机械系统轨迹集的定性分析

Q3 Mathematics

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 DOI:10.1016/j.jappmathmech.2016.05.005

V.I. Slyn’ko

{"title":"机械系统轨迹集的定性分析","authors":"V.I. Slyn’ko","doi":"10.1016/j.jappmathmech.2016.05.005","DOIUrl":null,"url":null,"abstract":"<div><p><span>The evolution of geometric measures (volume, surface area) of sets of attainability of linear controlled </span>mechanical systems<span> with constant parameters is studied. Lyapunov's direct method, the comparison method, and theory of mixed volumes are used. Based on the general comparison theorem, estimates are obtained for the solutions of differential equations with a generalized Hukuhara derivative that describe the evolution of regions of attainability. For linear controlled systems with one degree of freedom, the maximum boundedness conditions are obtained for the area of the set of attainability. Examples of the application of the obtained results are given.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 1","pages":"Pages 24-32"},"PeriodicalIF":0.0000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.05.005","citationCount":"0","resultStr":"{\"title\":\"A qualitative analysis of sets of trajectories of mechanical systems\",\"authors\":\"V.I. Slyn’ko\",\"doi\":\"10.1016/j.jappmathmech.2016.05.005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>The evolution of geometric measures (volume, surface area) of sets of attainability of linear controlled </span>mechanical systems<span> with constant parameters is studied. Lyapunov's direct method, the comparison method, and theory of mixed volumes are used. Based on the general comparison theorem, estimates are obtained for the solutions of differential equations with a generalized Hukuhara derivative that describe the evolution of regions of attainability. For linear controlled systems with one degree of freedom, the maximum boundedness conditions are obtained for the area of the set of attainability. Examples of the application of the obtained results are given.</span></p></div>\",\"PeriodicalId\":49686,\"journal\":{\"name\":\"Pmm Journal of Applied Mathematics and Mechanics\",\"volume\":\"80 1\",\"pages\":\"Pages 24-32\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.05.005\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pmm Journal of Applied Mathematics and Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021892816300429\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pmm Journal of Applied Mathematics and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021892816300429","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

研究了常参数线性控制机械系统可达性集几何测度(体积、表面积)的演化规律。使用了李亚普诺夫直接法、比较法和混合体积理论。基于一般比较定理，给出了描述可达区演化的广义Hukuhara导数微分方程解的估计。对于一自由度线性控制系统，得到了可达集面积的最大有界条件。给出了所得结果的应用实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A qualitative analysis of sets of trajectories of mechanical systems

The evolution of geometric measures (volume, surface area) of sets of attainability of linear controlled mechanical systems with constant parameters is studied. Lyapunov's direct method, the comparison method, and theory of mixed volumes are used. Based on the general comparison theorem, estimates are obtained for the solutions of differential equations with a generalized Hukuhara derivative that describe the evolution of regions of attainability. For linear controlled systems with one degree of freedom, the maximum boundedness conditions are obtained for the area of the set of attainability. Examples of the application of the obtained results are given.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Pmm Journal of Applied Mathematics and Mechanics 物理-力学

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal is a cover to cover translation of the Russian journal Prikladnaya Matematika i Mekhanika, published by the Russian Academy of Sciences and reflecting all the major achievements of the Russian School of Mechanics.The journal is concerned with high-level mathematical investigations of modern physical and mechanical problems and reports current progress in this field. Special emphasis is placed on aeronautics and space science and such subjects as continuum mechanics, theory of elasticity, and mathematics of space flight guidance and control.