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Asymptotic expansions and attractive invariant manifolds of strongly damped mechanical systems
Author(s) -
Stumpp Th.
Publication year - 2008
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200700057
Subject(s) - invariant manifold , invariant (physics) , mathematical analysis , asymptotic expansion , slow manifold , exponential function , reciprocal , manifold (fluid mechanics) , singular perturbation , mathematics , physics , classical mechanics , mechanical system , mathematical physics , computer science , mechanical engineering , linguistics , philosophy , artificial intelligence , engineering
We study analytical properties of strongly damped mechanical systems, for which the equations of motion form a singular singularly perturbed system. We show that slow solutions can be represented by an asymptotic expansion in powers of the reciprocal of the damping parameter. Further it is shown that the strong damping forces the motion to run into an invariant manifold at an exponential rate.