| INVARIANT IMBEDDING AND THE VARIATIONAL TREATMENT OF FREDHOLM INTEGRAL EQUATIONS WITH DISPLACEMENT KERNELS, |
NOV 1968 |
|
| Authors:
J. Casti; R. Kalaba; S. Ueno; RAND CORP SANTA MONICA CALIF
|
 | The report describes a new and computationally efficient method of solving Fredholm integral equations with displacement kernels, such as those arising in radiative transfer and optimal filtering theory. Frequently, studies of these equations are based on the fact that their solutions minimize certain quadratic functionals, which opens the way to the employment of the Rayleigh-Ritz method. The aim of the present study is radically different: It is shown that the ... |
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| A STATIONARY PROBLEM FOR A MULTI-COMMODITY INVENTORY SYSTEM WITH INTERACTING SET-UP COSTS. |
NOV 1968 |
|
| Authors:
B. D. Sivazlian; FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING
|
| The stationary characteristics of a periodic review multi-commodity inventory problem are investigated. The analysis is carried first for a two-commodity system and is then extended to an n-commodity system (n = or > 1). The stochastic model assumes a dyadic replenishment policy (either nothing is ordered or all commodities are ordered simultaneously) with proportional costs plus a single set-up cost. For n = 2 and when the demands for the ... |
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| CONTINUOUS TRANSFORMATIONS AND INTEGRAL MANIFOLDS. |
NOV 1968 |
|
| Authors:
Lamberto Cesari; MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS
|
| During the reporting the principal investigator and some of his collaborators completed seventeen research papers. This work is described. The major effort was devoted to problems of optimal control. Existence theorems were proved for lumped parameter control systems by a new type of analysis. A number of related conditions were analyzed with examples and applications. Existence theorems were proved for distributed parameter control systems by the use of Sobolev spaces ... |
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| STRESS WAVE ANALYSIS IN LAYERED THERMOVISCOELASTIC MATERIALS BY THE EXTENDED RITZ METHOD, VOLUME II. |
OCT 1968 |
|
| Authors:
Robert E. Nickell; ROHM AND HAAS CO HUNTSVILLE AL REDSTONE RESEARCH LABS
|
| Stress wave propagation in thermorheologically simple viscoelastic materials was studied through use of the extended Ritz method. A variational principle that characterizes these initial-boundary value problems was derived which yields, as its Euler equations, the equations of motion and of transient heat conduction. A type of thermomechanical coupling is included in the formulation. A direct method of the variational calculus, called the extended Ritz method, is then applied to a ... |
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| ON TWO DIMENSIONAL INCOMPRESSIBLE STEADY STATE FLOWS WITH SEPARATION. |
OCT 1968 |
|
| Authors:
Alexander Pal; POLYTECHNIC INST OF BROOKLYN FARMINGDALE N Y DEPT OF AEROSPACE ENGINEERING AND APPLIED MECHANICS
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| Contents: Formulation of the minimum problems; Convergence of the minimizing sequence; Topological properties of the solution; Integral equation and applications. |
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| INITIAL-VALUE METHODS IN OPTIMAL CONTROL THEORY, |
SEP 1968 |
|
| Authors:
R. Kalaba; R. Sridhar; RAND CORP SANTA MONICA CALIF
|
| A new approach to constrained variational problems is presented in which the variational problem is converted directly into a Cauchy problem, with no use made of Euler equations or dynamic programming techniques. Frequently the initial-value problem is stable, in contrast to the numerically unstable boundary-value problem for the Euler equations. Results are applicable in guidance and control studies and in those branches of mathematical physics described by variational principles. (Author) ... |
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| ON THE APPROXIMATE MINIMIZATION OF FUNCTIONALS. |
SEP 1968 |
|
| Authors:
James W. Daniel; WISCONSIN UNIV MADISON DEPT OF COMPUTER SCIENCES
|
| The paper considers in general the problem of finding the minimum of a given functional f(u) over a set B by approximately minimizing a sequence of functionals f sub n(u sub n) over a 'discretized' set B sub n; theorems are given proving the convergence of the approximating points u sub n in B sub n to the desired point u in B. Applications are given to the Rayleigh-Ritz method, ... |
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| A TACTICAL STUDY OF EVASIVE MANEUVERS, |
SEP 1968 |
|
| Authors:
Ulf Grenander; RESEARCH INST OF NATIONAL DEFENCE STOCKHOLM (SWEDEN)
|
| Some tactical aspects of pursuit and evasion are studied. The emphasis is on the analysis of the conceptual framework and on the construction of analytic models. In order that these models be able to describe real pursuit situations, an attempt is made to incorporate kinematic and dynamic restrictions to the extent that is possible without making the model too difficult to handle. In particular, the relation between the evasive tactics ... |
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| Optimum Ship Routing by the Method of Steepest Ascent. |
SEP 1968 |
|
| Authors:
Richard Allen Gregor; NAVAL POSTGRADUATE SCHOOL MONTEREY CA
|
| With the advent of the high speed digital computer, many problems heretofore considered unsolvable for all practical purposes are now well within the reach of the applied mathematician. One such problem is the routing of a ship through a time dependent ocean wave field, from one point on the earth's surface to another, so as to minimize a cost function of the form g(x,y,t,u). This paper considers a numerical solution ... |
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| DYNAMIC PROGRAMMING AND OPTIMAL TRAJECTORIES FOR QUADRATIC VARIATIONAL PROCESSES, |
AUG 1968 |
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| Authors:
R. E. Kalaba; RAND CORP SANTA MONICA CALIF
|
| Dynamic programming provides a standard tool for determining optimal feedback control policies for linear systems with quadratic measures of cost. The situation has been less satisfactory, however, with regard to optimal trajectories. A one-sweep initial-value method is presented in this study for determining both optimal policies and optical trajectories. It is shown also that the solution of the Cauchy problem satisfies the Euler equation and the boundary conditions. (Author) |
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| A GENERALIZED STEEPEST DESCENT ALGORITHM FOR MULTISTAGE OPTIMIZATION PROCESSES, |
01 JUN 1968 |
|
| Authors:
Rinaldo F. Vachino; FRANK J SEILER RESEARCH LAB UNITED STATES AIR FORCE ACADEMY CO
|
| The study analyzes two classes of multistage optimization processes, and presents computational algorithms for their solution. Two optimal control processes are considered. The first is characterized by a known ordering and number of stages, where the succession of the stages is dictated by the presence of staging conditions and jump discontinuity conditions on the state of the system. The second optimal control problem is characterized by an unspecified number and ... |
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| OPTIMUM SYSTEMS CONTROL, |
JUN 1968 |
|
| Authors:
Andrew P. Sage; SOUTHERN METHODIST UNIV DALLAS TEX INFORMATION AND CONTROL SCIENCES CENTER
|
| The book contains a comprehensive, up-to-date introduction to the basic concepts and principles employed in the optimization estimation and control of dynamic systems. Fifteen chapters are contained in the text. (1) Introduction, (2) Calculus of extrema and single stage decision processes, (3) Variational calculus and continuous optimal control, (4) The maximum principle and Hamilton Jacobi theory, (5) Optimum systems control examples, (6) Discrete variational calculus and the discrete maximum principle, ... |
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| OPTIMAL CONTROL OF NONLINEAR SYSTEMS WITH INPUT CONSTRAINTS. |
JUN 1968 |
|
| Authors:
Mohammed Azadul Alam; WASHINGTON UNIV ST LOUIS MO DEPT OF SYSTEMS MECHANICAL AND AEROSPACE ENGINEERING
|
| A new method of optimal control of nonlinear systems discussed in this dissertation. The system is optimized by minimizing a quadratic performance index, while the input is subjected to a constraint. This problem is considered as a nonlinear programming problem and some theorems of nonlinear programming are used to derive the necessary and sufficient conditions for optimal control. These conditions are then simplified to an integral equation which, for nonlinear ... |
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| RESEARCH IN 'OPTIMIZATION THEORY AND AEROSPACE APPLICATIONS.' |
APR 1968 |
|
| Authors:
Richard E. Kopp; GRUMMAN AIRCRAFT ENGINEERING CORP BETHPAGE NY RESEARCH DEPT
|
| The report summarizes the research performed in 'Optimization Theory and Aerospace Applications.' There were six basic areas studied: (1) Trajectory Optimization Techniques; (2) Stochastic Optimum Control Problems; (3) Theory of Distributions; (4) Synthesis of Optimum Distributed Networks; (5) Synthesis of Optimum Antenna Structures; and (6) Synthesis of Closed-Loop (Feedback) Optimal Control Systems. All these areas except Area 3 are directly related to the discipline of optimization. Area 3 had begun ... |
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| THEORETICAL AND NUMERICAL PROCEDURES FOR THE MAGNETIZATION OF FERROMAGNETIC OBJECTS OF VARIOUS SHAPES WHICH HAVE BEEN INTRODUCED INTO A PRE-EXISTING FIELD: THE METHOD OF INTEGRAL EQUATIONS, THE CALCULUS OF VARIATIONS, SEPARATION OF VARIABLES. |
05 MAR 1968 |
|
| Authors:
Bruce E. Goodwin; DELAWARE UNIV NEWARK
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| The purpose of this report is to give theoretical procedures for solving electromagnetic problems where there are two regions where the permeability and the dielectric constant have different values. The procedures are to be computable. (Author) |
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| TIME OPTIMAL CONTROL FOR A CLASS OF COMMON RANDOM DISTURBANCES. |
02 FEB 1968 |
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| Authors:
Norval P. Smith; MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB
|
| The report concerns the time optimal control of a system variable where the controlling input to the system is bounded, as is normally the case in practice. Optimal control is defined here as that control which yields time optimal trajectories. It is shown that time optimal control also yields optimal trajectories in the sense of minimizing the maximum error (if this is the initial error, minimize the overswing next) and ... |
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| OPTIMAL INTERCEPT GUIDANCE FOR MULTIPLE TARGET SETS, |
JAN 1968 |
|
| Authors:
Robert J. Norbutas; MASSACHUSETTS INST OF TECH CAMBRIDGE ELECTRONIC SYSTEMS LAB
|
| The problem of optimally guiding a vehicle to intercept more than one target is investigated. The major contributions are the following: (a) the extension of the variational calculus and two numerical algorithms (steepest-descent and Newton-Raphson) to multiple target set problems; and (b) the design of a suboptimal feedback controller for a specific problem of a vehicle intercepting two targets. The problems considered are in the form of N-point (N > ... |
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| A UNIFIED THEORY FOR CONSTRAINED MINIMIZATION ON HILBERT SPACE. |
JAN 1968 |
|
| Authors:
Harold O. Ladd Jr; MASSACHUSETTS INST OF TECH CAMBRIDGE INSTRUMENTATION LAB
|
| A codification, involving new, as well as known, results from several areas of investigation of the problem of constrained minimization, is presented in a unified geometric treatment. Specifically, a unified theory is given for the local minimization of a smooth functional phi(u), subject to a set of q smooth functional equality constraints psi(sub k) (u) = 0, phi and the psi(sub k) being defined on a Hilbert space H. There ... |
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| SOME OPTIMAL-CONTROL PROBLEMS IN DISTRIBUTED-PARAMETER SYSTEMS. |
JAN 1968 |
|
| Authors:
Manthri S. Narasimha; WASHINGTON UNIV ST LOUIS MO DEPT OF SYSTEMS MECHANICAL AND AEROSPACE ENGINEERING
|
| The dissertation concerns itself with the extension of some of the results known for the optimal control of lumped-parameter systems to distributed systems. The analytical design of the optimal regulator is worked out in detail for linear time-invariant distributed systems. The necessary conditions of optimality are derived using calculus of variations, and the boundary effects are studied in some generality. Two methods are suggested to solve the boundary value problems ... |
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| PURSUIT-EVASION DIFFERENTIAL GAMES. |
JAN 1968 |
123 pages |
| Authors:
John B. Berger; WASHINGTON UNIV ST LOUIS MO DEPT OF SYSTEMS MECHANICAL AND AEROSPACE ENGINEERING
|
 | Differential game theory is applied to several classes of pursuit-evasion problems. For these differential games the dynamics of the participants are described by linear nonstationary differential equations. One class of differential games that was formulated and studied is the differential game, where the evader has to out maneuver a pursuer, if it is to strike the target that the pursuer is defending. This differential game will be called the differential ... |
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| ESTIMATION OF PARAMETERS IN DIFFERENTIAL EQUATIONS FOR EXPERIMENTAL DATA, |
JAN 1968 |
|
| Authors:
E. Stanley Lee; KANSAS STATE UNIV MANHATTAN INST FOR SYSTEMS DESIGN AND OPTIMIZATION
|
| Estimator equations for the estimation of parameters in differential equations from noisy data are obtained by the combined use of the classical calculus of variations and invariant imbedding. Both input and output noises are allowed in obtaining the noisy measurements. As a numerical example, the concentration of the reactant in a chemical reaction is estimated by the estimators. These estimator equations can be used to obtain the parameters or coefficients ... |
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| MINIMUM WEIGHT DESIGN OF ELASTIC STRUCTURAL ELEMENTS, |
1968 |
|
| Authors:
Edward J. Haug Jr; ARMY WEAPONS COMMAND ROCK ISLAND IL
|
| The objective of this paper is to present a theory of optimal processes and show how it may be used to obtain minimum weight structural elements. One of the major difficulties in optimal process theory is the numerical construction of solution. This important topic is emphasized in the treatment which follows. (Author) |
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| EXISTENCE THEOREMS IN PROBLEMS OF OPTIMIZATION: ONE- AND MORE-DIMENSIONAL PROBLEMS. |
1968 |
|
| Authors:
Lamberto Cesari; CALIFORNIA UNIV LOS ANGELES NUMERICAL ANALYSIS RESEARCH
|
|
| BODIES OF MAXIMUM LIFT AT HYPERSONIC SPEEDS, |
1968 |
|
| Authors:
Angelo Miele; RICE UNIV HOUSTON TX AERO-ASTRONAUTICS GROUP
|
| An investigation of the maximum lift attainable by a conical body flying at hypersonic speeds is presented under the assumption that the pressure distribution is modified Newtonian. The length and the volume are given, and the values of the free-stream dynamic pressure and the factor modifying the Newtonian pressure law are known a priori. First, direct methods are employed, and attention is focused on the class of base sections such ... |
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| THRUST NOZZLE OPTIMIZATION INCLUDING BOUNDARY LAYER EFFECTS. |
DEC 1967 |
|
| Authors:
M. Peter Scofield; H. Doyle Thompson; Joe D. Hoffman; PURDUE UNIV LAFAYETTE IN JET PROPULSION CENTER
|
| An optimization analysis, a numerical method, and a computer program for the design of optimum thrust nozzles including boundary layer effects are presented. The analysis is based on the assumptions that the flow is homentropic and that the boundary layer is thin. The problem is formulated to maximize the pressure thrust integral along the supersonic wall contour for a general isoperimetric constraint. The results of the optimization analysis are a ... |
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| A REVIEW OF SOME QUALITATIVE RESULTS OBTAINED IN FLIGHT DYNAMICS BY THE OPTIMAL PROCESSES THEORY (OBZOR NEKOTORYKH KACHESTVENNYKH REZULTATOV, POLUCHENNYKH V DINAMIKE POLETA S POMOSHCHYU TEORII OPTIMALNYKH PROTSESSOV), |
28 NOV 1967 |
|
| Authors:
V. K. Isaev; Yu. M. Kopnin; FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
|
| Some features of optimal programming of the thrust magnitude and thrust direction structure during the motion of the variable mass point in a central gravitational field are studied. The presented results contain development and generalization of the authors' investigations, reported at the XIVth (1963) and XVth (1964) International Astronautical Congress of IAF. The paper consists of three parts. In the first part the results of the analysis of an optimal ... |
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| CAUCHY AND FREDHOLM METHODS FOR EULER EQUATIONS, |
NOV 1967 |
|
| Authors:
H. Kagiwada; R. Kalaba; A. Schumitzky; R. Stidhar; RAND CORP SANTA MONICA CALIF
|
| The report demonstrates alternative methods of minimizing a quadratic functional, which is frequently an essential step in the solution of problems in mathematical physics, mechanics, and engineering. Three methods are discussed: (1) the classical approach through Euler equations, subject to boundary conditions; (2) an approach through the solution of a Fredholm integral equation; (3) the initial-value approach, based on the dynamic programming and invariant imbedding. Each method has certain analytic ... |
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| EXISTENCE THEOREMS FOR OPTIMAL PROBLEMS WITH VECTOR VALUED COST FUNCTIONS. |
NOV 1967 |
|
| Authors:
Czeslaw Olech; BROWN UNIV PROVIDENCE R I CENTER FOR DYNAMICAL SYSTEMS
|
| The paper considers the following optimal control problem. Consider a control system (0.1) y dot = f(t,y,u) where f maps J sub o X Y X E into Y, J sub o = (a sub o, b sub o) is an interval, and Y,E are Euclidean spaces. By a solution of (0.1) is meant a triple (J,y,u), where J included in J sub o is an interval, y: J approaches ... |
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| OPTIMAL CROSS SECTION FOR A TOROIDAL INDUCTOR WITH A THIN WINDING. |
NOV 1967 |
|
| Authors:
Evan B. Wright; NAVAL RESEARCH LAB WASHINGTON D C
|
| For a toroidal inductor having a winding of fixed length, the core shape which maximizes the inductive energy is calculated. The solution of this isoperimetric problem is given in terms of Bessel and Struve functions, and some typical cross sections are illustrated. (Author) |
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| THE MOTION OF A BODY OF VARIABLE MASS WITH ACCUMULATION OF ENERGY AND AN ENGINE WITH RESTRICTED JET DISCHARGE VELOCITY. PART II, |
14 SEP 1967 |
|
| Authors:
G. L. Grodzovskii; B. N. Kiforenko; FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
|
| The article considers the variational problem of the optimum motion in a gravitational field (the useful-load maximum) with an engine system of limited power in conjunction with an energy accumulator and an engine of limited exhaust velocity. The general properties are determined for optimum motion exhibiting the indicated limitations. It is demonstrated that an optimum trajectory may be made up of those segments of motion with optimum variations in exhaust ... |
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| APPLICATION OF DYNAMIC PROGRAMMING TO THE BRACHISTOCHRONE PROBLEM, |
AUG 1967 |
|
| Authors:
Dorothy M. Pullen; ROYAL AIRCRAFT ESTABLISHMENT FARNBOROUGH (ENGLAND)
|
| The classical brachistochrone problem is formulated in dynamic programming terms and the resulting functional equation solved. The equation is first solved over a rectangular mesh and various methods of increasing the accuracy of the result and reducing the computer storage space required are considered. A good approximation to the true solution is obtained even though the numerical values chosen involve a singularity. (Author) |
|
| USE OF LONG-RANGE WEATHER FORECASTS IN SHIP ROUTING. |
01 JUL 1967 |
|
| Authors:
George J. Haltiner; Willard E. Bleick; Frank D. Faulkner; NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF
|
| The report presents an operational computer program for the calculus of variations method of minimal-time routing of single ships. Although written specifically for VC2AP3 and VC2AP2 vessels operating in a described area of the north Pacific Ocean, the program can be modified easily to provide routes for other type vessels in any ocean area of the northern hemisphere. An improved method is used for varying time-extremal ship tracks toward admissibility, ... |
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| A NEIGHBORING OPTIMUM FEEDBACK CONTROL SCHEME BASED ON ESTIMATED TIME-TO-GO WITH APPLICATION TO RE-ENTRY FLIGHT PATHS. |
JUN 1967 |
|
| Authors:
Jason L. Speyer; Arthur E. Bryston Jr; HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
|
| A modification of the perturbation feedback control scheme given in other references is presented that greatly increases its capability to handle disturbances in cases where the final time is not specified. The modified control scheme uses a set of precalculated gains which allows in-flight estimation of the change in the final time due to perturbations from a nominal path. The time-to-go, determined from the predicted change in final time, is ... |
|
| OPTIMAL STATION KEEPING AT THE L4 LIBRATION POINT |
JUN 1967 |
96 pages |
| Authors:
Isaac R. Steinberg; AIR FORCE INST OF TECH WRIGHT-PATTERSONAFB OH SCHOOL OF ENGINEERING
|
| A control system is devised for maintaining a space vehicle in close proximity to one of the earth-moon triangular libration points while minimizing fuel consumption. The problem is formulated as an optimal state regulator problem of variational calculus and then modern control theory is applied. A quadratic performance criterion is used which leads to a linear feedback control system. The feedback gains are obtained by solving a matrix differential equation ... |
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| A DESCENT ALGORITHM FOR CONSTRAINED STOCHASTIC EXTREMA. |
MAY 1967 |
|
| Authors:
Y. C. Ho; P. M. Newbold; HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
|
| In situations where it is not feasible to find an optimal feedback control law for a stochastic system, an open-loop law can often be derived by optimization. The report presents a method of finding the extremum of certain stochastic functionals analogous to the steepest descent method. Necessary conditions for the convergence of the algorithm are given. Two examples illustrate the use of the algorithm. (Author) |
|
| PROFILING THE SUPERSONIC SECTION OF AN AXISYMMETRIC MAXIMUM THRUST NOZZLE, |
28 APR 1967 |
|
| Authors:
A. A. Sergienko; I. D. Sandomirskaya; FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
|
| The problem of the optimum shaping of the supersonic portion of the nozzle is studied within the framework of the variational approach. Such degenerated variational problems are solved by means of the coupled variations at the different ends of the extremum curve which allow the positioning of the extremum curve through two assigned points. The basic relationships and the mathematical formulation of the problem are followed by a study of ... |
|
| OPTIMAL CONTROL AND THE USE OF THE PONTRYAGIN MAXIMUM PRINCIPLE. |
17 APR 1967 |
|
| Authors:
Bud J. Wimber; AIR FORCE MISSILE DEVELOPMENT CENTER HOLLOMAN AFB N MEX
|
| The first part of the thesis reviews the optimal control problem as expressed in terms of state space terminology and briefly discussed the use of the calculus of variations and dynamic programming in solving the optimal control problem. The remainder of the thesis is a detailed discussion of the Pontryagin Maximum Principle which appears to have a wider application to optimal control problems than either the calculus of variations or ... |
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| OPTIMUM PROCESSES IN SYSTEMS WITH DISTRIBUTED PARAMETERS AND SOME PROBLEMS OF INVARIANCE THEORY, |
02 MAR 1967 |
|
| Authors:
A. I. Egorov; REDSTONE SCIENTIFIC INFORMATION CENTER REDSTONE ARSENAL ALA TRANSLATION BRANCH
|
| The article presents a study of optimum processes in systems whose behavior is described by distinguishable boundary problems for equations with partial derivatives. The method is the same as that used by Rozonoer in 1959 to investigate the case where the control process is described by ordinary differential and finite-difference equations. |
|
| THE DEFINABILITY OF CARDINAL NUMBERS. |
MAR 1967 |
|
| Authors:
Azriel Levy; HEBREW UNIV JERUSALEM (ISRAEL)
|
| Cardinal numbers are known to be definable in set theory with the axiom of choice or with the axiom of foundation. In the absence of these two axioms the notion of a cardinal number is shown to be undefinable in ZF, in several strong senses. The proofs use models of the Fraenkel-Mostowski type. |
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| HOLDER CONDITIONS FOR GAUSSIAN PROCESSES WITH STATIONARY INCREMENTS, |
MAR 1967 |
|
| Authors:
M. B. Marcus; RAND CORP SANTA MONICA CALIF
|
| The study was motivated by the well-known results for Brownian motion, the law of the iterated logarithm and Paul Levy's uniform Holder condition. Holder conditions, both uniform and local, are obtained for a wide class of separable, real-valued Gaussian processes with stationary increments. Relations between upper and lower Holder conditions are discussed. |
|
| DRAG MINIMIZATION AS THE EXTREMIZATION OF PRODUCTS OF POWERS OF INTEGRALS, |
1967 |
|
| Authors:
Angelo Miele; RICE UNIV HOUSTON TX AERO-ASTRONAUTICS GROUP
|
| The paper considers the minimization of the pressure drag of an axisymmetric body in Newtonian hypersonic flow and a two-dimensional airfoil in Newtonian hypersonic flow or linearized supersonic flow. If suitable nondimensional coordinates are employed, that is, if the abscissa and the ordinate are respectively normalized in terms of a reference length and a reference thickness, the pressure drag can be expressed in terms of the products of the powers ... |
|
| AN APPLICATION OF NEWTON'S METHOD TO THE EULER-LAGRANGE EQUATION, |
1967 |
|
| Authors:
Richard A. Tapia; CALIFORNIA UNIV LOS ANGELES NUMERICAL ANALYSIS RESEARCH
|
| The theory developed in the report can be used to solve the generalized Euler-Lagrange equation. |
|
| MIMIMUM-DRAG BODY WITH SPECIFIED CENTER OF PRESSURE. |
OCT 1966 |
|
| Authors:
John W. Ellinwood; AEROSPACE CORP EL SEGUNDO CA LABS DIV
|
| A body profile is found that minimizes the zero-lift, Newtonian pressure drag of slender bodies of revolution when the center of pressure for small incidence is a specified percent of body length. Other constraints considered are those on body length, diameter or volume. The zero-lift drag is shown to increase when a constraint on center of pressure location is added to two of the other constraints, and the optimal profile ... |
|
| NATURAL FAMILIES OF PERIODIC ORBITS, |
OCT 1966 |
|
| Authors:
Andre Deprit; Jacques Henrard; BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB
|
| In reference to any solution of a conservative dynamical system with two degrees of freedom, Hill's equation is generalized to encompass non-necessarily isoenergetic displacements as well as the isonergetic displacements caused by a variation of a parameter. This new variational equation is made the foundation of a methodical procedure for continuing numerically natural families of periodic orbits. The method consists of two steps-- an isoenergetic corrector and a tangential predictor. ... |
|
| ON THE USE OF RESTRICTED VARIATIONAL PRINCIPLE METHODS FOR BOUNDARY VALUE PROBLEMS OF KINETIC THEORY. |
SEP 1966 |
|
| Authors:
Charles R. Ortloff; AEROSPACE CORP EL SEGUNDO CA LABS DIV
|
| The surface integral term resulting from application of Rosen's restricted variational principle to kinetic theory boundary value problems in a three-dimensional physical space is shown to result in a natural boundary condition equivalent to surface flux conservation. (Author) |
|
| OPTIMAL DECISION RULES FOR THE TRIANGULAR E MODEL OF CHANCE-CONSTRAINED PROGRAMMING. |
SEP 1966 |
|
| Authors:
Michael J. L. Kirby; Abraham Charnes; RESEARCH ANALYSIS CORP MCLEAN VA
|
| The paper deals with an n-period E model of chance-constrained programming in which each period j = 1,...,n generates exactly one new constraint. It is shown that there are cases in which the problem can be reduced to one of solving n rather simple one-variable nonlinear programming problems. The results of this paper are illustrated by means of an example giving the solution of a two-period problem of planning for ... |
|
| ON APPROXIMATING EXTREMALS OF FUNCTIONALS. PART II. THEORY AND GENERALIZATIONS RELATED TO BOUNDARY VALUE PROBLEMS FOR NON-LINEAR DIFFERENTIAL EQUATIONS. |
SEP 1966 |
|
| Authors:
Donald Greenspan; WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
|
| A combination variational-difference numerical method, applied recently to a large variety of nonlinear boundary value problems, is studied from the points of view of convergence and possible generalizations. The essence of the method lies in minimizing a functional numerically rather than in approximating the solution of the Euler differential equation of the functional. (Author) |
|
| FLUID MOTION IN A SHALLOW TRAPEZOIDAL CONTAINER. |
AUG 1966 |
|
| Authors:
B. A. Troesch; AEROSPACE CORP EL SEGUNDO CA LAB OPERATIONS
|
| The few lowest free sloshing modes in shallow containers with arbitrary trapezoidal cross sections are investigated for the plane and the axially symmetric cases. The frequencies and a dimensionless quantity which relates the frequencies to more elementary geometrical quantities, namely to the volume and to the rim dimensions, are computed and used to determine lower bounds for the eigenvalues of general convex containers. In the axially symmetric case, the optimum ... |
|
| INTEGRAL INEQUALITIES FOR TWO FUNCTIONS. |
AUG 1966 |
|
| Authors:
B. A. Troesch; AEROSPACE CORP EL SEGUNDO CA LAB OPERATIONS
|
| In the interval of 0 < or = x < or = 1, let f(x) be an arbitrary continuous, piecewise smooth function with f(0) = 0, and let h(x) be a positive concave function with piecewise smooth derivative h' (i.e., h'' < or = 0 where it exists) satisfying h'(0) < or = 0. Then the inequality L(h,f) =((the integral h(x) f' f' dx) / (the integral h(x) dx) (the ... |
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| OPTIMUM SUBMARINE ROUTING II COMPUTATIONAL ROUTINES. |
AUG 1966 |
|
| Authors:
George D. Schmieg; NAVAL POSTGRADUATE SCHOOL MONTEREY CA
|
| Computing an optimum route for a submarine is studied. Typical functions representing the listening devices were used. It was found that in some cases several extremals existed and it was necessary to set up tests for the Legendre and Weierstrass conditions. The problem is further complicated by the fact that the optimum control-variables may lie on the boundary of the region of allowed values and further routines must be adjoined ... |
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Reports by Keyword(s)
CALCULUS OF VARIATIONS
