郭铁丁, 康厚军. 理论力学研究性教学新探索——变质量系统动力学与连续介质Reynolds输运定理. 力学与实践, 2023, 45(3): 659-663. DOI: 10.6052/1000-0879-22-569
引用本文: 郭铁丁, 康厚军. 理论力学研究性教学新探索——变质量系统动力学与连续介质Reynolds输运定理. 力学与实践, 2023, 45(3): 659-663. DOI: 10.6052/1000-0879-22-569
Guo Tieding, Kang Houjun. A new research-oriented lecturing methodology in classical mechanics—dynamics of variable mass systems and Reynolds transport theorem in continuum. Mechanics in Engineering, 2023, 45(3): 659-663. DOI: 10.6052/1000-0879-22-569
Citation: Guo Tieding, Kang Houjun. A new research-oriented lecturing methodology in classical mechanics—dynamics of variable mass systems and Reynolds transport theorem in continuum. Mechanics in Engineering, 2023, 45(3): 659-663. DOI: 10.6052/1000-0879-22-569

理论力学研究性教学新探索−变质量系统动力学与连续介质Reynolds输运定理

A NEW RESEARCH-ORIENTED LECTURING METHODOLOGY IN CLASSICAL MECHANICS—DYNAMICS OF VARIABLE MASS SYSTEMS AND REYNOLDS TRANSPORT THEOREM IN CONTINUUM

  • 摘要: 本文探讨理论力学中变质量系统动力学与连续介质Reynolds输运定理的联系。Reynolds输运定理是连续介质(例如流体)质量/动量/能量输运规律的共同基础,因而具有基本的理论重要性。本文通过详细对比分析说明:在理论力学中,基于一般质点系模型的变质量系统动力学与连续介质力学的输运规律,本质上具有相同的理论框架和分析工具。如果在任意质点系模型的基础上引入质点空间连续分布的假设,则可以将变质量离散体系的力学结论拓展至连续介质的基本输运规律(包括质量/动量/能量)。

     

    Abstract: This paper focuses on theoretical connections between dynamics of variable mass systems and Reynolds transport theorem in continuum mechanics. Reynolds transport theorem is of fundamental importance as it is the general theoretical foundation for transport phenomenon of mass/momentum/energy in continuum mechanics (e.g., fluid mechanics). Based upon a thorough comparative study, we will show that: dynamics of variable mass systems in classical mechanics, although developed for general discrete particle systems, and transport laws in continuum mechanics essentially belong to the same theoretical framework and encompass similar analysis tools. If introducing continuous/smooth assumption into particle systems, conclusions in dynamics of variable mass systems can be extended to transport laws in continuum mechanics (including mass/momentum/energy).

     

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