## A generalized averaging method for linear differential equations with almost periodic coefficientsThomas J. Coakley, United States. National Aeronautics and Space Administration, Ames Research Center National Aeronautics and Space Administration ; [For sale by the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151], 1969 - Mathematics - 15 pages |

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ai(t Ames Research Center approximate solutions approximate system approximations or series arbitrary Asymptotic Expansions asymptotic series asymptotically stable AVERAGING METHOD Basic System behavior and stability bounded choose the cutoff classical Floquet theory Coakley Ames Research COEFFICIENTS By Thomas constant coefficients constant matrix convergent cutoff frequency e^+l easily analyzed easily shown equation 28 equation l9 equations 3l exact and approximate exact solutions Floquet theory refs form of equations Fourier series given by equations grow or decay icot identity matrix level of approximation Liapunov ref linear differential equations linear system Moffett Field nonsingular obtained from equations ojQt order of approximation Ordinary Differential Equations original system periodic coefficients periodic functions quantity proportional reduced system series expansions slowly varying coefficients slowly varying functions solutions may grow solutions to equation solving equation successive approximations symmetric matrix system with constant system with rapidly theory of linear tion York