TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

ON THE OPTIMAL CONTROL OF SYSTEMS WITH DISTRIBUTED PARAMETERS

APR 1961

Authors: A.G. BUTKOVSKII; A. YA. LERNER; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The full text of this report is not available and therefore is not for sale. This information is provided for reference purposes only.

THREE VERY GENERAL OPTIMAL CONTROL PROBLEMS ARE FORMULATED WHEREIN THE CONTROLLED PROCESS IS GOVERNED BY A PARTIAL DIFFERENTIAL EQUATION AND THE CONTROL FORCES ARE SUBJECTED TO CONSTRAINTS. As an example of the second of these three problems the author considers the optimal control of the temperature, Q, within a metal slab as it moves through a furnace. (Author)

MAGNETIC SHIELDING FACTORS OF A SYSTEM OF CONCENTRIC SPHERICAL SHELLS

APR 1961

Authors: FELIX SCHWEIZER; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

General expressions are developed for the shielding factors of concentric spherical shells of linear isotropic magnetic material. Approximate results are given for shells of highly permeable material which are thin compared to their radii. (Author)

INJECTION LOCKING OF KLYSTRON OSCILLATORS

15 MAR 1961

Authors: RICHARD C. MACKEY; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Research was concerned with the useful applications of synchronization phenomena. In order to take advantage of amplification by synchronization, a laboratory investigation of the locking phenomena of reflex klystrons was undertaken in connection with the secure communications phase of the AGS program. If certain criteria are met,A MICROWAVE OSCILLATOR MAY BE SYNCHRONIZED BY THE INJECTION OF A CONTROLLING SIGNAL INTO THE OSCILLATOR CAVITY. Locking was observed with injection signals 70 ...

TECHNICAL PLAN ERB 1-95 PHASE V TEST PROGRAM

15 MAR 1961

Authors: TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

A technical plan is presented for the ERB 1-95 Phase V test program. The ERB 1-95 Phase V program is intended (1) to develop a reliable liquid O boil-off valve configuration which will cause less vibration in the liquid O tank and associated propellant loading hardware, (2) to develop a more reliable and accurate propellant loading control system, such as differential pressure and other control systems, and loading control hardware, ...

THERMODYNAMIC PROPERTIES OF AIR FROM 1000K TO 10,600K ALONG CONTOURS OF CONSTANT DENSITY, ENTHALPY, AND ENTROPY,

03 MAR 1961

Authors: M. W. Curtis; H. E. Wohlwill; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The gas properties given in the report were computed from tables of thermodynamic properties furnished by the National Bureau of Standards. The NBS data have appeared as NBS(1959). It was the purpose of the computation to tabulate properties along isentropes and along constant enthalpy contours, based on the NBS data which are given along isotherms. (Author)

APPROXIMATE SOLUTION OF THE FUNDAMENTAL PROBLEM OF RADIANT ENERGY TRANSFER IN A PLANE-PARALLEL LAYER (CHAPTER X)

MAR 1961

Authors: V.V. SOBOLEV; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Study concerned the scattering of monochromatic radiation in a plane layer illuminated by parallel rays under stationary conditions. The indicatrix of scattering is held as arbitrary. First the case of pure scattering is considered, then the process of true absorption is included. The equations obtained are applied to the atmospheres of the earth and planets and to the sea. (Author)

PHOTOMETRICAL RELIEF OF THE LUNAR SURFACE

MAR 1961

Authors: N.S. ORLOVA; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Measurements of the brightness of the lunar surface and the absolute measurements of brightness were reduced. Supposing the surface of the continents and the surface of the seas as similar in all points of the lunar disk, average coefficients of brightness (brightness factor, albedo) were deduced for various combinations of the angles of incidence and reflection. Results related with the plane of incidence of the solar rays for seas and ...

OSCILLATION OF CURVE OF SUPERCONDUCTIVITY DESTRUCTION BY SONIC FREQUENCY CURRENTS AND ON SUPERCONDUCTIVITY AT A FREQUENCY OF 1.8 X 10,000,000,000 CYCLE/SEC

MAR 1961

Authors: A.A. GALKIN; B.G. LAZAREV; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

OSCILLOGRAMS OF DESTRUCTION OF SUPERCONDUCTIVITY OF TIN BY SONIC FREQUENCY ALTERNATING CURRENTS (100 to 20,000 cycle per sec) were obtained. On the basis of these oscillograms, the upper time limit necessary for transition from the normal state to the superconducting one, or inversely, is determined. The length of the transition process was less than 2 x 10 to the minus 6th power sec. The velocity boundary propagation between normal and ...

OPTIMAL PROCESSES WITH BOUNDED PHASE COORDINATES

MAR 1961

Authors: R.V. GAMKRELIDZE; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Optimal control processes with bounded phase coordinates are studied, and an extremal equation for the corresponding variational problem is dervied. (Author)

APPLICATION OF AN ELECTRICAL ANALOGY METHOD TO THE SOLUTION OF RADIANT HEAT EXCHANGE PROBLEMS

MAR 1961

Authors: V.N. ADRIANOV; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

PROBABILITY DENSITIES FOR THE DURATION OF OVERSHOOTS IN FLUCTUATIONS

MAR 1961

Authors: V.I. TIKHONOV; I.N. AMIANTOV; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Three approximate methods for calculating the probability densities for the urations of overshoots in normal stationary fluctuations are briefly examined and some experimental resultsARE GIVEN. The regions of applicability of the various methods are shown by a comparison of the calculated probability densities with the experimental results. (Author)

ON THE STABILITY OF THE SOLUTION OF A NONLINEAR EQUATION OF THE THIRD ORDER

MAR 1961

Authors: S.N. SHIMANOV; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

OPTIMAL PROCESSES IN AUTOMATIC PULSE SYSTEMS

MAR 1961

Authors: YA. Z. TSYPKIN; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Automatic pulse systems are described by difference equations. The solution of earlier optimal process problems was reduced to the detection of a trajectory connecting the origin of the coordinates with a point corresponding to initial conditions. This approach is based on the application of a convolution equation instead of a system of difference equations of the first order. This makes it possible to solve an optimal process problem on the ...

FIRST FLIGHT TO VENUS

MAR 1961

Authors: TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

THE STABILITY OF THIN CONICAL FRUSTUMS SUBJECTED TO AXIAL COMPRESSION AND INTERNAL OR EXTERNAL UNIFORM HYDROSTATIC PRESSURE

MAR 1961

Authors: Paul Seide; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Calculations are presented for the problems of the stability of conical shells subjected to (1) combined external uniform hydrostatic pressure and axial tension or compression, and (2) combined internal uniform hydrostatic pressure and axial compression. The interaction curves for the first problem are found to depend on the ratio of the end radii of the cone and are bounded by the limiting curves for a cylinder and for a complete ...

THE ROLE OF ELECTRON ATTACHMENT IN A ROCKET EXHAUST,

01 FEB 1961

Authors: Jerry H. Buss; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Numerous investigations have shown that a large number of free electrons are present in a rocket exhaust. Because these electrons interfere with telemetry they have been the subject of several studies ranging in motive from discovering their source to inhibiting their production. The puzzling feature of the problem has been the failure of thermodynamics to predict the measured concentration of free electrons in the exhaust. One theory which has been ...

ADVANCED TELEMETRY SYSTEM STUDIES

31 JAN 1961

Authors: A. EGGER; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Results of studies carried out on advanced telemetry systems are presented. Included is a brief discussion of the applications of conformal (adaptive) telemetry systems and a description of a prototype conformal unit designed and constructed to demonstrate feasibility of the concept, together with a complete PCM telemetry system designed to operate with the conformal unit. Other studies which are described include the design and fabrication of a small computational data ...

FORMULATION OF THE THEORY OF TURBULENCE IN AN INCOMPRESSIBLE FLUID,

01 JAN 1961

Authors: H. W. Wyld Jr.; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The theory of turbulence in an incompressible fluid is formulated using methods similar to those of quantum field theory. A systematic perturbation theory is set up, and the terms in the perturbation series are shown to be in one to one correspondence with certain diagrams analogous to Feynman diagrams. From a study of the diagrams it is shown that the perturbation series can be rearranged and partially summed in such ...

EQUATIONS OF MOTION FOR THE VARIABLE MASS SPINNING BODY,

JAN 1961

Authors: William T. Thomson; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The motion of a body under translation and rotation is examined from the point of view of a system of particles having relative motion between particles, leading to a varying configuration, and undergoing a change in mass with time, where constraints may be imposed on certain numbers of particles. Such a procedure accounts for every conceivable configuration of the system and the possibility of omitting terms in the equations of ...

THE SCIENTIFIC RESULTS OF THE PIONEER V SPACE PROBE,

JAN 1961

Authors: John W. LINDNER; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The pioneer V space probe was launched from Cape Canaveral on March 11, 1960, inwards towards the orbit of Venus. The scientific instrumentation included a spin coil magnetometer, two radiation experiments, and a micrometeorite detector. Data were obtained for distances up to 40 million kilometers from the earth. The most significant results of these experiments are summarized in this paper. (Author)

THE STABILITY UNDER AXIAL COMPRESSION AND LATERAL PRESSURE OF CIRCULAR-CYLINDRICAL SHELLS WITH A SOFT ELASTIC CORE.

JAN 1961

Authors: Paul Seide; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The stability under axial compression and lateral pressure of a finite circular-cylindrical shell with an elastic core is treated by means of Donnell's equations. The stability criterion is investigated in detail for the general cylinder under axial compression or lateral pressure and for a particular cylinder under combined loading. Comparisons are made with available experimental data. (Author)

PEAK CRITERION IN RANDOM-SINE VIBRATION TESTING,

JAN 1961

Authors: H. R. Spence; H. N. Luhrs; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Sinusoidal vibration has practical value as a substitute for random vibration in equipment qualification testing. How and when to employ a sinusoidal substitution is discussed in this paper. In particular a damage criteria is discussed which relates the number of sinusoidal peaks occurring while passing through a resonance to the number of random peaks exceeding a specified amplitude value. Formulae are given for the sine-random response relationship with formulae and ...

HORIZONTAL HYDRODYNAMIC IMPACT OF A SPHERE IN THE PRESENCE OF A FREE LIQUID SURFACE

JAN 1961

Authors: E.L. BLOKH; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

HORIZONTAL IMPACT ON AN ELLIPSOID OF REVOLUTION ON AN IDEAL LIQUID HAVING A FREE SURFACE

JAN 1961

Authors: E.L. BLOKH; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

THIS ANALYSIS IS AN IMMEDIATE CONTINUATION OF A PAPER (AD-264 149) in which the horizontal hydrodynamic impact of a sphere was examined. The impact represented the simplest case of the three-dimensional problem of a horizontal impact on a solid body in an ideal liquid having a free surface. As the investigation of all these cases is conducted by a general and sufficiently uniform method, this analysis presents a detailed solution ...

A STATISTICAL PROBLEM OF OPTIMAL CONTROL

JAN 1961

Authors: E.F. MISCHENKO; L.S. PONTRYAGIN; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

SYNCHRONIZATION OF A SELF-EXCITED OSCILLATOR WITH RADIO PULSES

JAN 1961

Authors: E.S. VORONIN; G.N. BERESTOVSKII; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

T e process of synchronizing a generator of harmonic oscillati ns wit rectangular radio pulses is investigated theoretically and experimentally. The calculati n f the processes of stabilizing the phase and amplitude of self-oscillations in a generator is presented. The results are verified experimentally for a frequency of one megacycle and agreement with theoretical derivations is obtained. It is shown that the settling time depends strongly on the initial phase. ...

APPLICATION OF THE LIAPUNOV-POINCARE METHOD TO THE INVESTIGATION OF AUTOMATIC CONTROL SYSTEMS WITH DELAY

JAN 1961

Authors: U.A. RYABOV; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The investigation of automatic control delay systems based n sing the delay as a mall parameter and on application of the method of Liapunov-Poincare is proposed. The auto atic control system con i ered is described by linear equations with constant coefficients and one constant delay. (Author)

CESIUM ION BEAM NEUTRALIZATION IN VEHICULAR SIMULATION.

1961

Authors: J. M. Sellen; R. F. Kemp; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

A series of experiments are described which relate to the charge neutralization of a broad cesium ion beam under circumstances which simulate the conditions of space. This was accomplished by the use of pulsed beams and by the control of the boundary conditions in such a manner as to reduce to an extremely low level the electric fields between these boundaries and the ejected plasma. The period of ion turn-around ...

SPACE PHYSICS INSTRUMENTATION.

31 DEC 1960

Authors: TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The properties of some new types of beta-ray spectrometers and proton spectrometers for use in space were studied. A laboratory prototype and a light-weight prototype of a high-energy beta-ray spectrometer were constructed. Tests were performed on these spectrometers as well as the high-energy beta-ray spectrometer reported in STL/TR-59-0000-09950. Support work included construction and testing of a pulse-height analyzer, a linear pulse amplifier, a nano-second coincidence circuit and gating circuitry for ...

LIQUID-GAS INTERFACE IN ZERO-G

31 DEC 1960

Authors: l. van der wal; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

An account is given of the progress made in an investigation of the behavior of a liquid-gas mixture in a zero-g field. An experiment unit was flown on an Atlas re-entry nosecone test vehicle. The experiment unit housed a movie camera, placed so as to observe and record the interaction of gas and water contained in a plastic cube during the 25-minute near-zero-g conditions present on an ICBM flight. Temperature ...

SATELLITE MATERIALS AND ENVIRONMENTAL CONTROL SYSTEMS INVESTIGATIONS

31 DEC 1960

Authors: J.T. BEVANS; ALLAN D. LEVANTINE; E.E. LUEDKE; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Spectral reflectances of approximately 30 different surfaces were measured. The computed solar absorptances are reported. The variation of the spectral reflectance and hence, the solar absorptance with the angle of incidence is presented for three specific types of materials. However, the major portion of the results were measured at an an angle of incidence of 15 degrees from the normal to the surface. The results of measurements of the uniformity ...

DIGITAL COMPUTER SYSTEMS STUDIES

31 DEC 1960

Authors: T. Winkler; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Methods are being investigated to improve the quality and reliability of missile guidance systems for WS 107A-1, WS 107A-2, WS 315A, and WS 133A. Study efforts were devoted to the following areas: (a) storage medium evaluation, (b) studies of input-output circuits, (c) design of circuit building blocks to support these efforts, and (d) studies of mechanical assembly methods. In addition to continuing work on circuits using delay lines as a ...

ON THE DETECTION OF ION OSCILLATIONS IN A MERCURY DISCHARGE,

09 DEC 1960

Authors: Burton D. Fried; Roy W. Gould; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The possibility of using a low pressure mercury discharge to detect ion plasma oscillations was examined. It was found that 1) collisions will not interfere with the phenomenon; 2) the current which maintains the discharge will cause the waves to grow (through the two-stream instability) in a time comparable with or less than the oscillation period. Aside from complications caused by the fact that the maximum growth occurs at rather ...

ANALYSIS OF OPERATIONAL READINESS OF MISSILE WEAPON SYSTEMS,

03 DEC 1960

Authors: Jack Coleman; Jack Abrams; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The objective of this analysis is to evaluate the 'SM-68 Periodic Checkout Frequency Study'. In order to properly appraise the study, it was found necessary to independently develop a mathematical model representing the operational readiness of a ballistic missile system from which the relevant probabilities were determined.

STUDY OF SONOTONE CORPORTATION NICKEL CADMIUM SIZE F BATTERY CELLS.

DEC 1960

Authors: Philip H. Greenler; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The tests were conducted by Space Technology Laboratories, Inc.. Final conclusions are not submitted: however, limited conclusions are drawn as a result of test accomplishments to date. Objectives of the laboratory investigations and studies which involve only Sonotone F cells were: (1) To subject cells to the various environmental conditions and duty cycles experienced in the Pioneer V vehicle and to duplicate in the laboratory the type of performance degradation ...

DEVELOPMENT OF INFORMATION PROCESSING CIRCUITRY FOR AN ALL-ELECTRONIC INFRARED HORIZON SCANNER,

DEC 1960

Authors: K. C. PRIORE; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The report describes the development of information processing circuitry for the all-electronic infrared horizon scanner. Two different information processing schemes are described: Video pulse switching and modulated carrier gating. In the video pulse switching scheme, pitch and roll attitude error signals are derived by proper processing of the vidicon tube's video pulse output. In the modulated carrier gating method, pitch and roll attitude error signals are derived by using the ...

DYNAMIC STABILITY OF PENDULOUS MISSILE SUSPENSION SYSTEM,

28 NOV 1960

Authors: V. Chobotov; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The stability of a pendulum with two degrees of freedom at the support point is considered. The differential equations for this system are two coupled second order differential equations with a periodic coefficient. The stability of such equations, which describe the motion of a missile on a shock mount, can be studied by the direct method of Liapunov. The basic technique is used to derive the stability criterion coefficients as ...

WEIGHT AND BALANCE CONTROL DATA FOR LIQUID ROCKET PROPULSION SYSTEMS.

15 NOV 1960

Authors: R. D. DeLauer; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

This document covers the requirements for data to be used in establishing and maintaining weight and balance control of liquid rocket propulsion systems during design and construction. (Author)

DERIVATION OF 3 DIMENSIONAL TRAJECTORY EQUATIONS FOR A LIFTING RE-ENTRY VEHICLE,

09 NOV 1960

Authors: J. A. Love; L. W. Neustadt; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

This memorandum presents the equations of motion of a lifting re-entry vehicle. They are derived in a form particularly suitable for mechanization on an analog computer. The vehicle is assumed to behave as if it were a point mass moving over a spherical, non-rotating earth which is assumed to be fixed in inertial space.

THE RADIATION ENVIRONMENT IN THE INTERIOR OF A SPACE VEHICLE (GEOMAGNETICALLY TRAPPED RADIATION AND INTERPLANETARY COSMIC FLUX),

NOV 1960

Authors: Alan ROSEN; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The purpose of this article is to summarize the characteristics of the penetrating radiation likely to be found in the extraterrestrial environment and to consider the attenuation of the radiation by shielding which may reasonably be expected to make up the wall surface of a spacecraft. The first section of this report deals with the characteristics of the radiation in various regions of space. The trapped radiation zones have only ...

MEASUREMENTS OF FREE MOLECULE HEAT TRANSFER IN AIR AT MACH NUMBERS FROM 10-18,

13 OCT 1960

Authors: R. L. Varwig; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Heat transfer measurements to fine wires in the freemolecule flow regime at Mach numbers typical of the conditions in which satellites move were made. Accommodation coefficients obtained within the accuracy of these experiments agree with those obtained at much lower Mach numbers. The heat transfer measurements taken indicate no Mach number effect. At high Reynolds numbers, where free-molecule flow is no longer obtained, agreement with previous data is reasonable down ...

PLASTIC ANALYSIS OF PRESSURE VESSEL INSTABILITY,

OCT 1960

Authors: R. P. Felgar; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Plasticity theory is used as a basis for analyzing the instability of pressure vessels for various ratios of biaxial stresses. Methods of analysis are developed which incorporate the behavior of the material with various degrees of precision. The methods are illustrated using Ladish D6AC. The predicted instability pressures are compared with the measured values. For the most precise method of analysis, predicted and measured values agree with 31/2% or better. ...

THE THEORY OF OPTIMAL PROCESSES. I. THE MAXIMUM PRINCIPLE

OCT 1960

Authors: V.G. BOLTYANSKII; R.V. GAMKRELIDZE; L.S. PONTRYAGIN; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The theory of the process of controlling some technical object is discussed. The conditions are expounded in the form of a maximum principle. It is assumed that the factors which control the motion of the object can be written in the form of differential equations which are presented. The system described is considered to be autonomous, i.e., its right-hand side is independent of the time, t.

THEORY OF ELECTRON DRIVEN SHOCK WAVES,

16 SEP 1960

Authors: R. G. Fowler; B. D. Fried; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Previous calculations of the time required for ion heating in the discharge or driver section of an electrical shock tube yielded values much greater than that in which formation and acceleration of the first luminous front is observed to occur. The model of an electron driven shock presented here shows that the relation between shock velocity, V, and electron temperature, T sub e, which has been established experimentally over a ...

GROUND-SHOCK SPECTRA FROM SURFACE BURSTS

15 SEP 1960

54 pages

Authors: J. F. Halsey; M. V. Barton; J. M. Lindahl; R. E. Hutton; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The full text of this report is available for sale.

Self-contained mechanical reed gages, capable of measuring the displacement-shock spectrum over a frequency range of 3 to 300 cps in any one direction, were used during Shots Cactus and Koa. Canisters containing the gages were normally placed with their tops flush to the ground level at predicted pressure levels from 75 to 200 psi on both shots. Additional gages were installed in earth-confined arch structures of Project 3.2. Satisfactory records ...

THE STABILITY OF PLASMAS IN THE PRESENCE OF CONDUCTING WALLS,

09 SEP 1960

Authors: Carl Iddings; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The report analyzes two situations where conducting surfaces are present. In the first, a plasma, bounded between two perfectly conducting walls, is supported against gravity by a magnetic field. The gravitational field is simply to simulate the centrifugal force on particles moving on curved lines of force or the field gradient forces, without complicating the geometry. The second situation is a wedge-shaped section of a cylindrical column of plasma, confined ...

ERROR ANALYSIS AND PERFORMANCE OPTIMIZATION OF ROCKET VEHICLE GUIDANCE SYSTEMS.

07 SEP 1960

Authors: G. A. Harter; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

NONLINEAR CONTROL SYSTEM STABILITY VIA THE SECOND METHOD OF LYAPUNOV,

01 SEP 1960

Authors: L. K. Timothy; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

The 'second method of Lyapunov' is, at present, the most general approach to investigating the stability of ordinary differential equations (linear or nonlinear with time varying coefficients). This disseration was primarily concerned with two areas: (1) To communicate to the engineer the basic principles of Lyapunov and (2) To demonstrate a rather general, but concise, approach to applying Lyapunov to the study of control systems.

THE PROBLEM OF NONUNIFORM DISCRETIZING OF CONTINUOUS SIGNALS

SEP 1960

Authors: Z. Fridrikh ; Z. Jakubski; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

ON THE BASIS OF THE THEORY OF APPROXIMATION OF FUNCTIONS, NEW METHODS ARE PROPOSED FOR DISCRETIZING CONTINUOUS SIGNALS WHEN THE READINGS ARE MADE AT UNEVEN DISTANCES. The intervals between readings are related to the order of the approximation polynomial by a permissible value of the error of approximation; in addition, readings are taken not of the instantaneous value of the signal, but using the approximation function. (Author)

WEIGHT ESTIMATES OF RING-STIFFENED, TRUNCATED CONE SHELLS, SUBJECTED TO EXTERNAL PRESSURE AND AXIAL COMPRESSION SIMULTANEOUSLY,

29 AUG 1960

Authors: Henry W. Baer; TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

Approximate expressions are evolved for the required weight of truncated, conical shells, stiffened at equal intervals with rings. Three cases of loading are considered, namely, external pressure only, axial compression only and a combination of the two. In the first and third loading cases, the number of ring-stiffened bays is determined by successive computations, until the number of stiffener rings is found for which the over-all weight of the structure ...