An upper bound for normal form asymptotic expansions

Abstract : In the nineties, analytical methods based on normal form theory have been used to obtain approximate expressions of free or forced responses of non-linear (smooth) mechanical systems. A large amount of interesting results can be obtained by these approaches, however no practical limits of validity are available. In this paper, a method to obtain simple upper bounds for amplitudes of changes of coordinates is proposed. Simple conservative mechanical examples are provided to illustrate the bounds estimation and their validity.
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Claude-Henri Lamarque, Cyril Touzé, Olivier Thomas. An upper bound for normal form asymptotic expansions. DSTA 2011, Dynamical Systems Theory and Applications, 2011, Lodz, Poland. ⟨hal-01154715⟩

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