On the (in)stability of quasi-static paths of smooth systems: definitions and sufficient conditions

被引：8
作者：
Martins, JAC
Rebrova, NV
Sobolev, VA
机构：
[1] Inst Super Tecn, Dept Engn Civil & Arquitectura, P-1049001 Lisbon, Portugal
[2] Inst Super Tecn, ICIST, P-1049001 Lisbon, Portugal
[3] Univ Samara, Samara, Russia
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2006年 / 29卷 / 06期
关键词：
differential equations; singular perturbations; dynamics; quasi-statics; stability;
D O I：
10.1002/mma.707
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A concept of stability of quasi-static paths is discussed in this paper that takes into account the existence of fast (dynamic) and slow (quasi-static) time scales in the evolution of many mechanical systems. The proposed concept is essentially a continuity property with respect to the smallness of the initial perturbations (as in Lyapunov stability) and the smallness of the quasi-static loading rate (that plays the role of the small parameter in singular perturbation problems). A related concept of attractiveness is also proposed. Several examples illustrate the relevance of the definitions. Sufficient conditions for attractiveness or for instability of quasi-static paths of smooth systems are proved. Copyright (c) 2005 John Wiley & Sons, Ltd.
引用
收藏
页码：741 / 750
页数：10
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