Marvin I. Freedman

Smooth representation of systems with differentiated inputs

Conditions are derived under which the nonlinear input-output system \dot{y}=f(y,u,\dot{u}) can be represented in the form \dot{z} =g(z,u) ; y= h(z,u) . Various implications of the results to stochastic differential equations are considered.

Singular Perturbations of Two-Point Boundary Value Problems Arising in Optimal Control

This paper considers a two-point boundary value problem which arises from an application of the Pontryagin maximal principle to some underlying optimal control problem. The system depends singularly upon a small parameter,

Boundary integral equation for wave equation with moving boundary and applications to compressible potential aerodynamics of airplanes and helicopters

\varepsilon

Nonlinear arithmetic operations on the delta sigma pulse stream

. It is assumed that there exists a continuous solution of the system when

Arithmetic ternary operations on delta-modulated signals and their application in the realization of digital filters

\varepsilon = 0

A perturbation method applied to the buckling of a compressed elastica

, known as the reduced solution. Conditions are given under which there exists an “outer solution”, and “left and right boundary-layer solutions” whose sum constitutes a solution of the system which degenerates uniformly on compact sets to the reduced solution. The principal tool used in the proof is a Banach space implicit function theorem.

A Perturbation Problem from Control Exhibiting on and off the Boundary Behavior

This work presents a general boundary-integral-equation methodology for the solution of the wave equation around objects moving in arbitrary motion, with applications to compressible potential aerodynamics of airplanes and helicopters. The paper includes the derivation of the boundary integral equation for the wave equation, in a frame of reference moving in arbitrary motion (in particular, in translation and in rotation). The formulation is then applied to study unsteady potential compressible aerodynamic flows around streamlined bodies, such as airplanes and helicopters. The formulation is given in terms of the velocity potential, for which an explicit treatment of the wake is required; a discussion of the formulation for the wake transport is included. The advantages of the velocity-potential formulation over the acceleration-potential formulation are discussed. The boundary-element algorithm used for the computational implementation is briefly outlined. Validation of the formulation is presented for airplane wings and helicopter rotors in hover. The test cases fall into two categories. prescribed-wake and free-wake analyses. The validation of the prescribed-wake analysis is presented for compressible flows, subsonic for helicopter rotors, transonic for airplanes. The numerical validation of the free-wake analysis of helicopter rotors is presented for incompressible flows.

BEM for Wave Equation with Boundary in Arbitrary Motion and Applications to Compressible Potential Aerodynamics of Airplanes and Helicopters

Abstract In this paper it is shown how a delta-sigma modulated (ΔΣM) pulse stream can be used to carry out many of the functions of nonlinear signal processing. It is demonstrated how to realize arbitrary nonlinear memoryless functions on the basis of ΔΣM. The error bounds for the delta demodulator (DDM) averaging filter are also given. An example of the squaring operation is given.

Buckled Elastica at Contact: A Perturbation Analysis

This correspondence shows a method for determining the ternary delta sequence of the third of the sum of two analog signals through their corresponding delta sequences. The hardware implementation proposed here is modular employing a universal logic T-gate which allows building both sequential and combinatorial circuits. The primary advantage of a ternary nonredundant symmetric presentation of the TDM over a binary DM presentation is the reduction of problems of carry propagation in arithemetic operation and reduction in connections and interconnections between chips and interchips.

Bifurcation Analysis in Systems with Switch-Type Coefficients

Abstract We consider the problem of carrying out an asymptotic analysis for the phenomenon of bifurcation which occurs at critical values of an axial force applied to an elastic column. In the present setting a discontinuous coefficient precludes the possibility of carrying out the usual asymptotic analysis. The problem is overcome via a nonlinear change of independent variables.