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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
Approximate analytical solutions were derived for the problem of low thrust propulsion, in the case of constant thrust, set at a constant angle to the velocity vector, for any type of initial orbit (elliptic, parabolic or hyperbolic). Simple expressions were obtained, giving energy, angular momentum and excentricity in terms of the excentric anomaly. The solutions allow for calculation of the fuel consumption. Their validity is restricted to the field of orbit correction. (Author).
A collection of analytical studies is presented related to unconstrained and constrained aircraft (a/c) energy-state modeling and to spacecraft (s/c) motion under continuous thrust. With regard to a/c unconstrained energy-state modeling, the physical origin of the singular perturbation parameter that accounts for the observed 2-time-scale behavior of a/c during energy climbs is identified and explained. With regard to the constrained energy-state modeling, optimal control problems are studied involving active state-variable inequality constraints. Departing from the practical deficiencies of the control programs for such problems that result from the traditional formulations, a complete reformulation is proposed for these problems which, in contrast to the old formulation, will presumably lead to practically useful controllers that can track an inequality constraint boundary asymptotically, and even in the presence of 2-sided perturbations about it. Finally, with regard to s/c motion under continuous thrust, a thrust program is proposed for which the equations of 2-dimensional motion of a space vehicle in orbit, viewed as a point mass, afford an exact analytic solution. The thrust program arises under the assumption of tangential thrust from the costate system corresponding to minimum-fuel, power-limited, coplanar transfers between two arbitrary conics. The thrust program can be used not only with power-limited propulsion systems, but also with any propulsion system capable of generating continuous thrust of controllable magnitude, and, for propulsion types and classes of transfers for which it is sufficiently optimal the results of this report suggest a method of maneuvering during planetocentric or heliocentric orbital operations, requiring a minimum amount of computation; thus uniquely suitable for real-time feedback guidance implementations. Markopoulos, Nikos and Calise, Anthony J. Unspecified Center AIRCRAFT GUIDANCE; CONTROLLERS; FLIGHT PATHS; OPTIMAL CONTROL...
Advanced Problems and Methods for Space Flight Optimization presents the optimization theory and its application to space flight. This book covers a wide range of topics, including optimal guidance, general mathematical methods of optimization, optimal transfer trajectories, and optimization of design parameters. Organized into 15 chapters, this book begins with an overview of the approximate analytic solution developed for minimum fuel guidance from an arbitrary point on a hyperbolic orbit into a definite circular orbit. This text then determines the maximum range trajectory for a glider entering the Earth's atmosphere at a supercircular velocity. Other chapters consider the economical transfers between Keplerian orbits, which has made considerable progress in the time-free case. This book discusses as well the Pontryagin Maximum Principle used to determine the optimal transfers between arbitrary coaxial ellipses. The final chapter deals with the synthesis of minimum-fuel controls for a class of aerospace control problems. This book is a valuable resource for aerospace engineers.