The von Zeipel method and the two-variable expansion procedure are briefly described for the case of a Hamiltonian which corresponds to the forced oscillations of a system with small nonlinearity. It is shown that the results of the two methods agree exactly to order E, where E is a small parameter measuring the nonlinearity. In achieving this correspondence the meaning of the long-periodic terms occurring in the two approaches is clarified and contrasted.
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J. Kevorkian (1966) studied this question.
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