[1]张 毅.非保守动力学系统的Herglotz型微分变分原理与守恒律[J].南京理工大学学报(自然科学版),2019,43(06):759-764.[doi:10.14177/j.cnki.32-1397n.2019.43.06.013]
 Zhang Yi.Differential variational principle of Herglotz type and conservationlaws for non-conservative dynamical systems[J].Journal of Nanjing University of Science and Technology,2019,43(06):759-764.[doi:10.14177/j.cnki.32-1397n.2019.43.06.013]
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非保守动力学系统的Herglotz型微分变分原理与守恒律()
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《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

卷:
43卷
期数:
2019年06期
页码:
759-764
栏目:
出版日期:
2019-12-31

文章信息/Info

Title:
Differential variational principle of Herglotz type and conservationlaws for non-conservative dynamical systems
文章编号:
1005-9830(2019)06-0759-06
作者:
张 毅
苏州科技大学 土木工程学院,江苏 苏州 215011
Author(s):
Zhang Yi
School of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China
关键词:
非保守动力学系统 微分变分原理 守恒律 Herglotz变分问题
Keywords:
non-conservative dynamical system differential variational principle conservation law Herglotz variational problem
分类号:
O316
DOI:
10.14177/j.cnki.32-1397n.2019.43.06.013
摘要:
为了研究非保守动力学系统的物理性态和动力学行为,利用Herglotz型微分变分原理构建非保守动力学系统的守恒律。基于Herglotz变分问题,导出完整非保守系统的Herglotz型微分变分原理。引进时间和空间的无限小生成元,建立微分变分原理不变性条件的变换式。建立完整非保守系统的守恒定理及其逆定理,给出了新守恒量存在的条件,得到了新守恒量。举例说明该文方法的应用。
Abstract:
To study the physical nature and dynamic behavior of a non-conservative dynamical system,the conservation law of the non-conservative dynamical system is constructed by using the differential variational principle of Herglotz type. The differential variation principle of Herglotz type for holonomic non-conservative system is derived based on Herglotz variational problem. The condition of invariance of the differential variational principle is established by introducing the infinitesimal generators of time and space. The conservation theorem and its inverse theorem of the holonomic non-conservative system are established,and the condition under which a new conserved quantity exists is given and the new conserved quality is obtained. Two examples are presented to illustrate the application of the results.

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备注/Memo

备注/Memo:
收稿日期:2017-12-13 修回日期:2019-02-09
基金项目:国家自然科学基金(11972241; 11572212; 11272227)
作者简介:张毅(1964-),男,博士,教授,主要研究方向:分析力学,E-mail:zhy@mail.usts.edu.cn。
引文格式:张毅. 非保守动力学系统的Herglotz型微分变分原理与守恒律[J]. 南京理工大学学报,2019,43(6):759-764.
投稿网址:http://zrxuebao.njust.edu.cn
更新日期/Last Update: 2019-12-31