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A Gusenkova, A. Steindl, H. Troger:
"On loss of stability of slow motions in stiff oscillatory systems";
Talk: GAMM 2004, Dresden; 2004-03-21 - 2004-03-27; in: "GAMM Annual Meeting Dresden 2004", PAMM/WILEY-VCH Verlag GmbH & Co., 4 (2004), 2 pages.

In stiff oscillatory systems often a reduction of the order of the system is possible by splitting the motion into an essential motion on a nearby slow manifold and neglecting the fast motion. However, if the system is conservative the question of stability of the slow motion is a delicate problem. For various spring pendulum systems we, first, perform numerical simulations showing that if the stiffness of the springs is gradually reduced the slow motion looses stability. For a single spring pendulum we give an explanation of this loss of stability.

http://aleph.ub.tuwien.ac.at/F?base=tuw01&func=find-c&ccl_term=AC04968944

http://www3.interscience.wiley.com/cgi-bin/fulltext/109800596/PDFSTART