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Homogenization in Time II: Mechanical Systems Subject to Friction and Gyroscopic Forces

Please always quote using this URN: urn:nbn:de:0297-zib-3348
  • In our previous work [Preprint SC 97-48] we have studied natural mechanical systems on Riemannian manifolds with a strong constraining potential. These systems establish fast nonlinear oscillations around some equilibrium manifold. Important in applications, the problem of elimination of the fast degrees of freedom, or {\em homogenization in time}, leads to determine the singular limit of infinite strength of the constraining potential. In the present paper we extend this study to systems which are subject to external forces that are non-potential, depending in a mixed way on positions {\em and}\/ velocities. We will argue that the method of weak convergence used in [1997] covers such forces if and only if they result from viscous friction and gyroscopic terms. All the results of [1997] directly extend if there is no friction transversal to the equilibrium manifold; elsewise we show that instructive modifications apply.

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Metadaten
Author:Folkmar A. Bornemann
Document Type:ZIB-Report
Date of first Publication:1997/12/16
Series (Serial Number):ZIB-Report (SC-97-65)
ZIB-Reportnumber:SC-97-65
Published in:Published as §II.5 in the monograph: Folkmar A. Bornemann. Homogenization in Time of Singularly Perturbed Mechanical Systems. Lecture Notes in Mathematics, 1687. Berlin u.a.: Springer 1998
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