綜述非保守動力學(xué)系統(tǒng)的Herglotz廣義變分原理及其對稱性與守恒量研究的最新進展。以Lagrange力學(xué)、Hamilton力學(xué)和Birkhoff力學(xué)作為研究框架,介紹其Herglotz廣義變分原理、Herglotz型動力學(xué)方程、Noether對稱性與守恒量,以及對時滯動力學(xué)、分數(shù)階動力學(xué)、時間尺度動力學(xué)的推廣,并提出若干問題作為未來研究的建議。 

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

【文章頁數(shù)】：14 頁

【文章目錄】：
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


【參考文獻】：
期刊論文
[1]Conservation laws for Birkhoffian systems of Herglotz type[J]. 張毅,田雪.  Chinese Physics B. 2018(09)
[2]Noether Symmetry and Conserved Quantities of Fractional Birkhoffian System in Terms of Herglotz Variational Problem[J]. 田雪,張毅.  Communications in Theoretical Physics. 2018(09)
[3]時間尺度上Herglotz變分原理及其Noether定理[J]. 田雪,張毅.  力學(xué)季刊. 2018(02)
[4]Noether Theorem for Generalized Birkhoffian Systems with Time Delay[J]. Zhai Xianghua,Zhang Yi.  Transactions of Nanjing University of Aeronautics and Astronautics. 2018(03)
[5]Generalized Chaplygin equations for nonholonomic systems on time scales[J]. 金世欣,張毅.  Chinese Physics B. 2018(02)
[6]Methods of reduction for Lagrange systems on time scales with nabla derivatives[J]. 金世欣,張毅.  Chinese Physics B. 2017(01)
[7]相空間中非保守系統(tǒng)的Herglotz廣義變分原理及其Noether定理[J]. 張毅.  力學(xué)學(xué)報. 2016(06)
[8]Birkhoff力學(xué)的研究進展[J]. 梅鳳翔,吳惠彬,李彥敏,陳向煒.  力學(xué)學(xué)報. 2016(02)
[9]基于聯(lián)合Caputo導(dǎo)數(shù)的分數(shù)階Hamilton力學(xué)和分數(shù)階正則變換（英文）[J]. 張毅.  蘇州科技學(xué)院學(xué)報(自然科學(xué)版). 2014(01)
[10]含時滯的非保守系統(tǒng)動力學(xué)的Noether對稱性[J]. 張毅,金世欣.  物理學(xué)報. 2013(23)



本文編號：3221865