Download or read book MINIMUM FUEL THRUST LIMITED TRANSFER TRAJECTORIES BETWEEN COPLANAR ELLIPTIC ORBITS written by Edward Adolph Kern and published by . This book was released on 1968 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: A method is developed for the efficient computation of minimum-fuel transfer trajectories between coplanar elliptic orbits with a thrust-limited variable-mass rocket moving in a central gravitation force field. Each orbit is defined through the eccentricity, semi-latus rectum, and argument of pericenter. Transfer time is left open. The minimum-fuel trajectory is assumed to consist of two thrusting phases separated by a coasting phase. Computation of the minimum-fuel transfer trajectory is accomplished by a direct integration of the rocket equations of motion and the associated adjoint equations which are developed from variational calculus techniques. This direct approach is made possible by a unique transformation of the adjoint equations into a set of equations which provide a much better understanding of the general behavior of minimum-fuel transfer trajectories. Reasonable estimates of the thrusting interval durations, initial thrust angle, and initial true anomaly are derived from the corresponding minimum-fuel, two-impulse transfer trajectory. The initial value of a newly discovered variable is used in conjunction with the initial thrust angle to obtain the thrusting interval durations specified by the two-impulse transfer. (Author).
Download or read book Improved Initial Value Estimates for Minimum Fuel Orbital Transfers written by Daniel E. Gill and published by . This book was released on 1969 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A method is developed for computing improved initial-value estimates for minimum-fuel transfer trajectories between coplanar, elliptic orbits with a thrust-limited, variable-mass rocket moving in an inverse square-law gravitational field. The initial and final orbits are specified by their eccentricities, semilateral recta and arguments of pericenter and the entire transfer consists of two finite-thrust phases. Estimates for the parameters of the optimal transfer trajectory are provided by the two-impulse solution and the techniques presented in this study provide good estimates for the unknown initial values of unspecified control, state and adjoint variables which are required to successfully compute the minimum-fuel transfer trajectory between specified orbits. (Author).
Download or read book Investigation of Minimum Fuel Limited Thrust Orbital Transfer Trajectories written by Harold Dean Childers and published by . This book was released on 1969 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of quasilinearization is applied to the solution of a system of lumped-parameter differential equations providing the necessary conditions for minimum-fuel finite-thrust transfers between coplanar orbits. A central gravitational field is assumed. The equations are derived from the basic equations describing the motion of a finite-thrust rocket. The method of optimization (a modification of quasilinearization for application to bang-bang control problems), and the computer program used to solve the problem are discussed. The method is found to be inapplicable to the problem as originally formulated, and reasons for the inapplicability are given. A new formulation is presented, and computer programming techniques relevant to its solution are discussed. A printout of the program is included. (Author).
Download or read book Minimum fuel Power limited Transfers Between Coplanar Elliptic Orbits written by Christine M. Haissig and published by . This book was released on 1992 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Minimum fuel Transfers Between Coaxial Orbits Both Coplanar and Concoplanar written by Stanford University. Department of Aeronautics and Astronautics and published by . This book was released on 1967 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1972 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nearly Circular Transfer Trajectories for Descending Satellites written by George M. Low and published by . This book was released on 1959 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simplified expressions describing the transfer from a satellite orbit to the point of atmospheric entry are derived. The expressions are limited to altitude changes that are small compared with the earth's radius, and velocity changes that are small compared with satellite velocity. They are further restricted to motion about a spherical, nonrotating earth. The transfer trajectory resulting from the application of thrust in any direction at any point in an elliptic orbit is considered. Expressions for errors in distance (miss distance) and entry angle due to an initial misalinement and magnitude error of the deflecting thrust are presented. The guidance and accuracy requirements to establish a circular orbit, and orbit corrections are also discussed.
Download or read book Investigation of Minimum fuel Limited thrust Orbital Transfer Trajectories written by Harold Dean Childers (CAPT, USAF.) and published by . This book was released on 1969 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Transfers Between Close Elliptical Orbits written by Jean Pierre Marec and published by . This book was released on 1969 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Minimum impulse Time free Transfer Between Elliptic Orbits written by Frank W. Gobetz and published by . This book was released on 1966 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Control with Aerospace Applications written by James M Longuski and published by Springer Science & Business Media. This book was released on 2013-11-04 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Want to know not just what makes rockets go up but how to do it optimally? Optimal control theory has become such an important field in aerospace engineering that no graduate student or practicing engineer can afford to be without a working knowledge of it. This is the first book that begins from scratch to teach the reader the basic principles of the calculus of variations, develop the necessary conditions step-by-step, and introduce the elementary computational techniques of optimal control. This book, with problems and an online solution manual, provides the graduate-level reader with enough introductory knowledge so that he or she can not only read the literature and study the next level textbook but can also apply the theory to find optimal solutions in practice. No more is needed than the usual background of an undergraduate engineering, science, or mathematics program: namely calculus, differential equations, and numerical integration. Although finding optimal solutions for these problems is a complex process involving the calculus of variations, the authors carefully lay out step-by-step the most important theorems and concepts. Numerous examples are worked to demonstrate how to apply the theories to everything from classical problems (e.g., crossing a river in minimum time) to engineering problems (e.g., minimum-fuel launch of a satellite). Throughout the book use is made of the time-optimal launch of a satellite into orbit as an important case study with detailed analysis of two examples: launch from the Moon and launch from Earth. For launching into the field of optimal solutions, look no further!
Download or read book Minimum Fuel Continuous Low Thrust Orbital Transfer written by Eugene A. Smith and published by . This book was released on 1974 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minimum fuel continuous low thrust orbit transfer is an optimal control problem which requires the application of iterative numerical methods to solve the resulting two point boundary value problem. A combination gradient- neighboring extremal algorithm gives accurate results when both the initial and terminal orbits are coplanar. These results are then used to extend the problem to include out-of-plane transfers between orbits of widely varying inclination. Control histories, in terms of thrust direction, are plotted as a function of time for both coplanar and non-coplanar transfers. Steering programs for coplanar transfers are characterized by a rapid thrust reversal which is dependent on eccentricity for the time of its occurrence. In the latter case, out-of-plane thrusting is primarily a function of the inclination change between orbits. On the basis of these results, the particular numerical approach used provides an effective method for generating optimal low thrust orbital transfer guidance.
Download or read book Some Necessary Conditions for Time Optimal Fixed Fuel Transfers Between Coplanar Orbits written by Ronald C. Tubbs and published by . This book was released on 1971 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some necessary conditions in terms of the state and costate variables are derived for time-optimal, thrust-coast-thrust (TCT) trajectories between coplanar, cofocal orbits in an inverse-square gravitational field. Assuming impulsive thrusting, the transfer trajectories are determined by solving a quartic polynomial in the square root of the semi-latus rectum of the transfer orbit. The IBM 7094 digital computer was programmed to solve the polynomial and isolate the root leading to the optimal trajectory. Final mass to initial mass ratios are specified, and initial mass is taken as unity. The necessary conditions are derived using plots of constant mass contours in the transfer angle vs. transfer time plane. The conditions are intended to indicate when the TCT trajectory is not optimal and should be replaced by another type of trajectory, such as coast-thrust-coast-thrust (CTCT) or thrust-coast-thrust-coast (TCTC). (Modified author abstract).
Download or read book Discontinuous Low Thrust Orbit Transfer written by and published by . This book was released on 1983 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines the use of discontinuous low thrust for orbital transfers between two non-coplanar, circular orbits. The vehicle is assumed to be a solar-powered, ion rocket that cannot operate when it is within the earth's shadow. Two timescales are used to derive a minimum fuel trajectory. The fast timescale solution maximizes a change in inclination when given a change in semi-major axis for a single orbit. The slow timescale solution combines fast timescale results to obtain the minimum fuel trajectory. Results are presented for three specific transfers requiring varying amounts of shadow penetration. It is shown that the fuel penalty caused by discontinuous thrust is small. However, there can be a moderate increase in total trip time if the time within the shadow is large.
Download or read book An Asymptotic Solution for Optimum Power limited Orbit Transfer written by Theodore N. EDELBAUM and published by . This book was released on 1965 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete first-order asymptotic solution was obtained for optimum power-limited transfer between coplanar elliptic orbits of arbitrary size, eccentricity, and orientation. The solution was obtained by the averaging method of Bogoliubov and Mitropolsky and corresponds to what they call 'the improved first approximation' including both secular and short-period terms. The problem for which the solution is presented corresponds to minimum-fuel transfer in fixed time of a low-thrust rocket operating at constant power and variable thrust. The average acceleration of the rocket is assumed small in relation to the acceleration of gravity. Analytic expressions were derived for the orbit elements, the payoff, and the optimum control. (Author).
Download or read book A Collection of Technical Papers written by and published by . This book was released on 1969 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Notices of Changes in Classification Distribution and Availability written by and published by . This book was released on 1977 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
