Abstract
The inhomogeneous Hill equation in which coefficients and right hand part are periodical with the same period T is considered. It is shown, that only some particular solutions of this equation can be periodical with period T. At the same time it is succeed to discover at certain values of equation’s parameters the general solution of inhomo-geneous Hill equation becomes periodical with period multiple of T. Necessary and sufficient conditions for periodicity of general solution of inhomogeneous Hill equation is obtained. A numerical algorithm for constructing of periodical fundamental system solutions to corresponding homogeneous Hill equation is worked out. It is shown, as the periodical general solution of inhomogeneous Hill equation can be obtained from this fundamental system. Some applications of obtained results in engineering practice are specified.
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