Attitude control requirements for various solar sail missions

The differences are summarized between the attitude control requirements for various types of proposed solar sail missions (Earth orbiting; heliocentric; asteroid rendezvous). In particular, it is pointed out that the most demanding type of mission is the Earth orbiting one, with the solar orbit case quite benign and asteroid station keeping only slightly more difficult. It is then shown, using numerical results derived for the British Solar Sail Group Earth orbiting design, that the disturbance torques acting on a realistic sail can completely dominate the torques required for nominal maneuvering of an 'ideal' sail. This is obviously an important consideration when sizing control actuators; not so obvious is the fact that it makes the standard rotating vane actuator unsatisfactory in practice. The reason for this is given, and a set of new actuators described which avoids the difficulty

Model reduction for Space Station Freedom

Model reduction is an important practical problem in the control of flexible spacecraft, and a considerable amount of work has been carried out on this topic. Two of the best known methods developed are modal truncation and internal balancing. Modal truncation is simple to implement but can give poor results when the structure possesses clustered natural frequencies, as often occurs in practice. Balancing avoids this problem but has the disadvantages of high computational cost, possible numerical sensitivity problems, and no physical interpretation for the resulting balanced 'modes'. The purpose of this work is to examine the performance of the subsystem balancing technique developed by the investigator when tested on a realistic flexible space structure, in this case a model of the Permanently Manned Configuration (PMC) of Space Station Freedom. This method retains the desirable properties of standard balancing while overcoming the three difficulties listed above. It achieves this by first decomposing the structural model into subsystems of highly correlated modes. Each subsystem is approximately uncorrelated from all others, so balancing them separately and then combining yields comparable results to balancing the entire structure directly. The operation count reduction obtained by the new technique is considerable: a factor of roughly r(exp 2) if the system decomposes into r equal subsystems. Numerical accuracy is also improved significantly, as the matrices being operated on are of reduced dimension, and the modes of the reduced-order model now have a clear physical interpretation; they are, to first order, linear combinations of repeated-frequency modes

Model reduction results for flexible space structures

This paper describes the novel subsystem balancing technique for obtaining reduced-order models of flexible structures, and investigates its properties fully. This method can be regarded as a combination of the best features of modal truncation (efficiency) and internal balancing (accuracy); it is particularly well suited to the typical practical case of structures which possess clusters of close modes. Numerical results are then presented demonstrating the results obtained by applying subsystem balancing to the Air Force Phillips Laboratory ASTREX testbed, the Jet Propulsion Laboratory antenna facility, and the NASA Marshall Space Flight Center ACES structure

Designing a Measure of Effectiveness for Exhibits Communicating Evolutionary Theory at the Sternberg Museum of Natural History

Specifically addressing and refuting common misconceptions about evolution is still a relatively new approach in education; this style of learning remains largely untested in adults outside of a classroom setting. As informal places of learning, natural history museums are the most likely environment for the general public to learn about evolutionary theory and test their misconceptions with scientific observation. Few natural history museums have evaluated their exhibits’ ability to explain evolutionary processes in a way that encourages scientific thought and addresses common misconceptions about evolutionary theory. A two-part (pre and post) survey was constructed to evaluate the educational effectiveness of the “Rattlers” and “Bringing Fossils to Life” exhibits at the Sternberg Museum of Natural History (FHSM). Both exhibits use live animals to contextualize evolutionary processes such as: (1) predator-prey relationships; (2) convergence; (3) life on land; and (4) extinction. In future research, this survey will be utilized in the first formal evaluation of educational effectiveness in FHSM exhibits by comparing the conceptual models utilized by visitors before and after seeing the exhibits. Results will provide feedback for the museum and further evidence for the usefulness of surveys in evaluating effectiveness of museum exhibits in adult education of evolutionary theory

Combinatorial Games on Graphs

Combinatorial games are intriguing and have a tendency to engross students and lead them into a serious study of mathematics. The engaging nature of games is the basis for this thesis. Two combinatorial games along with some educational tools were developed in the pursuit of the solution of these games. The game of Nim is at least centuries old, possibly originating in China, but noted in the 16th century in European countries. It consists of several stacks of tokens, and two players alternate taking one or more tokens from one of the stacks, and the player who cannot make a move loses. The formal and intense study of Nim culminated in the celebrated Sprague-Grundy Theorem, which is now one of the centerpieces in the theory of impartial combinatorial games. We study a variation on Nim, played on a graph. Graph Nim, for which the theory of Sprague-Grundy does not provide a clear strategy, was originally developed at the University of Colorado Denver. Graph Nim was first played on graphs of three vertices. The winning strategy, and losing position, of three vertex Graph Nim has been discovered, but we will expand the game to four vertices and develop the winning strategies for four vertex Graph Nim. Graph Theory is a markedly visual field of mathematics. It is extremely useful for graph theorists and students to visualize the graphs they are studying. There exists software to visualize and analyze graphs, such as SAGE, but it is often extremely difficult to learn how use such programs. The tools in GeoGebra make pretty graphs, but there is no automated way to make a graph or analyze a graph that has been built. Fortunately GeoGebra allows the use of JavaScript in the creation of buttons which allow us to build useful Graph Theory tools in GeoGebra. We will discuss two applets we have created that can be used to help students learn some of the basics of Graph Theory. The game of thrones is a two-player impartial combinatorial game played on an oriented complete graph (or tournament) named after the popular fantasy book and TV series. The game of thrones relies on a special type of vertex called a king. A king is a vertex, k, in a tournament, T, which for all x in T either k beats x or there exists a vertex y such that k beats y and y beats x. Players take turns removing vertices from a given tournament until there is only one king left in the resulting tournament. The winning player is the one which makes the final move. We develop a winning position and classify those tournaments that are optimal for the first or second-moving player

Our Shared Space and Threat Without Exit

Globalization is fraught with dangers due to institutional relationships that threaten humanity. These institutions, acting in unaware-concert, provide a looming danger for everyone in 21st century life. Humanity has created the threatening context; humanity bears the responsibility for its remedy. This is known as “world risk society” (Beck, 2009). The threat is all encompassing, grounded in material limits; no human is exempt from the danger. People can use these two features as fuel to politically engage and create meaningful change. It is this political context that requires generating everybody’s political will all the way from the heads of state to the average citizen.This fictitious slam poetry piece seeks to generate political will within the reader. The “Reflections from 2013” are meant to emphasize the role of “manufactured uncertainties” (2009)—the human-made risky elements of globalization-- which create a pressure within the reader as they travel from the present into the four possible futures. The order of the futures is intentionally designed to increasingly generate a sense of political will as the reader progresses from the most structurally unsustainable future (Future I) to the most sustainable future (Future IV). The movement of the piece is a transition from the possibility of destruction to the possibility of adapting to a life affirming way of organization in the end.Stories do not reveal how the future will go, only how it could go.Stories do not unpack ideas in linear form. Rather, they allow for the reader to encounter embodied ideas.Faculty Sponsor: Sherrie Steine

The Chilcot report and the law

Questions of law permeate the Chilcot Report. All are shrouded in uncertainty. From the constitutional relationship between Prime Minister, his Cabinet and Parliament to the legality of going to war, the Inquiry presided over by Sir John Chilcot touched upon many controversial legal issues. It resolved none. But then, it was not a court of law or a judicial inquiry and never pretended to be. No one could have reasonably expected it to pronounce with conviction any judgement on the lawfulness of acts and decisions made by those who took the UK to war in Iraq. Instead, the Report provides information useful for those who wish to reach such judgements. Lawyers are already searching the vast document to inspire possible litigation, though that was not the concern of the Inquiry. It was supposed to determine what happened and learn lessons. Those were its very broad terms of reference. But did the Inquiry deal effectively or properly with the legal issues which framed many of the decisions and actions it examined? In this article I look briefly at two key areas where law had particular relevance but, it is argued, received insufficient attention: the legal basis for going to war; and the conduct of the occupation after the initial hostilities were concluded. Both involve the application of international legal standards, a slippery subject for those seeking exactitude but valuable for judging the political and military leaders nonetheless

Space Station flexible dynamics under plume impingement

Assembly of the Space Station requires numerous construction flights by the Space Shuttle. A particularly challenging problem is that of control of each intermediate station configuration when the shuttle orbiter is approaching it to deliver the next component. The necessary braking maneuvers cause orbiter thruster plumes to impinge on the station, especially its solar arrays. This in turn causes both overall attitude errors and excitation of flexible-body vibration modes. These plume loads are predicted to lead to CMG saturation during the approach of the orbiter to the SC-5 station configuration, necessitating the use of the station RCS jets for desaturation. They are also expected to lead to significant excitation of solar array vibrations. It is therefore of great practical importance to investigate the effects of plume loads on the flexible dynamics of station configuration SC-5 as accurately as possible. However, this system possesses a great many flexible modes (89 below 5 rad/s), making analysis time-consuming and complicated. Model reduction techniques can be used to overcome this problem, reducing the system model to one which retains only the significant dynamics, i.e. those which are strongly excited by the control inputs or plume disturbance forces and which strongly couple with the measured outputs. The particular technique to be used in this study is the subsystem balancing approach which was previously developed by the present investigator. This method is very efficient computationally. Furthermore, it gives accurate results even for the difficult case where the structure has many closed-spaced natural frequencies, when standard modal truncation can give misleading results. Station configuration SC-5 is a good example of such a structure