The optimum one-dimensional magnetohydrodynamic slider bearing
Calculus of variations used for determining optimum one dimensional MHD slider bearing with bounded control variables
Shukla, J. B.↗
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An endpoint sufficiency test
Endpoint sufficiency test based on differential calculus method, considering Bolza problem of continuous state and piecewise control variables
Vincent, T. L.↗
Optimal control surface locations for aircraft flexure controllers
Optimal control surface location for flexible aircraft determined by matrix minimum principle and calculus of variations
Athans, M.↗
The optimum one-dimensional magnetohydrodynamic slider bearing
Calculus of variations used for determining optimum one dimensional MHD slider bearing with bounded control variables
Shukla, J. B.↗
A modified sweep method for control optimization
Solution of trajectory optimization problems by calculus of variations, dynamic programming, and Pontryagin's Principle
Colunga, D.↗
A modified linear membrane theory for the pressurized toroid
Pressurized toroid modified linear membrane theory, presenting approximate solutions for derived boundary value problem by variational calculus methods
Clark, S. K.↗
Optimal synthesis of a distributed RC circuit
Optimum synthesis and design of distributed RC filter for oscillator feedback circuit, using calculus of variations
Cohen, G. H.↗
Optimal control-surface locations for flexible aircraft
Aerodynamic control surfaces optimal location for flexible aircraft disturbed by random wind gusts, using matrix minimum principle and calculus of variations
Athans, M.↗
Theoretical study of corrugated plates: Shear stiffness of a trapezoidally corrugated plate with discrete attachments to a rigid flange at the ends of the corrugations
Analysis and numerical results are presented for the elastic shear stiffness of a corrugated shear web with a certain type of discrete attachments at the ends of the trough lines of the corrugations, namely point attachments to a rigid flange which interferes with the deformations of the end cross sections by preventing downward movement but permitting upward (lifting off) movement. The analysis is based on certain assumed modes of deformation of the cross sections in conjunction with the method of minimum total potential energy and the calculus of variations in order to obtain equations for the manner in which the assumed modes of deformation vary along the length of the corrugation. The numerical results are restricted to the case of equal-width crests and troughs but otherwise apply to a wide variety of geometries. They are in the form of graphs which give the overall shear stiffness as a fraction of the overall shear stiffness that could be obtained by having continuous attachment at the ends of the corrugations.
Hsiao, C.↗
A Transformation Approach to Optimal Control Problems with Bounded State Variables
A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.
Hanafy, Lawrence Hanafy↗
Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description
The following problems are considered: (1) methods for development of logic design together with algorithms, so that it is possible to compute a test for any failure in the logic design, if such a test exists, and developing algorithms and heuristics for the purpose of minimizing the computation for tests; and (2) a method of design of logic for ultra LSI (large scale integration). It was discovered that the so-called quantum calculus can be extended to render it possible: (1) to describe the functional behavior of a mechanism component by component, and (2) to compute tests for failures, in the mechanism, using the diagnosis algorithm. The development of an algorithm for the multioutput two-level minimization problem is presented and the program MIN 360 was written for this algorithm. The program has options of mode (exact minimum or various approximations), cost function, cost bound, etc., providing flexibility.
Roth, J. P.↗
Estimation in nonlinear systems with transport delay.
The problem of estimation of state in nonlinear dynamical systems containing time delays is studied. The plant is specified by a set of nonlinear differential-difference equations. Observations are a nonlinear function of current and/or delayed states. Both contain additive disturbances. The criterion used for the optimal estimates is the integral of the weighted squared error. Using the theory of the calculus of variations, equations are developed for the estimation. They are first expressed in the form of a split boundary value problem, which is then converted to an initial value problem for on-line estimation. The result yields a sequential estimation scheme in which filtered and smoothed estimates are computed in a sequential manner. The applicability of the procedure is demonstrated by a practical example.
Stoller, R. L.↗
Survey of recent work on the analysis of discretely attached corrugated shear webs.
Summary and progress report of more recent work by the author and his students on the theoretical analysis of stiffness, stresses, and deformations of corrugated shear webs with discrete, rather than continuous, attachment between the ends of the corrugations and the surrounding members. Various kinds of discrete attachment are considered, and two kinds of corrugation cross section: the trapezoidal and the curvilinear, the latter having crests and valleys made up of identical circular arcs. The more recent analyses employ the method of minimum total potential energy and the calculus of variations to obtain differential equations and boundary conditions governing the longitudinal variation of various component modes used to describe the deformations of a cross section. They are believed to be more accurate than earlier analyses in that they generally permit more degrees of freedom in the assumed deformations. In particular, they abandon the assumption, characteristic of the earlier analyses, that the straight-line generators of the corrugation remain straight during the shearing of the web.
Libove, C.↗
Nonlinear filtering for random signals in statistically unknown noise.
Natural and effective formulation of the filtering problem involved in satellite orbit determination, aircraft navigation, and missile tracking. The problem arises because the environment of the sensor keeps changing from time to time, and it is quite impractical and sometimes impossible to collect the statistical data of the noise incurred in the observation. Computable filtering equations are deduced. The idea of invariant imbedding along with stochastic differential calculus is used to derive differential equations for the optimal estimate.
Loo, J. T.↗
Perturbation guidance for minimum time flight paths of spacecraft.
The problem of transferring a rocket vehicle from a given circular orbit to a larger coplanar circular orbit in minimum time, using a constant low-thrust rocket engine, is considered. Parameters are chosen to correspond to a transfer from the earth's orbit in heliocentric space to the orbit of Mars. A path satisfying the first order necessary conditions of variational calculus is shown to be locally minimizing by application of a set of second order conditions. A physical explanation is offered to justify the retrothrust period occurring during the flight. A neighboring optimum feedback control law, based on estimated time-to-go, is applied to this problem. State variable and terminal constraint feedback gains are calculated while one of the second order conditions, involving the backward integration of a matrix Riccati equation, is being tested.
Wood, L. J.↗
Generation of NEP heliocentric trajectory data
A study, designed to generate representative nuclear electric propulsion data for rendezvous missions to the comet Encke using the variational calculus program HILTOP, is presented. Other purposes of the study include a comparison of the HILTOP data with equivalent data generated with QUICKTOP program and to propose approaches for storing and subsequently accessing the optimum trajectory and performance data in the QUICKLY program.
Horsewood, J. L.↗
Performance Analysis and Design Synthesis (PADS) computer program. Volume 1: Formulation
The program formulation for PADS computer program is presented. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module.
Source record↗
Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description
Methods for development of logic design together with algorithms for failure testing, a method for design of logic for ultra-large-scale integration, extension of quantum calculus to describe the functional behavior of a mechanism component-by-component and to computer tests for failures in the mechanism using the diagnosis algorithm, and the development of an algorithm for the multi-output 2-level minimization problem are discussed.
Roth, J. P.↗