Lagrangian descriptors and the action integral of classical mechanics

被引：8
作者：
Garcia-Garrido, Victor J. [1 ]
Wiggins, Stephen [2 ]
机构：
[1] Univ Alcala, Dept Fis & Matemat, Alcala De Henares 28871, Spain
[2] Univ Bristol, Sch Math, Fry Bldg, Woodland Rd, Bristol BS8 1UG, Glos, England
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2022年 / 434卷
基金：
英国工程与自然科学研究理事会;
关键词：
Lagrangian descriptors; Action functional; Phase space structure; Hamiltonian systems; GEOMETRY;
D O I：
10.1016/j.physd.2022.133206
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we bring together the method of Lagrangian descriptors and the principle of least action, or more precisely, of stationary action, in both deterministic and stochastic settings. In particular, we show how the action can be used as a Lagrangian descriptor. This provides a direct connection between Lagrangian descriptors and Hamiltonian mechanics, and we illustrate this connection with benchmark examples. (c) 2022 Elsevier B.V. All rights reserved.
引用
收藏
页数：11
相关论文
共 47 条
  • [1] Agaoglou M., 2019, ZENODO, DOI DOI 10.5281/ZENODO.3568210
  • [2] Agaoglou M., 2020, ZENODO, DOI [10.5281/zenodo.3958985, DOI 10.5281/ZENODO.3958985]
  • [3] Aguilar-Sanjuan B., J OPEN SOURCE SOFTW, V6, P3482, DOI [10.21105/joss.03482, DOI 10.21105/JOSS.03482]
  • [4] [Anonymous], 2003, INTRO APPL NONLINEAR, DOI DOI 10.1007/B97481
  • [5] Arnold V. I., 2013, MATH METHODS CLASSIC, V60
  • [6] Lagrangian Descriptors for Stochastic Differential Equations: A Tool for Revealing the Phase Portrait of Stochastic Dynamical Systems
    Balibrea-Iniesta, Francisco
    Lopesino, Carlos
    Wiggins, Stephen
    Mancho, Ana M.
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (13):
  • [7] Binary contraction method for the construction of time-dependent dividing surfaces in driven chemical reactions
    Bardakcioglu, Robin
    Junginger, Andrej
    Feldmaier, Matthias
    Main, Joerg
    Hernandez, Rigoberto
    [J]. PHYSICAL REVIEW E, 2018, 98 (03)
  • [8] Lagrangian descriptors of driven chemical reaction manifolds
    Craven, Galen T.
    Junginger, Andrej
    Hernandez, Rigoberto
    [J]. PHYSICAL REVIEW E, 2017, 96 (02)
  • [9] Deconstructing field-induced ketene isomerization through Lagrangian descriptors
    Craven, Galen T.
    Hernandez, Rigoberto
    [J]. PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 2016, 18 (05) : 4008 - 4018
  • [10] Lagrangian Descriptors of Thermalized Transition States on Time-Varying Energy Surfaces
    Craven, Galen T.
    Hernandez, Rigoberto
    [J]. PHYSICAL REVIEW LETTERS, 2015, 115 (14)
12345