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Global stability regions are found for class i orbits of the circular restricted three-body problem for primary masses equal and Jacobi constant K greater than 15.5. It is found that, this constant decreases, the stability region shrinks extremely rapidly.
We study numerically the effect of gas on the global stability of a two-component self-gravitating galactic disk embedded in a live halo. The stars are evolved by using a 3D collisionless N-body code, and the gas is represented by an ensemble of finite size inelastic particles. The gravitational interaction of stars and gas is calculated using a TREE method. We find that the evolution of the gaseous distribution in the globally unstable disks can be described by two different regimes. When the gas mass fraction is less than about 10 percent, the gas is channeled toward the galactic center by a growing stellar bar. For higher gas fractions, the gas becomes highly inhomogeneous, and the bar instability in the disk is heavily damped. The gas falls toward the inner kpc due to dynamical friction. Domains of both regimes depend on the efficiency of dissipation in the gas. We also discuss the relevance of the Jeans instability and give an empirical criterion for the global bar instability in a two-component self-gravitating disk.
Compressor stall phenomena are analyzed from the point of view of nonlinear control theory, based on bifurcation-catastrophe techniques. This new approach appears promising and offers insight into such well-known compressor instability problems as surge and rotating stall and suggests strategies for recovery. Three interlocking dynamic nonlinear state space models are developed. It is shown that the problem of rotating stall can be viewed as an induced bifurcation of solution of the unstalled model. Hysteresis effects are shown to exist in the stall/recovery process. Surge cycles are observed for some critical parameter values. The oscillatory behavior is seen to be due to development of limit cycles, generated by Hopf bifurcation of solutions. More specifically, it is observed that at certain critical values of parameters, a family of stable limit cycles with growning and then diminishing amplitudes is generated, then giving rise to an unstable family of limit cycles. This unstable family in turn bifurcates into other unstable families. To further illustrate the utility of the methodology, some partial computation of domains is carried out, and parameter sensitivity analysis is performed.
The fundamental notion of the consistent stability of semidiscrete analogues of evolution PDEs is explored. Lyapunov's direct method is used to develop CFD semidiscrete algorithms which yield the TVD constraint as a special case. A general formula for supplying dissipation parameters for arbitrary multidimensional conservation law systems is proposed. The reliability of the method is demonstrated by the results of two numerical tests for representative Euler shocked flows.
While international climate policies now focus on limiting global warming to well below 2 °C or pursuing a 1.5 °C level of global warming, the climate modelling community has not provided an experimental design in which all Earth system models (ESMs) converge and stabilize at the same prescribed global warming levels. This gap hampers accurate estimations based on comprehensive ESMs of the carbon emission pathways and budgets needed to meet such agreed warming levels and of the associated climate impacts under temperature stabilization. Here, we apply the Adaptive Emission Reduction Approach (AERA) with ESMs to provide such simulations in which all models converge at 1.5 and 2.0 °C warming levels by adjusting their emissions over time. These emission-driven simulations provide a wide range of emission pathways and resulting atmospheric CO 2 projections for a given warming level, uncovering uncertainty ranges that were previously missing in the traditional Coupled Model Intercomparison Project (CMIP) scenarios with prescribed greenhouse gas concentration pathways. Meeting the 1.5 °C warming level requires a 40 % (full model range: 7 % to 76 %) reduction in multi-model mean CO 2 -forcing-equivalent (CO 2 -fe) emissions from 2025 to 2030, a 98 % (57 % to 127 %) reduction from 2025 to 2050, and a stabilization at 1.0 (−1.7 to 2.9) PgC yr−1 from 2100 onward after the 1.5 °C global warming level is reached. Meeting the 2.0 °C warming level requires a 47 % (8 % to 92 %) reduction in multi-model mean CO 2 -fe emissions until 2050 and a stabilization at 1.7 (−1.5 to 2.7) PgC yr−1 from 2100 onward. The on-average positive emissions under stabilized global temperatures are the result of a decreasing transient climate response to cumulative CO 2 -fe emissions over time under stabilized global warming. This evolution is consistent with a slightly negative zero emissions commitment – initially assumed to be zero – and leads to an increase in the post-2025 CO 2 -fe emission budget by a factor of 2.2 (−0.8 to 6.9) by 2150 for the 1.5 °C warming level and a factor of 1.4 (0.9 to 2.4) for the 2.0 °C warming level compared to its first estimate in 2025. The median CO 2 -only carbon budget by 2150, relative to 2020, is 800 GtCO 2 for the 1.5 °C warming level and 2250 GtCO 2 for the 2.0 °C warming level. These median values exceed the median IPCC AR6 estimates by 60 % for the 1.5 °C warming level and 67 % for 2.0 °C. Some of the differences may be explained by the choice of the mitigation scenario for non-CO 2 radiative agents. Our simulations highlight shifts in carbon uptake dynamics under stabilized temperature, such as a cessation of the carbon sinks in the North Atlantic and in tropical forests. On the other hand, the Southern Ocean remains a carbon sink centuries after temperatures stabilize. Overall, this new type of warming-level-based emission-driven simulation offers a more coherent assessment across climate models and opens up a wide range of possibilities for studying both the carbon cycle and climate impacts, such as extreme events, under climate stabilization.
Spacecraft attitude determination and control is an important part of a spacecraft to achieve its designed mission. As of today, many spacecrafts have been successfully launched, and most of them have performed well as they were designed. Many research papers have been published to address the attitude determination and control design problems. Several text books are available for students to learn the technology and for engineers to use as references. The most popular spacecraft models for attitude determination algorithms and control design methods are the Euler angle models and the quaternion models . The Euler angle models have been proved very efficient as the linearized models are controllable, and all standard linear control system design methods are directly applicable. The drawbacks related to the Euler angle methods are (a) the designs based on linearized models may not globally stabilize the original nonlinear spacecraft, i.e., the design may not work when the attitude of the spacecraft is far away from the point where the linearization is performed; (b) the models depend on the rotational sequences, this can be error prone if several teams work on the same project and they use different rotational sequences; (c) for any rotational sequence, there is a singular point where the model is not applicable; and (d) since most attitude determination methods use quaternion to represent the spacecraft attitude, there is a need to transform quaternion into Euler angles. On the other hand, for quaternion models, people have found controllers that can globally stabilize nonlinear spacecraft systems; the models do not depend on rotational sequences and they have no singular point; and the quaternion is provided by attitude determination system and ready to use. The main problem with the quaternion model based control system design is that the linearized quaternion model is not controllable. Therefore, most published design methods heavily rely on Lyapunov functions for the nonlinear spacecraft system. But there is no systematic way to obtain a desired Lyapunov functions. Moreover, the Lyapunov function based designs focus on the closed-loop system stability but pay little attention to the closed-loop system performance. In a series of papers, the author proposed some reduced quaternion models which lead to some controllable linearized spacecraft models. Therefore, all standard linear system theory can be directly applied to analyze and design the spacecraft control systems. We showed that, in some cases, the designed control system is not only optimal for the linearized system, but also globally stabilize the original nonlinear system . Clearly, the reduced quaternion models do not depend on rotational sequences. Due to the special structure of the linearized spacecraft model, some most important design methods, such as LQR design and robust pole assignment design are very simple, enjoy the analytical solutions for some problems, have direct connection to the performance measures, such as settling time, rising time , and percentage of overshoot . All these features are attractive for high quality control system designs. The idea mentioned above is then extended to more spacecraft control problems using specific actuators such as magnetic torque bars and control momentum gyroscopes. These types of actuators may not provide exactly desired torques. Most existing methods use different conversions to get approximate solutions, meaning that these actuators may generate a torque close to but not equal to the desired one. Using the reduced quaternion models that incorporate the actuators into the system model, the control inputs are not torques but the operational parameters. The main benefit of this idea is that the control actions are not approximate but accurate. As all actuators have their operational limit, design with input constraints are also considered in this book by using recently developed interior-point optimization techniques. This book grows up from my research on the spacecraft attitude determination and control design methods in more than a decade which is focused on using reduced quaternion models because of their merits stated above. The book provides all necessary background materials on orbital dynamics, rotations and quaternion, frequently used reference frames, transformations between reference frames, space environment and disturbance torques, ephemeris astronomical vector calculations and measurement instruments, spacecraft control actuators and their models, so that the readers will get a global picture and can apply all these information into the spacecraft system modeling, attitude determination, and spacecraft control system designs, which is the main purpose of this book. This book is different from existing books in that we focus on quaternion based spacecraft control system designs and we consider only attitude control system design related problems, from spacecraft modeling, to attitude determination and estimation, to control system design method selection, to control algorithm development, and to the simulation of the control system designs. Moreover, this book addresses different attitude control tasks in the spacecraft life cycle, including spacecraft maneuver, orbit raising, attitude control, and rendezvous. Finally, this book emphasizes the state space design methods rather than the classical frequency design methods.
Evidence is presented that suggests there is a significant self-organized criticality (SOC) component in the dynamics of substorms in the magnetosphere. Observations of BBFs, fast flows, localized dipolarizations, plasma turbulence, etc. are taken to show that multiple localized reconnection sites provide the basic avalanche phenomenon in the establishment of SOC in the plasma sheet. First results are presented from a continuing plasma physical study of this avalanche process. A one-dimensional resistive MHD model of a magnetic field reversal is discussed. Resistivity, in this model, is self-consistently generated in response to the excitation of an idealized current-driven instability. When forced by convection of magnetic flux into the field reversal region, the model yields rapid magnetic field annihilation through a dynamic behavior that is shown to exhibit many of the characteristics of SOC. Over a large range of forcing strengths, the annihilation rate is shown to self-adjust to balance the rate at which flux is convected into the reversal region. Several analogies to magnetotail dynamics are discussed: (1) It is shown that the presence of a localized criticality in the model produces a remarkable stability in the global configuration of the field reversal while simultaneously exciting extraordinarily dynamic internal evolution. (2) Under steady forcing, it is shown that a loading-unloading cycle may arise that, as a consequence of the global stability, is quasi-periodic and, therefore, predictable despite the presence of internal turbulence in the field distribution. Indeed, it is shown that the global loading-unloading cycle is a consequence of the internal turbulence. (3) It is shown that, under steady, strong forcing the loading-unloading cycle vanishes. Instead, a recovery from a single unloading persists indefinitely. The field reversal is globally very steady while internally it is very dynamic as field annihilation goes on at the rate necessary to match the strong forcing. From this result we speculate that steady magnetospheric convection events result when the plasma sheet has been driven close to criticality over an extended spatial domain. During these events, we would expect to find localized reconnection sites distributed over the spatial domain of near criticality and we would expect to find plasma sheet transport in that domain to be closely related to that of BBF and fast flow events.
Sufficient conditions for global stability of a buck regulator using a discrete control law are found. The method of paired systems and Liapunov functions are used to establish global stability and to study the convergence of the regulator. A heuristic argument is given that the optimal switching curves associated with the paired continuous systems approximate the optimal switching curves of the discrete systems.
Global stability robustness with respect to unmodeled dynamics, arbitrary bounded internal noise, as well as external disturbance is shown to exist for a class of discrete-time adaptive control systems when the regressor vectors of these systems are persistently exciting. Although fast adaptation is definitely undesirable, so far as attaining the greatest amount of global stability robustness is concerned, slow adaptation is shown to be not necessarily beneficial. The entire analysis in this paper holds for systems with slowly varying return difference matrices; the plants in these systems need not be slowly varying.
The paper reports on high-resolution millimeter-wave spectroscopic observations of Io carried out in 1990 and 1991 which allowed the first unambiguous ground-based detection of SO2 in Io's atmosphere. A reassessment of the IRIS-Voyager observations of the nu3 band of SO2 is presented, and it is shown that non-LTE effects are important in the formation of this band. It is thus concluded that the global SO2 atmosphere observed from earth has characteristics (pressure, temperature) similar to those observed at Loki by Voyager. The paper concludes with a simple thermal model of Io's lower atmosphere and a discussion of new upper limits that can be placed on the presence of H2S, SO, and CO in Io's atmosphere.
The stability characteristics of dynamic dissipative compensators are investigated for multibody flexible space structures having nonlinear dynamics. The problem addressed is that of proving asymptotic stability of dynamic dissipative compensators. The stability proof uses the Liapunov approach and exploits the inherent passivity of such systems. For such systems these compensators are shown to be robust to parametric uncertainties and unmodeled dynamics. The results are applicable to a large class of structures such as flexible space structures with articulated flexible appendages.
Homoclinic and heteroclinic connections associated with unstable periodic orbits structure the global transport phenomena in phase space.
Methods and algorithms used for the simulation of elementary power conditioning units buck, boost, and buck-boost, as well as shunt PWM are described. Definitions are given of similar converters and reduced parameters. The various parts of the simulation to be carried out are dealt with; local stability, corrective network, measurements of input-output impedance and global stability. A simulation example is given.
A stability margin evaluation method in terms of simultaneous gain and phase changes in all loops of a multiloop system is presented. A universal gain-phase margin evaluation diagram is constructed by generalizing an existing method using matrix singular value properties. Using this diagram and computing the minimum singular value of the system return difference matrix over the operating frequency range, regions of guaranteed stability margins can be obtained. Singular values are computed for a wing flutter suppression and a drone lateral attitude control problem. The numerical results indicate that this method predicts quite conservative stability margins. In the second example if the eigenvalue magnitude is used instead of the singular value, as a measure of nearness to singularity, more realistic stability margins are obtained. However, this relaxed measure generally cannot guarantee global stability.
A linear stability analysis provides the basis for an analysis of the effects of prescribed changes upon the global stability characteristics of a bluff body wake. The analysis is applied in particular to the problem of placing a small cylinder in the wake of a larger one in order to suppress the vortex street. A prediction of the alteration in the critical Reynolds number of the system as a function of the location of the second cylinder relative to the first is presented and is shown to compare favorably with experimental results. The effect upon shedding frequency is also considered. The approach relies on the solution of an adjoint eigenvalue problem and an inhomogeneous adjoint boundary value problem. These adjoint solutions are shown to be a key component in the analysis of a variety of wake control strategies.
The recent Assessment of Standard Operating Procedures for OzoneSondes (ASOPOS 2.0; WMO/GAW Report #268) addressed questions of homogeneity and long-term stability in global electrochemical concentration cell (ECC) ozone sounding network time series. Among its recommendations was adoption of a standard for evaluating data quality in ozonesonde time series. Total column ozone (TCO) derived from the sondes compared to TCO from Aura’s Ozone Monitoring Instrument (OMI) is a primary quality indicator. Comparisons of sonde ozone with Aura’s Microwave Limb Sounder (MLS) are used to assess the stability of stratospheric ozone. This paper provides a comprehensive examination of global ozonesonde network data stability and accuracy since 2004 in light of the sudden post-2013 TCO “dropoff” of ~3-4% that was reported previously at select stations (Stauffer et al., 2020). Comparisons with Aura OMI TCO averaged across the network of 60 stations are stable within about ±2% over the past 18 years. Sonde TCO has similar stability compared to three other TCO satellite instruments, and the stratospheric ozone measurements average to within ±5% of MLS from 50 to 10 hPa. Thus, sonde data are reliable for trends, but with a caveat applied for a subset of dropoff stations in the tropics and subtropics. The dropoff is associated with only one of two major ECC instrument types. A detailed examination of ECC serial numbers pinpoints the timing of the dropoff. However, we find that overall, ozonesonde data are stable and accurate compared to independent measurements over the past two decades.
In 1975 Gerard O Neill published in the journal Science a model for the construction of solar power satellites. He found that the solar power satellites suggested by Peter Glaser would be too massive to launch economically from Earth, but could be financially viable if the workforce was permanently located in free space habitats and if lunar and asteroid materials were used for construction. All new worldwide electrical generating capacity could be then achieved by solar power satellites. The project would financially break even in about 20 years after which it would generate substantial income selling power below fossil fuel prices. Two NASA / Stanford University led studies at Ames Research center during the summers of 1974 and 1976 found the concept technically sound and developed a detailed financial parametric model. Although the project was not undertaken when suggested in the 1970s, several contemporary issues make pursuing the O Neill -- Glaser concept more compelling today. First, our analysis suggests that if in the first ten years of construction that small habitats (compared to the large vista habitats envisioned by O Neill) supporting approximately 300 people were utilized, development costs of the program and the time for financial break even could be substantially improved. Second, the contemporary consensus is developing that carbon free energy is required to mitigate global climate change. It is estimated that 300 GW of new carbon free energy would be necessary per year to stabilize global atmospheric carbon. This is about 4 times greater energy demand than was considered by the O Neill Glaser model. Our analysis suggests that after the initial investments in lunar mining and space manufacturing and transportation, that the profit margin for producing space solar power is very high (even when selling power below fossil fuel prices). We have investigated the financial scaling of ground launched versus space derived space solar power satellites. We find that for the carbon mitigation case even modernized ground launched space solar power satellites are not financially viable. For space derived solar power satellites, however, the increased demand makes them break even substantially sooner and yield much higher profit. Third, current awareness is increasing about the dangers of humanity remaining a single planet species. Our technological power has been increasing relative to the size of the planet Earth. Since the middle of the 20th century our technological power has grown large relative to our planet's size. This presents a very real potential for human self-extinction. We argue that the potential for human self-extinction is increasing with time in proportion to the exponential growth of our technological power making self-extinction likely within this century if humanity remains a single planet species. The O Neill model of multiple independent free space habitats, it is argued, can protect humanity from extinction in the same way that portfolio diversification protects ones assets from total loss. We show that about 1 million people for the electricity only case, and about 1 billion people for the carbon mitigation case, can be provided with permanent space habitats and transportation from Earth in 30 years and can be funded by the space derived solar power satellite program. 1.2 Scope of this Chapter The goal of this chapter is to illustrate the power and importance of the O'Neill-Glaser concept in the context of human survival and maintaining a healthy planet Earth. We argue that at this point in human history our technological power is too dangerous to our selves and our home planet for us not to expand into space. We show by the models presented in the chapter that the imminent dangers of global warming and human self-extinction mandate that humanity move aggressively into the solar system in this generation. We show that the production of solar power satellites using space resources and with a work foe living in space provides a viable financial model to mitigate CO2 preventing the worst global warming scenarios, and safeguards humanity against self-extinction by providing hundreds of habitats and a billion people living in space within about 35 years. To accomplish this goal we need only consider the classic O'Neill-Glaser model which was parameterized for 1970's technological projections. Only habitat size optimization for the first ten years of production is added. This is a conservative approach since the innovations of the last 30 years will make the financial projections more favorable. However, the classic O'Neill-Glaser model represented a broad technological consensus. The model is well documented in the references and our calculations can be easily reproduced In this chapter the economics of the O Neill - Glaser model is compared with models that rely exclusively on Earth launched materials. Although many studies of Earth launched Solar Power Satellites have been made, we found that the NASA "Fresh Look Study" was the most comprehensive and well documented. It also provided one of the most optimistic Earth launch financial projections. We thus chose it for comparison purposes.
The problem of vibration suppression in segmented reflector telescopes is considered. The decomposition of the structure into smaller components is discussed, and control laws for vibration suppression as well as conditions for stability at the local level are derived. These conditions and the properties of the interconnecting patterns are then utilized to obtain sufficient conditions for global stability.