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The development of the concept of direct separation of motions in nonlinear mechanics. (English) Zbl 0552.70017
Advances in theoretical and applied mechanics, 127-147 (1981).
[For the entire collection see Zbl 0537.00026.]
This paper deals with systems whose motion x(t) can be expressed by \(x=X(t)+\psi (t,\omega t)\); t is the slow and \(\omega\) t the fast time. The original differential equations are replaced by a system of integro- differential equations of ”double order” in which the vibrational forces of the slow motion are separated to be suitable for averaging. The method is applied to special questions and examples, e.g., the change of ”slow” rheological properties due to vibrations.
Reviewer: E.Brommundt

70K99 Nonlinear dynamics in mechanics
34C29 Averaging method for ordinary differential equations