2025年6月15日 22:42 星期日
首页 > 过刊浏览>2023年第55卷第1期 >164-168. DOI:10.16356/j.1005-2615.2023.01.020
PDF HTML阅读 XML下载 导出引用 引用提醒
El-Nabulsi型非保守动力学系统的近似Noether不变量
CSTR:
[cstr]
作者:
作者单位:

1.苏州科技大学数学科学学院，苏州215009;2.苏州科技大学土木工程学院，苏州215011

通讯作者:

张毅， 男， 教授，E-mail： zhy@mail.usts.edu.cn。

中图分类号:

O316

基金项目:

国家自然科学基金（11972241，11572212）； 江苏省自然科学基金（BK20191454）。


Approximate Noether Invariants for Nonconservative Dynamical Systems Under El-Nabulsi Models
Author:
Affiliation:

1.College of Mathematical Sciences， Suzhou University of Science and Technology， Suzhou 215009， China;2.College of Civil Engineering， Suzhou University of Science and Technology， Suzhou 215011， China

  • 摘要
    • | |
  • 访问统计
    • |
  • 参考文献 [16]
    • |
  • 相似文献
    • |
  • 引证文献
    • | |
  • 文章评论
    摘要:

    为了探究小扰动作用对动力学系统不变量的影响，研究El-Nabulsi指数模型和El-Nabulsi幂律模型下非保守系统的近似Noether不变量。根据Hamilton原理，并以非标准Lagrange函数作为其作用量泛函，建立非保守系统的El-Nabulsi型动力学方程。在此基础上，依据泛函在无限小变换下的不变性，给出非保守系统在小扰动作用下的近似Noether不变量。当未受扰动时，则给出精确Noether不变量。证明了El-Nabulsi指数模型和El-Nabulsi幂律模型下非保守系统的近似Noether不变量定理。本文方法为研究非保守系统动力学提供了一个新的思路，算例亦显示结果之有效性。

    Abstract:

    In order to investigate the influence of small perturbations on the invariants of dynamical systems， we study the approximate Noether invariants of nonconservative systems under El-Nabulsi exponential model and El-Nabulsi power-law model. According to Hamilton’s principle with nonstandard Lagrangians as its action functional， the dynamics equations of El-Nabulsi type for nonconservative systems are established. On this basis， due to the invariance of the functional under infinitesimal transformation， the approximate Noether invariants of nonconservative systems under small disturbance are obtained. When not disturbed， the exact Noether invariants are given. The approximate Noether invariant theorems for nonconservative systems under El-Nabulsi exponential model and El-Nabulsi power-law model are proved. This method provides a new idea for the study of nonconservative system dynamics， and two examples show the effectiveness of the results.

    参考文献
    [1] RIEWE F. Nonconservative Lagrangian and Hamiltonian mechanics[J]. Physical Review E, 1996, 53(2): 1890-1899.
    [2] EL-NABULSI A R. A fractional approach to nonconservative Lagrangian dynamical systems[J]. Fizika A, 2005, 14(4): 289-298.
    [3] EL-NABULSI A R. Non-linear dynamics with non-standard Lagrangians[J]. Qualitative Theory of Dynamical Systems, 2013, 12(2): 273-291.
    [4] EL-NABULSI A R. Non-standard fractional Lagrangians[J]. Nonlinear Dynamics, 2013, 74(1/2): 381-394.
    [5] EL-NABULSI A R. Non-standard power-law Lagrangians in classical and quantum dynamics[J]. Applied Mathematics Letters, 2015, 43: 120-127.
    [6] LONG Zixuan, ZHANG Yi. Fractional Noether theorem based on extended exponentially fractional integral[J]. International Journal of Theoretical Physics, 2014, 53(3): 841-855.
    [7] LONG Zixuan, ZHANG Yi. Noether’s theorem for fractional variational problem from El-Nabulsi extended exponentially fractional integral in phase space[J]. Acta Mechanica, 2014, 225(1): 77-90.
    [8] CHEN Ju, ZHANG Yi. Perturbation to Noether symmetries and adiabatic invariants for disturbed Hamiltonian systems based on El-Nabulsi nonconservative dynamics model[J]. Nonlinear Dynamics, 2014, 77(1/2): 353-360.
    [9] SONG Chuanjing, ZHANG Yi. Conserved quantities and adiabatic invariants for El-Nabulsi’s fractional Birkhoff system[J]. International Journal of Theoretical Physics, 2015, 54(8): 2481-2493.
    [10] LIU Shixing, GUAN Fang, WANG Yong, et al. The nonlinear dynamics based on the nonstandard Hamiltonians[J]. Nonlinear Dynamics, 2017, 88(2): 1229-1236.
    [11] ZHANG Yi, WANG Xueping. Lie symmetry perturbation and adiabatic invariants for dynamical system with non-standard Lagrangians[J]. International Journal of Non-linear Mechanics, 2018,105: 165-172.
    [12] SONG Jing, ZHANG Yi. Noether’s theorems for dynamical systems of two kinds of non-standard Hamiltonians[J]. Acta Mechanica, 2018, 229(1): 285-297.
    [13] ZHANG Yi, WANG Xueping. Mei symmetry and invariants of quasi-fractional dynamical systems with non-standard Lagrangians[J]. Symmetry, 2019. DOI: 10.3390/sym11081061.
    [14] 周小三, 张毅. 基于非标准Lagrange函数的动力学系统的广义能量积分与Whittaker降阶法[J]. 南京航天航空大学学报, 2017, 49(2): 269-275.ZHOU Xiaosan, ZHANG Yi. Generalized energy integral and Whittaker method of reduction for dynamics systems with non-standard Lagrangians[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2017, 49(2): 269-275.
    [15] 周小三, 张毅. El-Nabulsi模型下非标准Lagrange函数的动力学系统的Noether定理[J].四川大学学报(自然科学版), 2017, 54(3): 535-540.ZHOU Xiaosan, ZHANG Yi. Noether theorems for dynamical systems with non-standard Lagrangians based on El-Nabulsi models[J]. Journal of Sichuan University (Natural Science Edition), 2017, 54(3): 535-540.
    [16] 楼智美, 梅凤翔, 陈子栋. 弱非线性耦合二维各向异性谐振子的一阶近似Lie对称性与近似守恒量[J]. 物理学报, 2012, 61(11): 41-45.LOU Zhimei, MEI Fengxiang, CHEN Zidong. The first-order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator[J]. Acta Physica Sinica, 2012, 61(11): 41-45.
    相似文献
    引证文献
引用本文

王雪萍,张毅. El-Nabulsi型非保守动力学系统的近似Noether不变量[J].南京航空航天大学学报,2023,55(1):164-168

复制
分享
文章指标
  • 点击次数:
  • 下载次数:
  • HTML阅读次数:
  • 引用次数:
历史
  • 收稿日期:2021-03-09
  • 最后修改日期:2022-04-02
  • 在线发布日期: 2023-02-05
文章二维码
您是第位访问者
网站版权 © 南京航空航天大学学报
技术支持：北京勤云科技发展有限公司
请使用 Firefox、Chrome、IE10、IE11、360极速模式、搜狗极速模式、QQ极速模式等浏览器，其他浏览器不建议使用!