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Propellant chemistry
Book Reviews
tively, and are devoted to the determination of the switching surfaces in state space and the feedback structures for various low-order plants, the application is of a rather academic nature, though certainly not devoid of interest. However, the lack of applications, particularly at a time when practice lags behind theory, is not necessarily a drawback. The book, therefore, should be considered primarily as an introduction to the theory. The coverage of the theory is not as comprehensive (nor is it claimed to be) as a volume of nearly 996 pages might suggest. The first quarter of the book, contains a very good review of the mathematical prerequisites (algebra, analysis, differential equations), the state approach to system theory, and a formal definition of the optimal control problem. In the last chapter, the authors show that a restricted yet interesting class of problems can be neatly solved without recourse to the maximum principle. Thus, only Chaps. 5, 6, and 9, totaling some 356 pages, contain fundamental theory devoted exclusively to the deterministic control of systems described by ordinary differential equations. As to the coverage of the theory, the authors choose to treat certain material in thorough detail and to ignore entirely other, equally important topics. For example, a variational (weak variations only) treatment of the free-end-point optimal control problem, and a lengthy heuristic proof of the maximum principle is given. However, there is no discussion of the mathematical and historical relationship between the calculus of variations, the maximum principle, and dynamic programming. In fact, dynamic programming is not discussed at all, perhaps because of the exclusion of discrete systems. The theory of the linear optimal systems (with an unnecessary distinction between state-regulators and output-regulators) is developed in detail; but there is no mention of the important relation between this problem and the study of neighboring optimal trajectories. A number of other topics, some of them listed by the authors in the introduction, could have been discussed briefly for the benefit of those students who do not intend to go beyond an introductory course. Thus, from the point of view of an introductory text, the coverage of the subject is
Vol. 283, No. 4, April 1967
somewhat unbalanced. On the other hand, from the same point of view, the book has many merits. The exposition is meticulous (perhaps too much) and the book is written in a precise mathematical style in terms of definitions, lemmas and theorems. The proofs are mostly rigorous, the arguments easy to follow, and departures from mathematical rigor are carefully noted. The roles of necessary and sufficient conditions, existence and uniqueness, local and global minima, are emphasized. Compensating for the formal style are numerous remarks and discussions explaining the meaning and implications of the abstract formulations. All this is helpful to the beginner as it prepares him for the terminology and style in which many papers on optimal control are written. One should mention the very good Chap. 6 where the theory of minimum time, minimum fuel, and minimum energy control is given, and singular problems are discussed. A comprehensive bibliography is included. Reservations aside, the book is recommended for the material it contains since much of it is unavailable in any organised form. Indeed, the authors are to be commended for their pioneering effort in bringing out this work. ELIEZER KREINDLEE Research Department Grumman Aircraft Engineering Corporation Bethpage, New York
PROPELLANT CHEMISTRY by Stanley F. Sarner, 417 pages, 6 X 9 in. New York, Reinhold Pub., Corp., 1966, Price $20.00. One of the last paragraphs of this book epitomizes the nature of Sarner’s PropeUant Chemidry: “At the present state of knowledge, the use of force fields in space as aids to propulsion is impossible. As far as we know there is no direct interaction between magnetic and gravitational fields, and it does not appear that electrostatic fields exist. The concept of antigravity has yet to be demonstrated or refuted. However, the use of such fieldsmay prove feasible as our knowledge advances. Since external forces are used, the specific impulse of such devices is infinite, but it is expected that the thrust-to-weight ratios would be very low. ‘LFaster than light drives, hyperspace
Book Reviews
drives, and phenomena involving extra sensory perception will also have to wait significant advances in technology, if they are at all possible.” The author, it appears, is not going to take any chances in being scooped. The book has 8ome very interesting portions which deal with the chemistry of many substances, some of which may have use as rocket propellants. It suffers greatly in that the author has not exercised discrimination in the choice of his subject matter. Thus, in attempting to be all inclusive, he has frequently included material which is treated superiicially, hss doubtful value, or is technically wrong. What might otherwise have been, therefore, a most interesting book on the chemistry of new substances, whose synthesis or inveatigation was encouraged by the current interest in rocket propulsion, becomes a sort of catchall containing far too much material that is superficially treated, and leaves out a great deal of material which might be of value to the propellant chemist. The first six chapters, for example, dealing with propulsion rather than propellant chemistry, contain many statements which are over-simplified or incorrect. This is ironic because the author says: “the book is meant to be a prime reference for propellant data.” Much of the material in these chapters really is not necessary. But the casual reader instead of merely being left ignorant may be led into a false sense of security that he understands the fundamentals involved. The book improves when the author begins to discuss the chemistry of various substances that are used or have potential use as rocket propellants. The writing is quite journalistic, but much interesting new material is introduced. However, even in this section it sometimes appears that the author has accepted statements from technical reports or possibly even progress report.8without critically evaluating them. For example, of ozone he maintains: “The most diflicult problem in handling ozone is its tendency to detonate. Pure ozone is stable, but the presence of any impurities, including oxygen, may cause detonation. Shock sensitivity is severe. A gentle blow is usually sufficient to detonate even pure ozone.” After one has run the circle of thii paragraph, one worries about how critically the author has evaluated the “factual ma-
352
terial” presented-material which the reader has no means of evaluating for himself without consulting original references, many of which are virtually unobtainable. In Chapter 10, where Sarner deals with the ballistics of solid propellant rocket engines he again begins to tread a rather shaky tachnical path. For example, a critical look at the criterion he u8e9 for stability in a solid propellant rocket engine reveals that it is no criterion for stability at all. In spite of these criticisms, the book contains some very interesting chemistry. The author is to be commended for performing a useful service in asaemblying a great deal of information about the numerous rocket propellants. EDWARD A. FLETCHER Department of Mechanical Engineering
Universityof Minnesota Minneapolis,
Minnesota
BASIC DEVELOPMENTS IN FLUID DI*KAMICS, Vol. I, edited by Maurice Holt. 447 pages, diagrams, 6 X 9 in. New York, Academic Press Inc., 1965. Price, $17.50. This new series on topics of current interest in fluid dynamics was conceived, as indicated by editor Holt in the Preface, “to provide authors with the opportunity of giving an exposition of their own and related research, and of presenting material not readily accessible to the general reader.” The volume contains five articles which cover different areas. The first, Numerical Sol&ion of P~oblema in Gas llynamics, by 0. M. Belotirkovskii and P. I. Chushkin, is a survey of numerical methods of the gas dynamics problem based on the work done in recent years in the USSR. As such, the inverse blunt-body problem (works of Garabedian & Lieberstein, and Van Dyke), is completely absent. The methods discussed fall into three categories: (i) Method of finite differences; (ii) Method of integral relations; and (iii) Method of characteristics. Included are Godunov’s method for unsteady problems based on special difference schemes reflecting conservation laws which accommodate discontinuities, and Rusanov’s difference scheme for continuous computation (comparable to a scheme due to Lax developed earlier). In spite of the excellent presentation of
Journal of The Franklin Institute
tively, and are devoted to the determination of the switching surfaces in state space and the feedback structures for various low-order plants, the application is of a rather academic nature, though certainly not devoid of interest. However, the lack of applications, particularly at a time when practice lags behind theory, is not necessarily a drawback. The book, therefore, should be considered primarily as an introduction to the theory. The coverage of the theory is not as comprehensive (nor is it claimed to be) as a volume of nearly 996 pages might suggest. The first quarter of the book, contains a very good review of the mathematical prerequisites (algebra, analysis, differential equations), the state approach to system theory, and a formal definition of the optimal control problem. In the last chapter, the authors show that a restricted yet interesting class of problems can be neatly solved without recourse to the maximum principle. Thus, only Chaps. 5, 6, and 9, totaling some 356 pages, contain fundamental theory devoted exclusively to the deterministic control of systems described by ordinary differential equations. As to the coverage of the theory, the authors choose to treat certain material in thorough detail and to ignore entirely other, equally important topics. For example, a variational (weak variations only) treatment of the free-end-point optimal control problem, and a lengthy heuristic proof of the maximum principle is given. However, there is no discussion of the mathematical and historical relationship between the calculus of variations, the maximum principle, and dynamic programming. In fact, dynamic programming is not discussed at all, perhaps because of the exclusion of discrete systems. The theory of the linear optimal systems (with an unnecessary distinction between state-regulators and output-regulators) is developed in detail; but there is no mention of the important relation between this problem and the study of neighboring optimal trajectories. A number of other topics, some of them listed by the authors in the introduction, could have been discussed briefly for the benefit of those students who do not intend to go beyond an introductory course. Thus, from the point of view of an introductory text, the coverage of the subject is
Vol. 283, No. 4, April 1967
somewhat unbalanced. On the other hand, from the same point of view, the book has many merits. The exposition is meticulous (perhaps too much) and the book is written in a precise mathematical style in terms of definitions, lemmas and theorems. The proofs are mostly rigorous, the arguments easy to follow, and departures from mathematical rigor are carefully noted. The roles of necessary and sufficient conditions, existence and uniqueness, local and global minima, are emphasized. Compensating for the formal style are numerous remarks and discussions explaining the meaning and implications of the abstract formulations. All this is helpful to the beginner as it prepares him for the terminology and style in which many papers on optimal control are written. One should mention the very good Chap. 6 where the theory of minimum time, minimum fuel, and minimum energy control is given, and singular problems are discussed. A comprehensive bibliography is included. Reservations aside, the book is recommended for the material it contains since much of it is unavailable in any organised form. Indeed, the authors are to be commended for their pioneering effort in bringing out this work. ELIEZER KREINDLEE Research Department Grumman Aircraft Engineering Corporation Bethpage, New York
PROPELLANT CHEMISTRY by Stanley F. Sarner, 417 pages, 6 X 9 in. New York, Reinhold Pub., Corp., 1966, Price $20.00. One of the last paragraphs of this book epitomizes the nature of Sarner’s PropeUant Chemidry: “At the present state of knowledge, the use of force fields in space as aids to propulsion is impossible. As far as we know there is no direct interaction between magnetic and gravitational fields, and it does not appear that electrostatic fields exist. The concept of antigravity has yet to be demonstrated or refuted. However, the use of such fieldsmay prove feasible as our knowledge advances. Since external forces are used, the specific impulse of such devices is infinite, but it is expected that the thrust-to-weight ratios would be very low. ‘LFaster than light drives, hyperspace
Book Reviews
drives, and phenomena involving extra sensory perception will also have to wait significant advances in technology, if they are at all possible.” The author, it appears, is not going to take any chances in being scooped. The book has 8ome very interesting portions which deal with the chemistry of many substances, some of which may have use as rocket propellants. It suffers greatly in that the author has not exercised discrimination in the choice of his subject matter. Thus, in attempting to be all inclusive, he has frequently included material which is treated superiicially, hss doubtful value, or is technically wrong. What might otherwise have been, therefore, a most interesting book on the chemistry of new substances, whose synthesis or inveatigation was encouraged by the current interest in rocket propulsion, becomes a sort of catchall containing far too much material that is superficially treated, and leaves out a great deal of material which might be of value to the propellant chemist. The first six chapters, for example, dealing with propulsion rather than propellant chemistry, contain many statements which are over-simplified or incorrect. This is ironic because the author says: “the book is meant to be a prime reference for propellant data.” Much of the material in these chapters really is not necessary. But the casual reader instead of merely being left ignorant may be led into a false sense of security that he understands the fundamentals involved. The book improves when the author begins to discuss the chemistry of various substances that are used or have potential use as rocket propellants. The writing is quite journalistic, but much interesting new material is introduced. However, even in this section it sometimes appears that the author has accepted statements from technical reports or possibly even progress report.8without critically evaluating them. For example, of ozone he maintains: “The most diflicult problem in handling ozone is its tendency to detonate. Pure ozone is stable, but the presence of any impurities, including oxygen, may cause detonation. Shock sensitivity is severe. A gentle blow is usually sufficient to detonate even pure ozone.” After one has run the circle of thii paragraph, one worries about how critically the author has evaluated the “factual ma-
352
terial” presented-material which the reader has no means of evaluating for himself without consulting original references, many of which are virtually unobtainable. In Chapter 10, where Sarner deals with the ballistics of solid propellant rocket engines he again begins to tread a rather shaky tachnical path. For example, a critical look at the criterion he u8e9 for stability in a solid propellant rocket engine reveals that it is no criterion for stability at all. In spite of these criticisms, the book contains some very interesting chemistry. The author is to be commended for performing a useful service in asaemblying a great deal of information about the numerous rocket propellants. EDWARD A. FLETCHER Department of Mechanical Engineering
Universityof Minnesota Minneapolis,
Minnesota
BASIC DEVELOPMENTS IN FLUID DI*KAMICS, Vol. I, edited by Maurice Holt. 447 pages, diagrams, 6 X 9 in. New York, Academic Press Inc., 1965. Price, $17.50. This new series on topics of current interest in fluid dynamics was conceived, as indicated by editor Holt in the Preface, “to provide authors with the opportunity of giving an exposition of their own and related research, and of presenting material not readily accessible to the general reader.” The volume contains five articles which cover different areas. The first, Numerical Sol&ion of P~oblema in Gas llynamics, by 0. M. Belotirkovskii and P. I. Chushkin, is a survey of numerical methods of the gas dynamics problem based on the work done in recent years in the USSR. As such, the inverse blunt-body problem (works of Garabedian & Lieberstein, and Van Dyke), is completely absent. The methods discussed fall into three categories: (i) Method of finite differences; (ii) Method of integral relations; and (iii) Method of characteristics. Included are Godunov’s method for unsteady problems based on special difference schemes reflecting conservation laws which accommodate discontinuities, and Rusanov’s difference scheme for continuous computation (comparable to a scheme due to Lax developed earlier). In spite of the excellent presentation of
Journal of The Franklin Institute