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Guidance regime for optimal multistage lunar trajectory derived by applying calculus of variations to generalized Bolza problem
Multiple solutions to problem of bolza in calculus of variation
Calculus of variations minimized under linearized differential constraint for hybrid gradient method
Minimum drag bodies in hypersonic flow using calculus of variations
Low thrust trajectories for minimum time rendezvous between continuous thrust interceptor and passive target vehicle, comparing calculus of variations and steepest ascent analyses
Bolza problem of calculus of variations extended to trajectory optimization problems with several subarcs
Transforming optical control problem into equivalent Lagrange problem in calculus of variations
Second order endpoint condition considered in solution of Bolza problem in calculus of variations
Calculus of variations used for determining optimum one dimensional MHD slider bearing with bounded control variables
Optimal control surface location for flexible aircraft determined by matrix minimum principle and calculus of variations
Calculus of variations used for determining optimum one dimensional MHD slider bearing with bounded control variables
Solution of trajectory optimization problems by calculus of variations, dynamic programming, and Pontryagin's Principle
Optimum synthesis and design of distributed RC filter for oscillator feedback circuit, using calculus of variations
Aerodynamic control surfaces optimal location for flexible aircraft disturbed by random wind gusts, using matrix minimum principle and calculus of variations
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.
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.
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.
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.