A counterexample to analyticity in frictional dynamics

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2022-04-18 DOI:10.1051/m2an/2022033

Christopher Roger Dance

引用次数: 0

Abstract

We consider the motion of a particle acted on by dry friction and a force that is an analytic function of time. We give a counterexample to the claim that such motions are given by analytic functions of time. Several published arguments concerning existence and uniqueness in unilateral dynamics with friction rely on the analyticity of such motions. The counterexample invalidates those arguments for motions in three or more dimensions.

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摩擦动力学分析的一个反例

我们考虑一个质点在干摩擦作用下的运动和一个力是时间的解析函数。对于这种运动是由时间解析函数给出的说法，我们给出一个反例。一些已发表的关于带有摩擦的单边动力学的存在性和唯一性的论点依赖于这种运动的分析性。反例在三维或多维运动中使这些论点无效。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.