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。
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.
作者
张毅
Zhang Yi(School of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China)
出处
《南京理工大学学报》
EI
CAS
CSCD
北大核心
2019年第6期759-764,共6页
Journal of Nanjing University of Science and Technology
基金
国家自然科学基金(11972241
11572212
11272227)
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
non-conservative dynamical system
differential variational principle
conservation law
Herglotz variational problem
