An Efficient Algorithm for Computing the Low-thrust Escape Trajectory
An Efficient Algorithm for Computing the Low-thrust Escape Trajectory

Author: John A. Gall

Publisher:

Published: 2004

Total Pages: 122

ISBN-13:

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An algorithm to improve the computational efficiency of the low-thrust escape trajectory is developed. The algorithm reduces computational effort while maintaining accuracy, making it desirable for use in computing optimal escape trajectory by direct method. As low-thrust ionic propulsion engines are considered for use in interplanetary missions, design and planning includes the optimization of the spacecraft trajectory. The low-thrust escape phase evolves in the form of a slowly unwinding spiral. The computational expense required to accurately propagate the dense spiraling trajectory of the planetocentric escape phase through the numerical integration of the ordinary differential equations is undesirable. Implementation of an algorithm that approximates the trajectory while maintaining accuracy and improving computational efficiency is beneficial. The algorithm developed is demonstrated with the optimization of a sample Earth-escape trajectory. An inexpensive trajectory calculation with little error is produced.

Escape Trajectories for Low Thrust Vehicles
Escape Trajectories for Low Thrust Vehicles

Author: John Joseph Dell

Publisher:

Published: 1962

Total Pages: 117

ISBN-13:

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The escape parameters (time, range angle and position) are studied for achieving optimum escape missions using low-thrust vehicle . Results are compared with previously reported analytical and numerical calculations. The equations of motion in addition to Euler-Lagrange optimization equations were solved using an IBM 7090 Low-Thrust Digital Computer Program. Specific impulses were varied from 1,000 to 25,000 sec and electrical power outputs were varied from 100 KW to 100 MW. Planar orbits initially circular) were assumed. Results of the parametric investigation are presented both in tabular and graphical form. Analy is of generated escape data indicate that the analytical equations previously reporte have deviations ranging from approximately -25% to 44%. Numerical results previously reported are in general agreement with this study. (Author).

Fast Interplanetary Missions with Low-thrust Propulsion Systems
Fast Interplanetary Missions with Low-thrust Propulsion Systems

Author: W. E. Moeckel

Publisher:

Published: 1961

Total Pages: 40

ISBN-13:

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A simple family of indirect-transfer trajectories between circular orbits is used to evaluate the mass ratio required to complete round-trip interplanetary missions using low-thrust propulsion systems. These trajectories, although not optimum, yielded very substantial reductions in total round-trip time for Mars missions with moderate increases in initial weight. For a powerplant specific weight [alpha] of 10 pounds per kilowatt of jet power, trip times were reduced from 1200 to 600 days, for a typical manned mission, with an initial weight increase of a factor of two. Comparison with a nuclear rocket with 1000-second specific impulse indicated that the electric-propulsion system required less initial weight for trip times as low as 550 days with [alpha]=10 and as low at 400 days with [alpha]=5 pounds per kilowatt. Further weight reductions would be expected with more nearly optimum trajectories.

Optimal Control with Aerospace Applications
Optimal Control with Aerospace Applications

Author: James M Longuski

Publisher: Springer Science & Business Media

Published: 2013-11-04

Total Pages: 286

ISBN-13: 1461489458

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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!

Spacecraft Trajectory Optimization
Spacecraft Trajectory Optimization

Author: Bruce A. Conway

Publisher: Cambridge University Press

Published: 2010-08-23

Total Pages: 313

ISBN-13: 113949077X

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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.