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摘要翻译：
本文介绍了约束力学微积分在经济学中的指导性跨学科应用，以适合本科物理教育的水平。本文的研究目的如下：1。以满足说明性例子的需求，适合于呈现经济物理学研究领域的高度扩展的背景，甚至在本科层次和2。使学生从经济学的不同角度看力学中常用的原理和方法，从而更深入地理解力学中常用的原理和方法。用经济术语直观地给出了两个有约束的动态经济问题。首先，将Phillips经济周期模型描述为一个受迫振荡系统，并用非完整动力学方法求解两个经济相互作用的一般问题。其次，利用vakonomic方法，将经济增长的Cass-Koopmans-Ramsey模型解为一个具有速度相关约束的变分问题。详细讨论了与力学相比较的经济学解解释的细节，讨论了力学和经济学中约束问题的非完整和vakonomic方法，并仔细解释了拉格朗日乘子的经济学解释（可能对物理学的学生来说是令人惊讶的）。本论文可供对跨学科物理应用感兴趣的物理学本科生使用，以接触基于物理背景的当前经济学科学方法，也可供大学教师作为经典力学课程的有吸引力的补充。
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英文标题：
《Applications of a constrained mechanics methodology in economics》
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作者：
Jitka Janov\'a
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最新提交年份：
2011
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分类信息：
一级分类：Physics 物理学
二级分类：Physics Education 物理教育
分类描述：Report of results of a research study, laboratory experience, assessment or classroom practice that represents a way to improve teaching and learning in physics. Also, report on misconceptions of students, textbook errors, and other similar information relative to promoting physics understanding.
一项研究、实验室经验、评估或课堂实践的结果报告，它代表了一种改进物理教与学的方法。此外，报告学生的误解，教科书错误，以及其他与促进物理理解有关的类似信息。
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一级分类：Physics 物理学
二级分类：Classical Physics 经典物理学
分类描述：Newtonian and relativistic dynamics; many particle systems; planetary motions; chaos in classical dynamics. Maxwell's equations and dynamics of charged systems and electromagnetic forces in materials. Vibrating systems such as membranes and cantilevers; optomechanics. Classical waves, including acoustics and elasticity; physics of music and musical instruments. Classical thermodynamics and heat flow problems.
牛顿和相对论动力学；许多粒子系统；行星运动；经典动力学中的混沌。材料中带电系统和电磁力的麦克斯韦方程组和动力学。振动系统，如薄膜和悬臂；光学力学。经典波，包括声学和弹性；音乐和乐器物理学。经典热力学和热流问题。
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一级分类：Physics 物理学
二级分类：Physics and Society 物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
The paper presents instructive interdisciplinary applications of constrained mechanics calculus in economics on a level appropriate for the undergraduate physics education. The aim of the paper is: 1. to meet the demand for illustrative examples suitable for presenting the background of the highly expanding research field of econophysics even on the undergraduate level and 2. to enable the students to understand deeper the principles and methods routinely used in mechanics by looking at the well known methodology from the different perspective of economics. Two constrained dynamic economic problems are presented using the economic terminology in an intuitive way. First, the Phillips model of business cycle is presented as a system of forced oscillations and the general problem of two interacting economies is solved by the nonholonomic dynamics approach. Second, the Cass-Koopmans-Ramsey model of economical growth is solved as a variational problem with a velocity dependent constraint using the vakonomic approach. The specifics of the solution interpretation in economics compared to mechanics is discussed in detail, a discussion of the nonholonomic and vakonomic approaches to constrained problems in mechanics and economics is provided and an economic interpretation of the Lagrange multipliers (possibly surprising for the students of physics) is carefully explained. The paper can be used by the undergraduate students of physics interested in interdisciplinary physics applications to get in touch with current scientific approach to economics based on a physical background or by university teachers as an attractive supplement to the classical mechanics lessons.
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PDF链接：
https://arxiv.org/pdf/1106.3455
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