This book presents a theoretical background to the new discipline of space flight mechanics. This discipline aims at simultaneously solving the problems of selecting the optimum weight parameters of a spacecraft, the optimum control functions of its propulsion system, and the optimum flight trajectories which ensure delivery of a maximum payload. The necessity for a simultaneous treatment of these three problems stems from the high relative weight and the wide possibilities of adjusting parameters for conceivable types of space propulsion systems including chemical (at high thrust-to-weight ratios), thermonuclear, and electric propulsion engines.The main sections are illustrated with examples of the characteristics for flight to the solar-system planets, maneuvers of guided satellites, and flight inhomogeneous gravitational fields; these examples elucidate the requirements which the propulsion systems must meet, and the possibilities of achieving space flight.The book is intended for scientists, engineers, and graduate students. It is assumed that the reader is familiar with the fundamentals of variational calculus; however, one may use the basic results given in the book even if the sections devoted to variational calculus are omitted.(Mekhanika kosmicheskogo poleta s maloi tyagoi)Izdatel'stvo "Nauka"Glavnaya RedaktsiyaFiziko-Matematicheskoi LiteraturyMoskva 1966Translated from RussianIsrael Program for Scientific TranslationsTtanslated by A. Baruch , M.Sc.Edited by Dr. Y. M. Timnat and IPST StaffPREFACEINTRODUCTIONPart I PHYSICAL PRINCIPLES AND GENERALIZED PARAMETERS OF SPACE PROPULSION SYSTEMS1. BASIC PARAMETERS AND LAYOUT OF SPACE PROPULSION SYSTEMS2. PHYSICAL PRINCIPLES OF THE ELEMENTS OF SPACE PROPULSION SYSTEMS3. GENERALIZED PARAMETERS OF SPACE PROPULSION SYSTEMSPart II PROBLEMS OF OPTIMIZATION4. IDEAL POWER-LIMITED ENGINE. SEPARATION OF THE VARIATIONAL PROBLEM. OPTIMUM WEIGHT RATIOS5. IDEAL POWER-LIMITED ENGINE. OPTIMUM PROGRAMS OF THRUST ACCELERATION6. UNTHROTTLED ENGINES. SEPARATION OF THE VARIATIONAL PROBLEM. OPTIMUM PROGRAMS OF THE THRUST VECTOR7. REAL POWER-LIMITED ENGINES8. ENGINES WITH LIMITED EXHAUST VELOCITY. OPTIMUM COMBINATION OF ENGINES WITH LIMITED EXHAUST VELOCITY AND LIMITED POWER9. PROPULSION SYSTEMS WITH ENERGY AND MASS ACCUMULATION. ENGINES WHOSE THRUST AND POWER ARE FUNCTIONS OF THE COORDINATES AND TIME10. MODIFICATIONS OF THE OPTIMUM CRITERION11. RELIABILITY CONSIDERATIONS IN OPTIMIZATION PROBLEMS12. EXTRA WEIGHT REQUIRED FOR TRAJECTORY CORRECTIONPart III ESTABLISHING OPTIMUM SOLUTIONS13. ANALYTIC SOLUTIONS OF THE EQUATIONS OF DYNAMICS14. FUNCTIONAL NUMERICAL METHODS FOR ESTABLISHING OPTIMUM SOLUTIONS15. FINITE-DIMENSIONAL NUMERICAL METHODS OF ESTABLISHING OPTIMUM SOLUTIONS