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The normal Fourier modes of a closed ring polymer chain constitute a complete basis for decoupling the hydrodynamic equations. In this Fourier space, the hydrodynamic interaction terms are converted to a frequency-dependent friction constant. The method is exact for ring polymers, and is approximately correct for linear polymer chains. In this paper, the strengths and weaknesses of the approximation are explored. The approximation is satisfactory except (a) at low frequencies and (b) for motion of the chain ends. [ABSTRACT FROM AUTHOR]