Geometry and physics of averaging with applications

被引：28

作者：

Levi, M ^{[1
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

PHYSICA D | 1999年 / 132卷 / 1-2期

关键词：

Paul trap; averaging; normal form; vibration; constraints;

D O I：

10.1016/S0167-2789(99)00022-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main point of this paper is an observation that behind the standard averaging procedure there lies some simple previously unobserved geometry. Ln particular, the averaged forces in a rapidly forced system are, as it turns out, the constraint forces of an associated auxiliary non-holonomic system. The curvature of these constraints enters the expression for the averaged system. For example, the curvature of the pursuit curve enters the averaged equation of the pendulum with vibrating suspension point. This observation gives a new physical and geometrical insight into the mechanics of the Paul traps and the stability of forced inverted pendula. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：150 / 164

页数：15

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