Guidance, flight mechanics and trajectory optimization. Volume 7 - The Pontryagin maximum principle
Maxima-minima theory, Pontryagin principle, and calculus of variations for optimal trajectory and control analysis
Mc Intyre, J. E.↗
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Optimal control surface locations for aircraft flexure controllers
Optimal control surface location for flexible aircraft determined by matrix minimum principle and calculus of variations
Athans, M.↗
Optimal control-surface locations for flexible aircraft
Aerodynamic control surfaces optimal location for flexible aircraft disturbed by random wind gusts, using matrix minimum principle and calculus of variations
Athans, M.↗
Dynamics of disconnectable microdrives of mine hoisting units
A model study is presented of drives for the electromagnetic clutches used in hoists. Equations are set up and solved, describing the principles of the slip variation during the transient period of the plate engagement.
Pampura, D. P.↗
Optimal trajectories in atmospheric flight
Aspects of optimization theory and switching theory are discussed, taking into account the necessary conditions for extrema, a solution subject to constraints, the calculus of variations, the Pontryagin maximum principle, the canonical transformation, Contensou's domain of maneuverability, optimal switching, a junction with singular arc, and linearized singular control. Equations of motion are considered along with aerodynamic and propulsive forces, the general properties of optimal trajectories, flight in a horizontal plane, optimal coasting flight, supersonic cruise, the supersonic turn, supersonic maneuvers in a vertical plane, energy state approximation, a modified Chapman's formulation for optimal reentry trajectories, optimal planar reentry trajectories, and an optimal glide of reentry vehicles. Orbital aerodynamic maneuvers are examined, giving attention to aerodynamic capture, a change in the apogee, a change in the eccentricity, a change in the perigee, an orbital maneuver, an aerodynamic maneuver, and a combined maneuver.
Vinh, N. X.↗
An X-Ray Reprocessing Model of Disk Thermal Emission in Type 1 Seyfert Galaxies
Using a geometry consisting of a hot central Comptonizing plasma surrounded by a thin accretion disk, we model the optical through hard X-ray spectral energy distributions of the type 1 Seyfert. galaxies NGC 3516 and NGC 7469. As in the model proposed by Poutanen, Krolik, and Ryde for the X-ray binary Cygnus X-1 and later applied to Seyfert galaxies by Zdziarski, Lubifiski, and Smith, feedback between the radiation reprocessed by the disk and the thermal Comptonization emission from the hot central plasma plays a pivotal role in determining the X-ray spectrum, and as we show, the optical and ultraviolet spectra as well. Seemingly uncorrelated optical/UV and X-ray light curves, similar to those which have been observed from these objects can, in principle, be explained by variations in the size, shape, and temperature of the Comptonizing plasma. Furthermore, by positing a disk mass accretion rate which satisfies a condition for global energy balance between the thermal Comptonization luminosity and the power available from accretion, one can predict the spectral properties of the heretofore poorly measured hard X-ray continuum above approximately 50 keV in type 1 Seyfert galaxies. Conversely, forthcoming measurements of the hard X-ray continuum by more sensitive hard X-ray and soft gamma-ray telescopes, such as those aboard the International Gamma-Ray Astrophysics Laboratory (INTEGRAL) in conjunction with simultaneous optical, UV, and soft X-ray monitoring, will allow the mass accretion rates to be directly constrained for these sources in the context of this model.
Chiang, James↗
Tests of gravity Using Lunar Laser Ranging
Lunar laser ranging (LLR) has been a workhorse for testing general relativity over the pa~t four decades. The three retrorefiector arrays put on the Moon by the Apollo astronauts and the French built array on the second Soviet Lunokhod rover continue to be useful targets, and have provided the most stringent tests of the Strong Equivalence Principle and the time variation of Newton's gravitational constant. The relatively new ranging system at the Apache Point :3.5 meter telescope now routinely makes millimeter level range measurements. Incredibly. it has taken 40 years for ground station technology to advance to the point where characteristics of the lunar retrorefiectors are limiting the precision of the range measurements. In this article. we review the gravitational science and technology of lunar laser ranging and discuss prospects for the future.
Merkowitz, Stephen M.↗
Can Vertical Profiles of Tropospheric Methane on Titan Be Derived from Radio-Occultation Soundings?
The intensity of the received signal at Earth in the radio occultations of Titan is attenuated both by refractive defocusing and pressure-induced absorption from N2-N2 and CH4-N2 pairs. Because the absorption strength is different for the two sets of pairs, matching the retrieved absorptivity profile can in principle yield the vertical variation in gaseous methane in the troposphere. There are two factors that make this difficult. The first is the propagation of noise in the phase and amplitude of the received signal in the absorption retrieval. The phase data is first inverted to retrieve vertical profiles of refractivity, from which the refractive defocusing is calculated. This is then subtracted from the observed. intensity attenuation of the received signal to generate a profile of atmospheric absorption. The second problem is the uncertainty in the pressure-induced absorption coefficients. Laboratory data at radio wavelengths is only available near room temperature (see, e.g., [1] for N2-N2), and the extrapolation to the low temperatures in Titan's troposphere is not well established. Ab initio calculations by Borysow et al. [2, 3] provide absorption coefficients at low temperatures and long wavelengths, but their accuracy has come into question. We present examples from Cassini radio occultations of Titan to illustrate the difficulties. For methane mole fractions in the lower troposphere comparable to that inferred from the Huygens probe (approximately 0.05), it will be difficult to separate the contributions of N2-N2 collisions from those of N2-CH4, collisions to the retrieved absorption. However, higher concentrations of CH4 and/or a higher signal-to-noise ratio from a future uplink experiment could result in a successful separation of the two components. However, key to this are highly accurate estimates of the absorption from a combination of laboratory measurements at love temperatures and long wavelengths, and possibly improved theoretical calculations.
Flasar, F. Michael↗
Application of Variational Methods to the Thermal Entrance Region of Ducts
A variational method is presented for solving eigenvalue problems which arise in connection with the analysis of convective heat transfer in the thermal entrance region of ducts. Consideration is given, to both situations where the temperature profile depends upon one cross-sectional coordinate (e.g. circular tube) or upon two cross-sectional coordinates (e.g. rectangular duct). The variational method is illustrated and verified by application to laminar heat transfer in a circular tube and a parallel-plate channel, and good agreement with existing numerical solutions is attained. Then, application is made to laminar heat transfer in a square duct as a check, an alternate computation for the square duct is made using a method indicated by Misaps and Pohihausen. The variational method can, in principle, also be applied to problems in turbulent heat transfer.
Sparrow, E. M.↗
Robustness of quasi-symmetry along parametric boundary variation
Quasi-symmetry is a guiding principle to modern stellarator optimization for improved plasma confinement. However, the robustness of optimized configurations, which can be crucial for maintaining performance under diverse engineering constraints and practical limitations, has received relatively little attention. Here, in this work, we present various case studies on this robustness, by investigating variations in 1/ v neoclassical transport when plasma configurations are smoothly altered across distinct optimized targets. These targets, optimized from different families—quasi-axisymmetric, quasi-helical, and quasi-isodynamic—are approximately matched in major radius as part of a flexible stellarator design. Our study shows that an optimized target does not always represent a local minimum in transport and that the robustness of a local minimum when present can vary significantly. Furthermore, there are configurations which belong to no established families but have transport levels as low as those of optimized targets. These results highlight the importance of conducting extended searches with key parametric variations around optimized configurations, to ensure its robustness as well as flexibility if desired.
neoclassical transport↗
Aeroacoustic and aerodynamic applications of the theory of nonequilibrium thermodynamics
Recent developments in the field of nonequilibrium thermodynamics associated with viscous flows are examined and related to developments to the understanding of specific phenomena in aerodynamics and aeroacoustics. A key element of the nonequilibrium theory is the principle of minimum entropy production rate for steady dissipative processes near equilibrium, and variational calculus is used to apply this principle to several examples of viscous flow. A review of nonequilibrium thermodynamics and its role in fluid motion are presented. Several formulations are presented of the local entropy production rate and the local energy dissipation rate, two quantities that are of central importance to the theory. These expressions and the principle of minimum entropy production rate for steady viscous flows are used to identify parallel-wall channel flow and irrotational flow as having minimally dissipative velocity distributions. Features of irrotational, steady, viscous flow near an airfoil, such as the effect of trailing-edge radius on circulation, are also found to be compatible with the minimum principle. Finally, the minimum principle is used to interpret the stability of infinitesimal and finite amplitude disturbances in an initially laminar, parallel shear flow, with results that are consistent with experiment and linearized hydrodynamic stability theory. These results suggest that a thermodynamic approach may be useful in unifying the understanding of many diverse phenomena in aerodynamics and aeroacoustics.
Horne, W. Clifton↗
A dual extremum principle for a population equation
A dual extremum principle for the Verhulst-Pearl population equation is constructed using a complementary variational technique. The dual formulation utilizes a minimum principle recently developed by Leitmann to convert the functional optimization problem into a parameter optimization problem.
Chan, W. L.↗
Hamilton's principle - Finite-element methods and flexible body dynamics
A variational formulation is given for the equations of motion for an unconstrained elastic body, and Hamilton's principle is used to derive the equations of motion and deformation of the body. Finite-element approximations are developed for these dynamical equations with respect to a body axis system satisfying the mean axis conditions. The free-body influence matrix for the body then is developed in terms of the finite-element model parameters.
Cavin, R. K., III↗
Visualizing the interplay of Dirac mass gap and magnetism at nanoscale in intrinsic magnetic topological insulators
In intrinsic magnetic topological insulators, Dirac surface-state gaps are prerequisites for quantum anomalous Hall and axion insulating states. Unambiguous experimental identification of these gaps has proved to be a challenge, however. Here, we use molecular beam epitaxy to grow intrinsic MnBi 2 Te 4 thin films. Using scanning tunneling microscopy/spectroscopy, we directly visualize the Dirac mass gap and its disappearance below and above the magnetic order temperature. We further reveal the interplay of Dirac mass gaps and local magnetic defects. We find that, in high defect regions, the Dirac mass gap collapses. Ab initio and coupled Dirac cone model calculations provide insight into the microscopic origin of the correlation between defect density and spatial gap variations. Finally, this work provides unambiguous identification of the Dirac mass gap in MnBi 2 Te 4 and, by revealing the microscopic origin of its gap variation, establishes a material design principle for realizing exotic states in intrinsic magnetic topological insulators.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Mirror dark sector solution of the Hubble tension with time-varying fine-structure constant
Here we explore a model introduced by Cyr-Racine et al. that resolves the Hubble tension by invoking a “mirror world” dark sector with energy density a fixed fraction of the “ordinary” sector of Λ+ cold dark matter. Although it reconciles cosmic microwave background and large-scale structure observations with local measurements of the Hubble constant, H 0 , the model requires a value of the primordial helium mass fraction, Y p = 0.170 ± 0.025, that is discrepant with observations and with the predictions of big bang nucleosynthesis. We consider a variant of the model with standard helium mass fraction but with the value of the electromagnetic fine-structure constant, α, slightly different during photon decoupling from its present value. If α at that epoch is lower than its current value by Δα ≃ -2 x 10 -5 , then we can achieve the same Hubble tension resolution as in the work by Cyr-Racine et al. but with consistent helium abundance. As an example of such time evolution of α, we consider a toy model of an ultralight scalar field, with mass m < 4 x 10 -29 eV, coupled to electromagnetism, which evolves after photon decoupling at redshift z ≃ 10 3 , and that with appropriate coupling appears to be consistent with late-time constraints on α variation and the weak equivalence principle.
79 ASTRONOMY AND ASTROPHYSICS↗
Two applications of potential vorticity thinking
The phenomena of dissipative destabilization of external Rossby waves and the acceleration of the zonal mean jet during baroclinic life cycles are described in terms of potential vorticity. The main principle of the potential temperature variations at rigid boundaries have the same effect on the interior flow as do sheets of potential vorticity located just within the boundaries. It is noted that the potential vorticity theory is useful for understanding the dynamical behavior of meterological phenomena.
Robinson, Walter A.↗
Multipath noise reduction spread spectrum signals
The concepts of early-prompt delay tracking, multipath correction of early-prompt delay tracking from correlation shape, and carrier phase multipath correction are addressed. In early-prompt delay tracking, since multipath is always delayed with respect to the direct signals, the system derives phase and pseudorange observables from earlier correlation lags. In multipath correction of early-prompt delay tracking from correlation shape, the system looks for relative variations of amplitude across the code correlation function that do not match the predicted multipath-free code cross-correlation shape. The system then uses deviations from the multipath-free shape to infer the magnitude of multipath, and to generate corrections pseudorange observables. In carrier phase multipath correction, the system looks for variations of phase among plural early and prompt lags. The system uses the measured phase variations, along with the general principle that the multipath errors are larger for later lags, to infer the presence of multipath, and to generate corrections for carrier-phase observables.
Meehan, Thomas K.↗
Evaluation of Leak Detection Technologies for Low Global Warming Potential (GWP), Flammable Refrigerants
Current commercial refrigeration systems use refrigerants with global warming potential (GWP) values ranging from 1250 to 4000. The emergence of low GWP alternatives (GWP <150) is expected to significantly reduce direct emissions in this sector, playing a crucial role in the ongoing electrification and decarbonization initiatives. However, many of these low GWP alternatives pose a flammability risk, necessitating robust sensing solutions to ensure the reliable and safe operation of the equipment. This paper examines various sensing mechanisms suitable for potential applications in systems that employ flammable refrigerants, specifically those designated as A2L class. It provides a summary of A2L refrigerants and their properties, followed by a comprehensive review of sensor classes, covering their working principles, features, advantages, and limitations. Additionally, the article delves into key performance characteristics such as accuracy, selectivity, sensitivity, dynamic characteristics, and durability, among other properties. The article discusses areas for improvement and suggests corresponding approaches for potential sensors in facilitating the successful adoption of flammable refrigerants. Finally, this paper presents the latest findings from experimental evaluation of 5 different sensing principles in detecting the composition variation as a result of various operational conditions. Reliability and sensitivity of the sensor in responding to shifts in true composition and the resultant LFL value is also discussed.
Reshniak, Viktor↗