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NASA NTRS1987

Boundary layer simulator (BLIMPJ) improvement

Improvements were made to advance the current Boundary Layer Integral Matrix Procedure - Version J (BLIMPJ) containing previously modeled simplified calculation methods accounting for surface roughness, relaminarization, and thick boundary layer effects. These improvements have potential applications in the design of the future Orbit Transfer Vehicles (OTV) engines. The coded wall roughness module was validated successfully against measured data from the LeRC 60-15 degree half-angle conical nozzle. The relaminarization model was modified to include wall cooling and roughness based on a set of test data from the same nozzle. The model was compared against typical data sets for validation in different flow regimes. The thrust loss calculation for thick boundary layer effects was computerized where the iterations between TDK and BLIMPJ proceeded automatically until convergence was achieved. An example is given for a typical OTV nozzle with an area ratio 1293.

Praharaj, S. C.↗

DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗

DOE OSTI2022

An additively-manufactured molten salt-to-supercritical carbon di-oxide primary heat exchanger for solar thermal power generation – Design and techno-economic performance

The design and techno-economic performance of a compact additively manufactured (AM) molten salt (MS)-to-supercritical carbon di-oxide (sCO2) primary heat exchanger (PHE) for solar thermal application is described. The PHE design consists of sCO2 flow through an array of microscale pin fins while the MS flows through mm-scale rectangular channels. Constraints imposed by AM using laser powder bed fusion method are considered in the design. Structural and fluid flow simulations are performed to arrive at a viable design of the core and headers. A simplified one-dimensional steady state model for the PHE is developed including the impact of surface roughness from the AM process. A process-based cost model is used to determine the tradeoff between thermofluidic design and manufacturing cost. A parametric study is performed using the thermo-fluidic and cost models to determine the set of geometrical and flow variables that result in high power density and low cost, while restricting the pressure drop on the sCO2 side to less than 2% of line pressure. Flow rates of MS and sCO2 were varied over heat capacity rate ratios ranging from 0.2 to 1. Results indicate that it is possible to design a low-pressure drop AM PHE with an effectiveness of 90% and a power density in excess of 10 MW/m3 (including headers). Fabrication of representative nickel superalloy specimens are shown to demonstrate that low-porosity parts with the requisite dimensional tolerance of PHE core can be generated.

14 SOLAR ENERGY↗

DOE OSTI2023

Finding middle ground: Flow regimes designed for salmon and energy value

In regulated rivers, shaping seasonal flows to recover species at risk depends on understanding when to expect conflicts with competing water users and when their interests are aligned. Multi-objective optimization can be used to reveal such conflicts and commonalities. When species are involved, multi-objective optimization is challenged by the need to simulate complex species responses to flow regimes. Previously, we addressed that challenge by developing a simplified salmon model (Quantus) that defines cohorts of salmon by the river section and time in which they were spawned. Salmon in these space-time cohorts are tracked from the time redds (nests) are constructed until the cohort exits the tributary en route to the ocean. In this study, we modeled seasonal patterns in energy value and developed a Pareto-optimal frontier of seasonal flow patterns to maximize in-river salmon survival and hydropower value. Candidate flow regimes were characterized by two pulse flows varying in magnitude, timing, and duration and constrained by a total annual flow near the historical median. Our analysis revealed times when economic and salmon objectives were aligned and times when they differed. Pulse flows that favored higher energy value were timed to meet demand during extreme temperatures. Both salmon and hydropower objectives produced optimal flow regimes with pulse flows in early summer, but only solutions favoring hydropower value included high flows in mid-winter. Solutions favoring higher age-0 salmon survival provided an extended pulse flow in late winter/early spring, which suggests that access to productive floodplain habitat allowed faster growth and earlier out-migration and reduced the need for higher temperature-moderating flows later in spring. Minimum flows were also higher among solutions favoring salmon over energy. The tools used to produce these results can help to design simplified seasonal flow regimes by revealing compromise solutions that satisfy both fish and energy producers and highlighting when potential conflicts are likely.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Structure–Thermodynamic Relationship of a Polysaccharide Gel (Alginate) as a Function of Water Content and Counterion Type (Na vs Ca)

Biofilms are the predominant mode of microbial life on Earth, and so a deep understanding of microbial communities-and their impacts on environmental processes-requires a firm understanding of biofilm properties. Because of the importance of biofilms to their microbial inhabitants, microbes have evolved different ways of engineering and reconfiguring the matrix of extracellular polymeric substances (EPS) that constitute the main non-living component of biofilms. This ability makes it difficult to distinguish between the biotic and abiotic origins of biofilm properties. An important route toward establishing this distinction has been the study of simplified models of the EPS matrix. This study builds on such efforts by using atomistic simulations to predict the nanoscale (≤10 nm scale) structure of a model EPS matrix and the sensitivity of this structure to interpolymer interactions and water content. To accomplish this, we use replica exchange molecular dynamics (REMD) simulations to generate all-atom configurations of ten 3.4 kDa alginate polymers at a range of water contents and Ca–Na ratios. Simulated systems are solvated with explicitly modeled water molecules, which allows us to capture the discrete structure of the hydrating water and to examine the thermodynamic stability of water in the gels as they are progressively dehydrated. Our primary findings are that (i) the structure of the hydrogels is highly sensitive to the identity of the charge-compensating cations, (ii) the thermodynamics of water within the gels (specific enthalpy and free energy) are, surprisingly, only weakly sensitive to cation identity, and (iii) predictions of the differential enthalpy and free energy of hydration include a short-ranged enthalpic term that promotes hydration and a longer-ranged (presumably entropic) term that promotes dehydration, where short and long ranges refer to distances shorter or longer than ~0.6 nm between alginate strands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

High Performance, High Fidelity: A GPU‐Accelerated Doubly‐Periodic Configuration of the Simple Cloud‐Resolving E3SM Atmosphere Model Version 1 (DP‐SCREAMv1)

The development of the Simplified Cloud Resolving Energy Exascale Earth System Atmosphere Model (SCREAMv1) enables global storm-resolving simulations on modern GPU-based supercomputers. However, the high computational cost of SCREAMv1 limits its routine use for process-level studies, creating a need for efficient proxy configurations. This study addresses this gap by introducing DP-SCREAMv1, a doubly periodic cloud-resolving model designed to be fully consistent with SCREAMv1 while enabling high-resolution, long-duration simulations at significantly reduced computational expense by simulating a limited doubly periodic domain rather than the entire globe. Built on a C++/Kokkos architecture, DP-SCREAMv1 achieves exceptional performance scalability on GPU systems and includes a rich library of cases for validation and scientific exploration. In this work, we demonstrate short wall-clock times at SCREAMv1's default resolution and show that DP-SCREAMv1 supports routine execution of large-domain, high-resolution experiments that were previously challenging in practice. Furthermore, we show that DP-SCREAMv1 enables routine execution of “Giga-LES” style simulations and facilitates large-domain, high-resolution simulations that were recently considered burdensome to perform. These results document an efficient, fully consistent process-level configuration for SCREAMv1 (DP-SCREAMv1) and illustrate its use for long-duration and large-domain experiments at cloud-resolving to eddy-permitting resolution.

Environmental sciences↗

DOE OSTI2024

Characteristics of Vertical Ground Motions and Their Effect on the Seismic Response of Bridges in the Near-Field: A State-of-the-Art Review

Despite the evidence from past earthquakes and several numerical investigations demonstrating the detrimental impact of vertical ground motions (VGMs) on the integrity of bridge structures, incorporating their effects into seismic assessment and design procedures has traditionally been given limited consideration. Current codes utilize rather simplistic approaches to account for the concurrent effects of vertical and horizontal motions in structural performance evaluations, potentially leading to unconservative estimates of structural demands. This paper reviews the main features of VGMs and their effect on the seismic response of bridges. The methods and empirical models available to estimate vertical motions for design purposes are discussed, and research gaps and related research needs are identified. Finally, the emerging role of physics-based ground-motion simulations, as well as their limitations, in supporting future research and informing the development of simplified design procedures is examined. The main areas of interest for future research are identified in the need to carry out systematic sensitivity studies to gain insight into the main earthquake parameters that influence key VGMs features, understand the influence of soil nonlinearities on VGMs amplitude and frequency content, inform the development of empirical models that cover a range of site conditions and source-to-site distances where current models are poorly constrained, generate arrays of motions to update coherency models to properly inform the analysis of distributed infrastructure, investigate the impulsive character of VGMs, and assess the approximations made in estimating VGMs with 1D site response analyses. Furthermore, specific focus is laid on large-magnitude earthquakes in the near-field.

Asynchronous ground motion↗

DOE OSTI2023

Impact of fusion reactor neutronics modeling for transmutation and thermal feedback *

Abstract Fusion neutronics calculations provide important metrics pertinent to fusion device operations, such as tritium breeding ratios (TBRs) and data on heat deposition, material activation, and damage. Because of the high computational burden required to generate a high-fidelity Monte Carlo simulation of a 3D fusion device, various assumptions are made to reduce computational time by simplifying the reactor model or the calculation iteration. This paper explores the impact of fusion neutronics metrics such as the TBR and decay heat of structural materials based on assumptions of material composition in the fusion reactor and temperature modeling of materials. Results show that for compact tokamaks with high power and long operational cycles, the transmutation of structural materials is significant enough to cause a substantial change in the flux spectrum and decrease the TBR by 1.68% after 2 years of full power operation. Additionally, assuming a constant temperature and material density can impact the TBR calculations up to 3%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Nonlinear quantum behavior of ultrashort-pulse optical parametric oscillators

The quantum features of ultrashort-pulse optical parametric oscillators (OPOs) are investigated theoretically in the nonlinear regime near and above threshold. Viewing the pulsed OPO as a multimode open quantum system, we rigorously derive a general input-output model that features nonlinear coupling among many cavity (i.e., system) signal modes and a broadband single-pass (i.e., reservoir) pump field. Under appropriate assumptions, our model produces a Lindblad master equation with multimode nonlinear Lindblad operators describing two-photon dissipation and a multimode four-wave-mixing Hamiltonian describing a broadband, dispersive optical cascade, which we show is required to preserve causality. To simplify the multimode complexity of the model, we employ a supermode decomposition to perform numerical simulations in the regime where the pulsed supermodes experience strong single-photon nonlinearity. We find that the quantum nonlinear dynamics induces pump depletion as well as corrections to the below-threshold squeezing spectrum predicted by linearized models. We also observe the formation of non-Gaussian states with Wigner-function negativity and show that the multimode interactions with the pump, both dissipative and dispersive, can act as effective decoherence channels. Finally, we briefly discuss some experimental considerations for potentially observing such quantum nonlinear phenomena with ultrashort-pulse OPOs on nonlinear nanophotonic platforms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1981

Equations of motion for a free-electron laser with an electromagnetic pump field and an axial electrostatic field

The equations of motion for a free-electron laser (FEL) with an electromagnetic pump field and a static axial electric field are derived using a Hamiltonian formalism. Equations governing the energy transfer between the electron beam and each of the electromagnetic fields are given, and the phase shift for each of the electromagnetic fields is derived from a linearized Maxwell wave equation. The relation between the static axial electric field and the resonant phase is given. Laser gain and the fraction of the electron energy converted to photon energy are determined using a simplified resonant particle model. These results are compared to those of a more exact particle simulation code.

Hiddleston, H. R.↗

NASA NTRS1986

Solar dynamic power for the Space Station

This paper describes a computer code which provides a significant advance in the systems analysis capabilities of solar dynamic power modules. While the code can be used to advantage in the preliminary analysis of terrestrial solar dynamic modules its real value lies in the adaptions which make it particularly useful for the conceptualization of optimized power modules for space applications. In particular, as illustrated in the paper, the code can be used to establish optimum values of concentrator diameter, concentrator surface roughness, concentrator rim angle and receiver aperture corresponding to the main heat cycle options - Organic Rankine and Brayton - and for certain receiver design options. The code can also be used to establish system sizing margins to account for the loss of reflectivity in orbit or the seasonal variation of insolation. By the simulation of the interactions among the major components of a solar dynamic module and through simplified formulations of the major thermal-optic-thermodynamic interactions the code adds a powerful, efficient and economic analytical tool to the repertory of techniques available for the design of advanced space power systems.

Archer, J. S.↗

NASA NTRS1993

Delay analysis of combinations of pass transistors and classical logic gates

Combinations of pass transistors and logic gates driving nonlinear capacitive loads are analyzed for the presence of characteristics that will permit easier and more accurate digital logic simulation. Accurate time delay models are developed by studying the nature of the response of simplified circuit models to variations of input waveform rise and fall times and output loading. The nonlinear effects of the CMOS logic devices are minimized to permit easier interpretation of the influence of nonlinear capacitive loads. The performance of a CMOS inverter with a complex nonlinear load consisting of a pass transistor that separates a range of capacitances is compared to the same inverter circuit with a linear capacitive load to develop an understanding of the unique requirements of modeling a nonlinear system. Several methods of modeling the delay of CMOS circuits are reviewed, and a multi-parameter linear model is described. General guidelines for designing CMOS circuits with complex load circuits are developed, emphasizing that the circuit output rise delays and fall delays must be separately analyzed.

Gibson, Jonathan S.↗

NASA NTRS1998

Ultrafast Modulation and Switching of Quantum-Well Lasers using Terahertz Fields

Modulation and switching of semiconductor lasers are important for laser-based information technology. Typically the speed of modulation and switching is limited by interband processes such as stimulated and spontaneous recombinations which occur on a nanosecond time scale. This is why the diode laser modulation has been restricted to tens of GHz. Modulation at higher speed is highly desirable as the information technology enters into the so-called tera-era. In this paper, we study the possibility of utilizing THz-field-induced plasma heating to modulate quantum-well lasers. This is a timely study since, with the advancement of THz solid-state sources and free-electron lasers, THz physics and related technology is currently coming out of its infancy. The investigation of interplaying THz and optical fields is also of intruiging fundamental interest. First, we introduce theoretical plasma heating results for the quantum-well optical amplifier in the presense of an intense half-cycle THz pulse. The heated carrier distributions are then utilized to calculate the THz-pulse-induced change in refractive index and gain profile. Since the electron-hole-plasma is heated using intraband transitions, we circumvent the usual complications due to an overall change in density, and the nonlinear recovery is governed solely by the carrier-LO-phonon interactions, typically 5 ps for a complete recovery. This procedure implies THz and sub-THz switching and recovery rates, respectively; using either gain modulation or index modulation. Plasma heating via steady-state THz fields is also studied. Finally, numerical simulation of a coupled set of equations to investigate the THz modulation based on a simplified model for quantum-well lasers is presented. Our results show that a semiconductor laser can be modulated at up to 1 THz with little distortion with a THz field amplitude at the order of a few kV/cm. Laser responses to a change in THz frequency will be shown. Constraints, practicalities, and applications will be discussed.

Ning, Cun-Zheng↗

NASA NTRS2012

Towards an Improved Pilot-Vehicle Interface for Highly Automated Aircraft: Evaluation of the Haptic Flight Control System

The control automation and interaction paradigm (e.g., manual, autopilot, flight management system) used on virtually all large highly automated aircraft has long been an exemplar of breakdowns in human factors and human-centered design. An alternative paradigm is the Haptic Flight Control System (HFCS) that is part of NASA Langley Research Center s Naturalistic Flight Deck Concept. The HFCS uses only stick and throttle for easily and intuitively controlling the actual flight of the aircraft without losing any of the efficiency and operational benefits of the current paradigm. Initial prototypes of the HFCS are being evaluated and this paper describes one such evaluation. In this evaluation we examined claims regarding improved situation awareness, appropriate workload, graceful degradation, and improved pilot acceptance. Twenty-four instrument-rated pilots were instructed to plan and fly four different flights in a fictitious airspace using a moderate fidelity desktop simulation. Three different flight control paradigms were tested: Manual control, Full Automation control, and a simplified version of the HFCS. Dependent variables included both subjective (questionnaire) and objective (SAGAT) measures of situation awareness, workload (NASA-TLX), secondary task performance, time to recognize automation failures, and pilot preference (questionnaire). The results showed a statistically significant advantage for the HFCS in a number of measures. Results that were not statistically significant still favored the HFCS. The results suggest that the HFCS does offer an attractive and viable alternative to the tactical components of today s FMS/autopilot control system. The paper describes further studies that are planned to continue to evaluate the HFCS.

Schutte, Paul↗

NASA NTRS2012

An Integrated Approach for Aircraft Engine Performance Estimation and Fault Diagnostics

A Kalman filter-based approach for integrated on-line aircraft engine performance estimation and gas path fault diagnostics is presented. This technique is specifically designed for underdetermined estimation problems where there are more unknown system parameters representing deterioration and faults than available sensor measurements. A previously developed methodology is applied to optimally design a Kalman filter to estimate a vector of tuning parameters, appropriately sized to enable estimation. The estimated tuning parameters can then be transformed into a larger vector of health parameters representing system performance deterioration and fault effects. The results of this study show that basing fault isolation decisions solely on the estimated health parameter vector does not provide ideal results. Furthermore, expanding the number of the health parameters to address additional gas path faults causes a decrease in the estimation accuracy of those health parameters representative of turbomachinery performance deterioration. However, improved fault isolation performance is demonstrated through direct analysis of the estimated tuning parameters produced by the Kalman filter. This was found to provide equivalent or superior accuracy compared to the conventional fault isolation approach based on the analysis of sensed engine outputs, while simplifying online implementation requirements. Results from the application of these techniques to an aircraft engine simulation are presented and discussed.

imon, Donald L.↗

NASA NTRS2017

Development of a High-Fidelity Simulation Environment for Shadow-Mode Assessments of Air Traffic Concepts

This paper will describe the purpose, architecture, and implementation of a gate-to-gate, high-fidelity air traffic simulation environment called the Shadow Mode Assessment using Realistic Technologies for the National Airspace System (SMART-NAS) Test Bed.The overarching purpose of the SMART-NAS Test Bed (SNTB) is to conduct high-fidelity, real-time, human-in-the-loop and automation-in-the-loop simulations of current and proposed future air traffic concepts for the Next Generation Air Transportation System of the United States, called NextGen. SNTB is intended to enable simulations that are currently impractical or impossible for three major areas of NextGen research and development: Concepts across multiple operational domains such as the gate-to-gate trajectory-based operations concept; Concepts related to revolutionary operations such as the seamless and widespread integration of large and small Unmanned Aerial System (UAS) vehicles throughout U.S. airspace; Real-time system-wide safety assurance technologies to allow safe, increasingly autonomous aviation operations. SNTB is primarily accessed through a web browser. A set of secure support services are provided to simplify all aspects of real-time, human-in-the-loop and automation-in-the-loop simulations from design (i.e., prior to execution) through analysis (i.e., after execution). These services include simulation architecture and asset configuration; scenario generation; command, control and monitoring; and analysis support.

human-in-the-loop↗

NASA NTRSDate not supplied

Impacts of aerosol size-dependent below-cloud scavenging on tropospheric aerosol in the NASA GEOS model

Cloud scavenging is the major sink for a suite of tropospheric aerosols, and thus largely affects the global distribution and lifetime of aerosols as well as the formation of clouds. Simplified model parameterizations of cloud scavenging of aerosols substantially contribute to large uncertainties in the simulated aerosol burdens, spatial distributions, lifetimes, as well as aerosol radiative forcing. Here we evaluate the wet scavenging scheme in the current NASA GEOS model, develop more physically-based parameterizations of below-cloud scavenging, and assess the impacts of the new scavenging parameterizations on the GEOS simulations of aerosols. The current below-cloud scavenging (BCS; washout) scheme uses a first-order removal with a constant scavenging coefficient. We replaced the current scheme with a size-dependent parameterization of Croft et al.(Atmos. Chem. Phys., 2009; hereafter referred to as C09). The C09 BCS parameterizations calculate aerosol below-cloud scavenging coefficients based on a size-dependent collision efficiency between aerosol particles and raindrops (or snow crystals). A look-up table of compiled collision efficiencies provides values for sixty aerosol sizes and nine rain flux rates. Snow-aerosol collision efficiencies are a function of the sixty aerosol sizes only. We assume a log-normal size distribution for aerosols (bulk) in GOCART. The collision efficiencies are then calculated online using a bilinear interpolation from the look-up table for the given aerosol sizes and precipitation flux rates in the model.

aerosols↗

NASA NTRS2022

Human Stability While Exercising on a VIS Device in Zero Gravity

BACKGROUND: A Vibration Isolation and Stabilization (VIS) system is being designed for use with the European Enhanced Exploration Exercise Device (E4D) [1]. The exercise bar is attached to cables that extend and retract through openings in the E4D platform, which the subject stands on while exercising. Since the E4D is mounted on a moving VIS device, the whole system moves under the subject’s feet. While tension in the cables does help stabilize a crew member in 0g by bracing him or her against the moving platform, flexible cables do not offer full support against falling. This raises the question of whether various exercises that are successfully performed in 1g on a stationary device can be performed without losing balance in 0g on a moving device. Quantifying stability conditions and establishing stability requirements for exercise countermeasure systems is a long-standing challenge and this work helped to inform this specific need for integrated E4D/VIS flight project development. METHODS AND RESULTS: A simplified stability analysis can be attempted based on platform accelerations generated by the VIS device simulation. In this type of analysis, the subject is conceived as standing on the platform in 0g while being held down to it by the tension in the cables. If the sideways acceleration of the platform is such that the cables cannot generate a sufficient moment relative to, e.g., the heels or the toes of the subject to overcome the tipping moment from the inertial forces on the accelerated subject’s body, the subject becomes unstable. This approach, which we refer to as the ‘static’ approximation, indicated failure of all the exercises that were considered in the comprehensive VIS analysis of the E4D. It was realized, however, that platform accelerations are not externally imposed but are themselves induced by the motion of the subject’s body during exercise, and a model calculation confirmed that this drastically altered the tipping moment on the subject, with the potential to even switch the direction in which the body would tip over. This made it imperative to consider in a coupled manner both the motion of the exercising subject’s body and the induced VIS platform motion while considering stability. The coupled dynamics requirement was met by the VIS simulation incorporating time-dependent human mass properties atop the platform and driven by the inertial forces from the prescribed subject motion relative to the platform based on motion-capture recorded human trajectories in 1g on a stationary E4D [2]. To analyze simulation results, a stability criterion was also needed. We do not know how to account for the human ‘control system’ that would take visual and vestibular cues as inputs as the platform moves in 0g. We thus chose to follow an approach we had previously used to analyze the dynamic feasibility of performing a task in lunar gravity along the human body trajectory recorded in 1g [3]. In this approach, one analyzes the center of pressure (COP) between the shoes and the ground (or platform) and checks if the COP remains within the convex hull of the footprints on the ground (or platform), commonly referred to as base of support (BOS). Since pressure is vertical and, in the absence of foot restraints, positive, the COP going outside the BOS indicates that the trajectory recorded in 1g is not dynamically feasible in microgravity and/or on the moving platform of the device. The outcome of the COP-based analysis was that some of the key exercises, especially the deadlift and the back squat exercises, were found to be dynamically feasible for at least some number of the exercise cycles, this number increasing with the cable tension. While this type of stability analysis does not account for the likely alteration of the exercise trajectory from its 1g form in space, it does show that there exist at least some realistic trajectories that pass the dynamic feasibility criterion. This adds confidence that, with further adjustment by the subject of the exercise form in 0g on a moving device, a number of exercises can be performed without losing balance.

D Frenkel↗