A one-dimensional system of equimass particles coupled by identical nonlinear springs is studied. The equations of motion are expressed in terms of the normal coordinates of the corresponding linear system. Selection rules are developed for interactions among the modes and the number of interaction terms in the modal equations is reduced by considering the case of a single dominant mode. The equations are considerably simplified by judicious ap¬proximation and their validity checked by direct numerical computation. In terms of the resulting coupled Mathieu equations, it is possible to investigate stability questions and to explain recent results of computational experiments. The bearing on ergodicity and time-correlation is discussed.
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