A Comparative Study of Liapunov Stability Analyses of Flexible Damped Satellites

A literal Liapunov stability analysis of a spacecraft with flexible appendages often requires a division of the associated dynamic potential into as many dependent parts as the number of appendages. First part of this paper exposes the stringency in the stability criteria introduced by such a division and shows it to be removable by a “reunion policy.” The policy enjoins the analyst to piece together the sets of criteria for each part. Employing reunion the paper then compares four methods of the Liapunov stability analysis of hybrid dynamical systems illustrated by an inertially coupled, damped, gravity stabilized, elastic spacecraft with four gravity booms having tip masses and a damper rod, all skewed to the orbital plane. The four methods are the method of test density function, assumed modes, and two and one-integral coordinates. Superiority of one-integral coordinate approach is established here. The design plots demonstrate how elastic effects delimit the satellite boom length.

Strategies for three dimensional deployment of tethered satellites

Tethered satellites deployed from the Space Shuttle have been proposed for diverse applications. A funda- mental issue in the utilization of tethers is quick deployment and retrieval of the attached payload. Inordinate librations of the tether during deployment and retrieval is undesirable. The structural damping present in the system is too low to contain the librations. Rupp [1] proposed to control the tether reel located in the parent spacecraft to alter the tension in the tether, which in turn changes the stiffness and the damping of the system. Baker[2] applied the tension control law to a model which included out of plane motion. Modi et al.[3] proposed a control law that included nonlinear feedback of the out-of plane tether angular rate. More recently, nonlinear feedback control laws based on Liapunov functions have been proposed. Two control laws are derived in [4]. The first is based on partial decomposition of the equations of motion and utilization of a two dimensional control law developed in [5]. The other is based on a Liapunov function that takes into consideration out-of-plane motion. It is shown[4] that the control laws are effective when used in conjunction with out-of-plane thrusting. Fujii et al.,[6] used the mission function control approach to study the control law including aerodynamic drag effect explicitly into the control algorithm.

Dissipativeness and Stability of a Class of Distributed Parameter Systems

Input-output stability of linear-distributed parameter systems of arbitrary order and type in the presence of a distributed controller is analyzed by extending the concept of dissipativeness, with certain modifications, to such systems. The approach is applicable to systems with homogeneous or homogenizable boundary conditions. It also helps in generating a Liapunov functional to assess asymptotic stability of the system.

Some recent results on the stability of linear time varying systems

Some theorems derived recently by the authors on the stability of multidimensional linear time varying systems are reported in this paper. To begin with, criteria based on Liapunov�s direct method are stated. These are followed by conditions on the asymptotic behaviour and boundedness of solutions. Finally,L 2 andL ? stabilities of these systems are discussed. In conclusion, mention is made of some of the problems in aerospace engineering to which these theorems have been applied.

Denumerable state stochastic games with limiting average payoff

We study stochastic games with countable state space, compact action spaces, and limiting average payoff. ForN-person games, the existence of an equilibrium in stationary strategies is established under a certain Liapunov stability condition. For two-person zero-sum games, the existence of a value and optimal strategies for both players are established under the same stability condition.

The top 100 questions of importance to the future of global agriculture

Despite a significant growth in food production over the past half-century, one of the most important challenges facing society today is how to feed an expected population of some nine billion by the middle of the 20th century. To meet the expected demand for food without significant increases in prices, it has been estimated that we need to produce 70-100 per cent more food, in light of the growing impacts of climate change, concerns over energy security, regional dietary shifts and the Millennium Development target of halving world poverty and hunger by 2015. The goal for the agricultural sector is no longer simply to maximize productivity, but to optimize across a far more complex landscape of production, rural development, environmental, social justice and food consumption outcomes. However, there remain significant challenges to developing national and international policies that support the wide emergence of more sustainable forms of land use and efficient agricultural production. The lack of information flow between scientists, practitioners and policy makers is known to exacerbate the difficulties, despite increased emphasis upon evidence-based policy. In this paper, we seek to improve dialogue and understanding between agricultural research and policy by identifying the 100 most important questions for global agriculture. These have been compiled using a horizon-scanning approach with leading experts and representatives of major agricultural organizations worldwide. The aim is to use sound scientific evidence to inform decision making and guide policy makers in the future direction of agricultural research priorities and policy support. If addressed, we anticipate that these questions will have a significant impact on global agricultural practices worldwide, while improving the synergy between agricultural policy, practice and research. This research forms part of the UK Government's Foresight Global Food and Farming Futures project.