摘要
提出并研究时间尺度上非完整系统的Noether准对称性与守恒量.首先,将时间尺度上非完整系统的运动微分方程化为时间尺度上一般完整系统的Lagrange方程,在Lagrange框架下建立时间尺度上Noether定理,给出时间尺度上Noether守恒量;其次将时间尺度上非完整系统的运动微分方程化为时间尺度上相空间中一般完整系统的Hamilton方程,在Hamilton框架下建立时间尺度上Noether定理,给出时间尺度上Noether守恒量;再次,将时间尺度上非完整系统的运动微分方程化为时间尺度上广义Birkhoff方程,在Birkhoff框架下依据时间尺度上Noether准对称性的定义,建立时间尺度上Noether定理和广义Noether等式,给出时间尺度上Noether守恒量.最后,举例说明结果的应用.
The Noether quasi-symmetry and conservation laws on time scales for nonholonomic systems are proposed and studied.Firstly,the differential equations of motion for nonholonomic dynamical system are transformed into the generalized Birkhoff’s equations on time scales.Under the Birkhoffian framework,the Noether theories and the generalized Noether identities on time scales are established,and the Noether conservation laws on time scales are obtained,which based on the definition of Noether quasi-symmetry.Secondly,the nonholonomic dynamical equations are transformed into the Lagrange equations on time scales for general holonomic system.Under the Lagrangian framework,the Noether theories on time scales are established,and the Noether conservation laws on time scales are obtained.Thirdly,the nonholonomic dynamical equations are transformed into the Hamilton equations on time scales for general holonomic system in phase space.Under the Hamiltonian framework,the Noether theories on time scales are established,and the Noether conservation laws on time scales are obtained.Finally,several examples are given to illustrate the applications of the results.
作者
金世欣
李莉
李彦敏
JIN Shixin;LI Li;LI Yanmin(School of Mathematics and Statistics,Shangqiu Normal University,Shangqiu 476000,China;School of Physics and Information Engineering,Shangqiu Normal University,Shangqiu 476000,China)
出处
《商丘师范学院学报》
CAS
2023年第9期1-7,共7页
Journal of Shangqiu Normal University
基金
国家自然科学基金(11572212,12102241)
河南省高等学校重点科研基金(20A130003)
