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.↗
SEARCH · Engineering Papers
Results for “Variational Calculus”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
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.↗
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↗
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.↗
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↗
Performance Analysis and Design Synthesis (PADS) computer program. Volume 2: Program description, part 1
The Performance Analysis and Design Synthesis (PADS) computer program has a two-fold purpose. 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. For Volume 1 see N73-13199.
Source record↗
Performance Analysis and Design Synthesis (PADS) computer program. Volume 3: User manual
The two-fold purpose of the Performance Analysis and Design Synthesis (PADS) computer program is discussed. The program 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. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent. The second module uses the method of quasi-linearization, which requires a starting solution from the first trajectory module.
Source record↗
Optimum configurations for bangless sonic booms.
A number of optimization problems are posed and solved for supersonic aircraft flight subject to the condition that a shock wave appears only incipiently in the sonic boom signal at a given point. The principal result is one giving the maximum effective gross weight of an aircraft of given effective length under given flight conditions. The calculus of variations with inequality constraints is used, with the novel features of a non-local isoperimetric relation and of only an upper bound on a control variable.
Hayes, W. D.↗
Optimization of multiple target electric propulsion trajectories.
Development of the mathematical basis for the generation of multiple target low-thrust trajectories. The unique trajectory shaping capabilities of electric propulsion make it ideally suited for modifying the path of the spacecraft to effect close encounters of selected asteroids with only slight penalties in performance. Each intermediate encounter with an asteroid involves the optimization of four parameters, the encounter time and the three components of the relative velocity at encounter. A second type of mission amenable to this analysis is that of asteroid or comet sample return missions. For missions of this type, both launch date and division of departure and return flight times are capable of being optimized. Use is made of the traditional calculus of variations to derive the necessary conditions that must be satisfied for both types of missions. In addition, examples are presented of both a Comet Encke rendezvous mission with multiple encounters of the asteroids Aschera and Alekto and also a sample return mission from the asteroid Flora.
Sauer, C. G., Jr.↗
Computer simulation for time optimal or energy optimal attitude control of spin-stabilized spacecraft.
An original technique for determining the optimal magnetic torque strategy for control of the attitude of spin stabilized spacecraft is presented. By employing Lagrange multipliers and the Calculus of Variations, optimal control equations are derived which define minimum time and minimum energy attitude maneuvers. Computer program algorithms to numerically solve these optimal control equations are also described. The performance of this technique is compared with a commonly employed planning method.
Woolley, R. D.↗
A macroscopic plasma Lagrangian and its application to wave interactions and resonances
The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.
Peng, Y. K. M.↗
Control optimization of a lifting body entry problem by an improved and a modified method of perturbation function
A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.
Garcia, F., Jr.↗
Effects of inclination and eccentricity on optimal trajectories between earth and Venus
The true optimal transfers, including the effects of the inclination and eccentricity of the planets' orbits, between earth and Venus are presented as functions of the corresponding idealized Hohmann transfers. The method of determining the optimal transfers using the calculus of variations is presented. For every possible Hohmann window, specified as a continuous function of the longitude of perihelion of the Hohmann trajectory, the corresponding numerically exact optimal two-impulse transfers are given in graphical form. The cases for which the optimal two-impulse transfer is the absolute optimal, and those for which a three-impulse transfer provides the absolute optimal transfer are indicated. This information furnishes everything necessary for quick and accurate orbit calculations for preliminary Venus mission analysis. This makes it possible to use the actual optimal transfers for advanced planning in place of the standard Hohmann transfers.
Gravier, J.-P.↗