摩尔斯族和狄拉克系

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-04-13 DOI:10.3934/jgm.2019024

M. B. Liñán, Hernán Cendra, Eduardo García Toraño, D. M. Diego

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引用次数: 11

摘要

用Dirac结构和Morse族得到了一种几何形式，它统一了力学中的大多数情形(约束微积分、非完整系统、最优控制理论、高阶力学等)，如文中的例子所示。这种方法推广了前人关于狄拉克结构与拉格朗日子流形相关的研究结果。对于所研究的广义狄拉克动力系统，给出了一种Mendela、Marmo和Tulczyjew意义上的可积算法，用于确定隐式微分方程的解集。

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Morse families and Dirac systems

Dirac structures and Morse families are used to obtain a geometric formalism that unifies most of the scenarios in mechanics (constrained calculus, nonholonomic systems, optimal control theory, higher-order mechanics, etc.), as the examples in the paper show. This approach generalizes the previous results on Dirac structures associated with Lagrangian submanifolds. An integrability algorithm in the sense of Mendela, Marmo and Tulczyjew is described for the generalized Dirac dynamical systems under study to determine the set where the implicit differential equations have solutions.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.