Eric A. Butcher

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SUMMARY This paper presents a new technique for studying the stability properties of dynamic systems modeled by delay-differential equations (DDEs) with time-periodic parameters. By employing a shifted Cheby-shev polynomial approximation in each time interval with length equal to the delay and parametric excitation period, the dynamic system can be reduced(More)
The dynamics of a rotating tool, commonly employed in deep hole honing, is considered. A mathematical model of the process including a dynamic representation of tool, workpiece surface and honing stones interaction is suggested and analyzed. It is shown that interaction forces are non-conservative. The honing tool is modeled as a rotating continuous slender(More)
This chapter provides a brief literature review together with detailed descriptions of the authors' work on the stability and control of systems represented by linear time-periodic delay-differential equations using the Chebyshev and temporal finite element analysis (TFEA) techniques. Here, the theory and examples assume that there is a single fixed(More)
In this paper, we obtain an analytical Lyapunov-based stability conditions for scalar linear and nonlinear stochastic systems with discrete time-delay. The Lyapunov– Krasovskii and Lyapunov–Razumikhin methods are applied with techniques from stochastic calculus to obtain the regions of mean square asymptotic stability in the parameter space. Both(More)
Chebyshev polynomials are utilized to obtain solutions of a set of pth order linear differential equations with periodic coefficients. For this purpose, the operational matrix of differentiation associated with the shifted Chebyshev polynomials of the first kind is derived. Utilizing the properties of this matrix, the solution of a system of differential(More)
Some new techniques for reduced order (macro) modeling of nonlinear systems with time periodic coefficients are discussed in this paper. The dynamical evolution equations are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the new set of equations become time-invariant. The techniques presented here reduce the order(More)
A technique for dimensional reduction of nonlinear delay differential equations with time-periodic coefficients is presented. The DDEs considered here have at most cubic nonlinearities multiplied by a perturbation parameter. The periodic terms and matrices are not assumed to have predetermined norm bounds, thus making the method applicable to systems with(More)
A symbolic computational technique is used to study the secondary bifurcations of a para-metrically excited simple pendulum as an explicit function of the periodic parameter. This is made possible by the recent development of an algorithm which approximates the fundamental solution matrix of linear time-periodic systems in terms of system parameters in(More)