非保守动力学的Herglotz广义变分原理的研究进展（英文）

发布时间：2021-06-10 06:25

　　综述非保守动力学系统的Herglotz广义变分原理及其对称性与守恒量研究的最新进展。以Lagrange力学、Hamilton力学和Birkhoff力学作为研究框架,介绍其Herglotz广义变分原理、Herglotz型动力学方程、Noether对称性与守恒量,以及对时滞动力学、分数阶动力学、时间尺度动力学的推广,并提出若干问题作为未来研究的建议。 

【文章来源】：Transactions of Nanjing University of Aeronautics and Astronautics. 2020,37(01)EICSCD

【文章页数】：14 页

【文章目录】：
0 Introduction
1 Lagrangian Mechanics of Her-glotz Type
    1.1 Herglotz’s generalized variational principle
    1.2 Euler-Lagrange equations of Herglotz type
    1.3 Noether symmetry for the Lagrange system of Herglotz type
    1.4 Generalization to nonholonomic dynamics
    1.5 Generalization to time-delay dynamics
    1.6 Generalization to fractional dynamics
    1.7 Generalization to time-scale dynamics
    1.8 Other generalization
    1.9 Problems to be further studied in Lagrang-ian mechanics of Herglotz type
2 Hamiltonian Mechanics of Her-glotz Type
    2.1 Herglotz’s generalized variational principle
    2.2 Hamilton canonical equations of Herglotz type
    2.3 Noether symmetry for the Hamilton system of Herglotz type
    2.4 Generalization to time-delay dynamics
    2.5 Generalization to fractional dynamics
    2.6 Generalization to time-scale dynamics
    2.7 Problems to be further studied in Hamilto-nian machanics of Herglotz type
3 Birkhoffian Mechanics of Her-glotz Type
    3.1 Herglotz’s generalized variational principle
    3.2 Birkhoff’s equations of Herglotz type
    3.3 Noether symmetry for the Birkhoff system of Herglotz type
    3.4 Generalization to constrained Birkhoff sys-tem
    3.5 Generalization of time-delay dynamics
    3.6 Generalization to fractional dynamics
    3.7 Generalization to time-scale dynamics
    3.8 Problems to be further studied in Birkhof-fian mechanics of Herglotz type
4 Conclusions


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