-bandwidth highly-reliable communications. Since unintended results occur fairly rarely, one way to relax the bandwidth requirements involves only monitoring unexpected events in spacecraft. Unfortunately, this disables the ability to monitor for unexpected events between spacecraft and leads to a host of coordination problems among the slaves. Also, failures in the communications system can result in losing slaves. The other two architectures improve robustness while reducing communications by progressively distributing more of the other three remote agent components across the constellation. In a teamwork architecture, all spacecraft have executives and real-time subsystems - only the leader has the planner/scheduler and mission manager. Finally, distributing all remote agent components leads to a peer-to-peer approach toward constellation control.

Barrett, Anthony↗
NASA NTRS1994

Advanced information processing system: Hosting of advanced guidance, navigation and control algorithms on AIPS using ASTER

This program demonstrated the integration of a number of technologies that can increase the availability and reliability of launch vehicles while lowering costs. Availability is increased with an advanced guidance algorithm that adapts trajectories in real-time. Reliability is increased with fault-tolerant computers and communication protocols. Costs are reduced by automatically generating code and documentation. This program was realized through the cooperative efforts of academia, industry, and government. The NASA-LaRC coordinated the effort, while Draper performed the integration. Georgia Institute of Technology supplied a weak Hamiltonian finite element method for optimal control problems. Martin Marietta used MATLAB to apply this method to a launch vehicle (FENOC). Draper supplied the fault-tolerant computing and software automation technology. The fault-tolerant technology includes sequential and parallel fault-tolerant processors (FTP & FTPP) and authentication protocols (AP) for communication. Fault-tolerant technology was incrementally incorporated. Development culminated with a heterogeneous network of workstations and fault-tolerant computers using AP. Draper's software automation system, ASTER, was used to specify a static guidance system based on FENOC, navigation, flight control (GN&C), models, and the interface to a user interface for mission control. ASTER generated Ada code for GN&C and C code for models. An algebraic transform engine (ATE) was developed to automatically translate MATLAB scripts into ASTER.

Brenner, Richard↗
NASA NTRS1991

A controls engineering approach for analyzing airplane input-output characteristics

An engineering approach for analyzing airplane control and output characteristics is presented. State-space matrix equations describing the linear perturbation dynamics are transformed from physical coordinates into scaled coordinates. The scaling is accomplished by applying various transformations to the system to employ prior engineering knowledge of the airplane physics. Two different analysis techniques are then explained. Modal analysis techniques calculate the influence of each system input on each fundamental mode of motion and the distribution of each mode among the system outputs. The optimal steady state response technique computes the blending of steady state control inputs that optimize the steady state response of selected system outputs. Analysis of an example airplane model is presented to demonstrate the described engineering approach.

Arbuckle, P. Douglas↗
NASA NTRS1999

Emergence of postural patterns as a function of vision and translation frequency

Emergence of postural patterns as a function of vision and translation frequency. We examined the frequency characteristics of human postural coordination and the role of visual information in this coordination. Eight healthy adults maintained balance in stance during sinusoidal support surface translations (12 cm peak to peak) in the anterior-posterior direction at six different frequencies. Changes in kinematic and dynamic measures revealed that both sensory and biomechanical constraints limit postural coordination patterns as a function of translation frequency. At slow frequencies (0.1 and 0.25 Hz), subjects ride the platform (with the eyes open or closed). For fast frequencies (1.0 and 1.25 Hz) with the eyes open, subjects fix their head and upper trunk in space. With the eyes closed, large-amplitude, slow-sway motion of the head and trunk occurred for fast frequencies above 0.5 Hz. Visual information stabilized posture by reducing the variability of the head's position in space and the position of the center of mass (CoM) within the support surface defined by the feet for all but the slowest translation frequencies. When subjects rode the platform, there was little oscillatory joint motion, with muscle activity limited mostly to the ankles. To support the head fixed in space and slow-sway postural patterns, subjects produced stable interjoint hip and ankle joint coordination patterns. This increase in joint motion of the lower body dissipated the energy input by fast translation frequencies and facilitated the control of upper body motion. CoM amplitude decreased with increasing translation frequency, whereas the center of pressure amplitude increased with increasing translation frequency. Our results suggest that visual information was important to maintaining a fixed position of the head and trunk in space, whereas proprioceptive information was sufficient to produce stable coordinative patterns between the support surface and legs. The CNS organizes postural patterns in this balance task as a function of available sensory information, biomechanical constraints, and translation frequency.

NASA Discipline Neuroscience↗
NASA NTRS1972

The influence of laser ranging on selenodetic control.

In this paper, a mathematical model is presented which can be used to perform an adjustment using laser distances to improve coordinates of points of the earth and on the moon. The observation equations are given and the orientation of the earth and the moon is defined in terms of three Eulerian angles. Parameters related to the orientation of the two bodies are the six initial conditions in each case, for the numerical integration of the three angles and their time derivatives. Numerical experiments were performed for the purpose of investigating the expected accuracies of the various parameters in the adjustment model under differing conditions. The results of the experiments indicate that the statistics for both the coordinates of points on earth and on the moon, and for the orientation parameters of the two bodies, are favorable.

Mueller, I. I.↗
NASA NTRS1973

Selenographic control

Evaluation of selenographic data obtained with use of different observational means requires the formulation of rigorous algorithms connecting the systems of coordinates, which the various methods have been referred to. The lunar principal axes of inertia are suggested as most appropriate for reference in lunar mapping and selenographic coordinate catalogues. The connection between the instantaneous axis of lunar rotation (involved in laser ranging, radar studies, astronomical observations from the surface of the moon and VLBI observations of ALSEPs), the ecliptic system of coordinates (which in reductions of observations was considered as fixed in space), the 'Cassini' mean selenographic coordinates (to which physical libration measures were referred), the lunar principal axes of inertia, and the invariable plane of the solar system is discussed.

Moutsoulas, M. D.↗