摘要
该文基于微分变分原理研究相空间中含时滞的非保守力学系统的守恒律.首先,建立了相空间中含时滞的非保守系统的微分变分原理;其次,通过引进空间和时间的无穷小生成函数,给出此微分变分原理在无限小变换下的不变性条件;最后,导出了相空间中含时滞的非保守系统的守恒律存在的条件及形式.文末,举例说明结果的应用.
Based on the differential variational principle, the conservation laws of nonconservative mechanical systems with time delay in phase space is studied. Firstly, the differential variational prin- ciple of nonconservative systems with time delay in the phase space is established by using the Hamil ton principle. Secondly, by introducing the generalized variational, the invariance conditions of the dif- ferential variational principle under the infinitesimal transformation are given. Finally, the conditions and the forms of the conservation laws for the nonconservative systems with time delay in the phase space are deduced. The application of the result is illustrated by example in the end.
出处
《广西师范学院学报（自然科学版）》
2015年第4期40-46,共7页
Journal of Guangxi Teachers Education University(Natural Science Edition)
基金
国家自然科学基金资助项目(10972151
11272227)
苏州科技学院研究生科研创新计划资助项目(SKCX15_061)
关键词
相空间
时滞
微分变分原理
守恒律
phase space
time delay
differential variational principle
conservation law
