Authoritative reference covering essential concepts of orbital mechanics and explaining how they relate to advanced space trajectory applications Space Trajectories is the first book to offer a comprehensive exploration of orbital mechanics and trajectory optimization in a single volume. Beginning with a review of essential concepts, the book progresses to advanced space applications, highlighting methods used in today's space missions. The contents are organized into three parts. The first part delves into free orbital motion, covering topics such as Keplerian motion, perturbed motion, the three-body problem, orbit determination, and collision risks in orbit. The second part focuses on controlled orbital motion, discussing impulsive transfer, orbital rendezvous, thrust level optimization, low-thrust transfer, and space debris cleaning. The third part examines ascent and reentry, including launch into orbit, launcher staging, analytical solutions in flat Earth, interplanetary missions, and atmospheric reentry. Each chapter is written in a modular way, featuring conclusion summaries, key points, and suggestions for further investigation. Examples are included with detailed solutions methods that readers can apply to solve their own trajectory problems. Written by an expert of the topic who has performed guidance of Ariane launchers for 30 years, Space Trajectories includes information on: Keplerian motion, motion time law, universal formulation, equinoctial parameters, and Lagrange coefficients Osculating orbit, Gauss equations, gravitational and third body perturbations, Lissajous and Halo orbits, and invariant manifolds Astrometry measurements, Kalman filtering, orbit uncertainties, and collision probability Transfer in one, two, or three impulses, minimum-energy transfer, Lambert's problem, high- and low-thrust transfer, and interplanetary path Launch and reentry trajectories, propulsion systems, optimized thrust profiles, and launcher staging Space Trajectories is an essential reference for students and researchers aiming to quickly understand the main issues in astrodynamics and the way to design trajectories, as well as space engineers seeking to consolidate their knowledge in the field of optimization and optimal control applied to aerospace and space missions.

Studies in Astronautics, Volume 1: Optimal Space Trajectories focuses on the concept of optimal transfer and the problem of optimal space trajectories. It examines the relative performances of the various propulsion systems (classical and electrical propulsions) and their optimization (optimal mass breakdown), along with parametric and functional optimizations and optimal transfers in an arbitrary, uniform, and central gravitational field. Organized into 13 chapters, this volume begins with an overview of optimal transfer and the modeling of propulsion systems. It then discusses the Hohmann transfer, the Hoelker and Silber bi-elliptical transfer, and the deficiencies of parametric optimization. The book explains the canonical transformation, optimization of the thrust law using the Maximum Principle, and optimal orbit corrections. The time-free orbital transfers and time-fixed orbital transfers and rendezvous are also discussed. Moreover, this volume explains the classical high-thrust and electric low-thrust propulsion systems and rendezvous between two planets. This book is written primarily for engineers who specialize in aerospace mechanics and want to pursue a career in the space industry or space research. It also introduces students to the different aspects of the problem of optimal space trajectories.

Space Trajectories covers the proceedings of a symposium sponsored by the American Astronautical Society, Advanced Research Projects Agency, and Radiation Incorporated, held on December 14-15, 1959. The book focuses on the field of trajectory analysis, including orbital and trajectory computations, tracking of satellites, and the use of computer programs in space missions. The selection first tackles satellite and probe orbit determination, general survey of the field, and astrodynamics, as well as theoretical, computational, and operational problems, application to lunar orbits, and contributions of satellite observations. The book then examines trajectory constants and trajectory computation and optimization. Discussions focus on the classical method of orbital computation, effect of uncertainty on interplanetary orbits, masses, diameter, and flattening of planets, and determination of the physical constants of the moon. The manuscript takes a look at trajectory computation and optimization, trajectory computation in systems design, and computer programs for space missions. Topics include simulation and targeting programs, satellite tracking methods, direct numerical integration, classical methods of orbital computation, and references on trajectory computation and optimization. Space-born computer design, space maneuvers, and re-entry trajectories and problems of hypersonic flow are also mentioned. The selection is a valuable source of data for astronauts and readers interested in space trajectories.

Reflecting the results of twenty years; experience in the field of multipurpose flights, this monograph includes the complex routes of the trajectories of a number of bodies (e.g., space vehicles, comets) in the solar system. A general methodological approach to the research of flight schemes and the choice of optimal performances is developed. Additionally, a number of interconnected methods and algorithms used at sequential stages of such development are introduced, which allow the selection of a rational multipurpose route for a space vehicle, the design of multipurpose orbits, the determination of optimal space vehicle design, and ballistic performances for carrying out the routes chosen. Other topics include the practical results obtained from using these methods, navigation problems, near-to-planet orbits, and an overview of proven and new flight schemes.

Analytical Solutions for Extremal Space Trajectories presents an overall treatment of the general optimal control problem, in particular, the Mayer's variational problem, with necessary and sufficient conditions of optimality. It also provides a detailed derivation of the analytical solutions of these problems for thrust arcs for the Newtonian, linear central and uniform gravitational fields. These solutions are then used to analytically synthesize the extremal and optimal trajectories for the design of various orbital transfer and powered descent and landing maneuvers. Many numerical examples utilizing the proposed analytical synthesis of the space trajectories and comparison analyses with numerically integrated solutions are provided. This book will be helpful for engineers and researchers of industrial and government organizations, and is also a great resource for university faculty and graduate and undergraduate students working, specializing or majoring in the fields of aerospace engineering, applied celestial mechanics, and guidance, navigation and control technologies, applied mathematics and analytical dynamics, and avionics software design and development. - Features an analyses of Pontryagin extremals and/or Pontryagin minimum in the context of space trajectory design - Presents the general methodology of an analytical synthesis of the extremal and optimal trajectories for the design of various orbital transfer and powered descent and landing maneuvers - Assists in developing the optimal control theory for applications in aerospace technology and space mission design

This is a long-overdue volume dedicated to space trajectory optimization. Interest in the subject has grown, as space missions of increasing levels of sophistication, complexity, and scientific return - hardly imaginable in the 1960s - have been designed and flown. Although the basic tools of optimization theory remain an accepted canon, there has been a revolution in the manner in which they are applied and in the development of numerical optimization. This volume purposely includes a variety of both analytical and numerical approaches to trajectory optimization. The choice of authors has been guided by the editor's intention to assemble the most expert and active researchers in the various specialities presented. The authors were given considerable freedom to choose their subjects, and although this may yield a somewhat eclectic volume, it also yields chapters written with palpable enthusiasm and relevance to contemporary problems.

A bold new spatial perspective on modern sculpture, with 800 color images of work by artists including Henry Moore, Lygia Clark, Anish Kapoor, and Ana Mendieta. This monumental, richly illustrated volume from ZKM | Karlsruhe approaches modern sculpture from a spatial perspective, interpreting it though contour, emptiness, and levitation rather than the conventional categories of unbroken volume, mass, and gravity. It examines works by dozens of twentieth- and twenty-first-century artists, including Hans Arp, Marcel Duchamp, Henry Moore, Barbara Hepworth, Lygia Clark, Anish Kapoor, Olafur Eliasson, Ana Mendieta, Fujiko Nakaya, Tomás Saraceno, and Alicja Kwade. The large-scale book contains over 800 color images. Negative Space comes out of an epic exhibition at ZKM, and volume editor Peter Weibel (Chairman and CEO of ZKM) takes a curatorial approach to the topic. The last exhibition to deal comprehensively with the question “What is modern sculpture?” was at the Centre Georges Pompidou in 1986. Weibel and ZKM pick up where the Pompidou left off, examining sculptures not as figurative, solid, and self-contained monoliths but in terms of open and hollow spaces; reflection, light, shadow; innovative materials; data; and the moving image. Weibel puts advances in science, architecture, and mathematics in the context of avant-garde sensibilities to show how modern sculpture significantly deviates from the work of the past. Texts in the volume include an introduction and twelve chapters written by Weibel with contributions by cocurators as well as facsimiles and reproductions of artist-authored manifestos.

A textbook on the theory and applications of optimal spacecraft trajectories

French sociologist and anthropologist Pierre Bourdieu’s relevance for studies of spatiality and mobility has received less attention than other aspects of his work. Here, Deborah Reed-Danahay argues that the concept of social space, central to Bourdieu’s ideas, addresses the structured inequalities that prevail in spatial choices and practices. She provides an ethnographically informed interpretation of social space that demonstrates its potential for new directions in studies of mobility, immobility, and emplacement. This book traces the links between habitus and social space across the span of Bourdieu’s writings, and places his work in dialogue with historical and contemporary approaches to mobility.