力学与实践 ›› 2014, Vol. 36 ›› Issue (5): 642-646.DOI: 10.6052/1000-0879-13-406

• 应用研究 • 上一篇    下一篇

再论实位移与虚位移——从“无功约束”概念谈起

王怀磊1, 苏振超2   

  1. 1. 南京航空航天大学机械结构力学及控制国家重点实验室, 南京 210016;
    2. 厦门大学嘉庚学院土木工程系, 福建漳州 363105
  • 收稿日期:2013-10-09 修回日期:2013-11-27 出版日期:2014-10-15 发布日期:2014-02-25
  • 通讯作者: 王怀磊,E-mail:whlay@nauu.edu.cn
  • 基金资助:

    江苏高校优势学科建设工程资助项目.

ON THE REAL DISPLACEMENT AND THE VIRTUAL DISPLACEMENT——AN IN-DEPTH DISCUSSION STARTING FROM THE CONCEPT OF NULL-WORK CONSTRAINT

WANG Huailei1, SU Zhenchao2   

  1. 1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
    2. Department of Civil Engineering Xiamen University Tan Kah Kee College, Fujian, Zhangzhou 363105, China
  • Received:2013-10-09 Revised:2013-11-27 Online:2014-10-15 Published:2014-02-25

摘要:

阐述了分析力学中“理想约束”与理论力学动能定理部分“理想约束”概念的区别,举例说明了由此同名可能导致的问题,并建议在动能定理部分使用“无功约束”或“零功约束”的概念,以保持力学概念的一致性和独立性;对微分形式的动能定理在广义坐标空间进行变换得到了以广义坐标微分为指标的和式形式,并通过与Lagrange 方程的比较及实例论证了不能由此而得到系统动力学方程的原因。上述内容均从不同侧面反映了实位移与虚位移的本质区别,因此可作为对实位移与虚位移概念进行深刻理解的一种途径。

关键词:

实位移|虚位移|无功约束|理想约束|动能定理|Lagrange方程

Abstract:

This paper first discusses the intrinsic distinction of the term "ideal constraint" used both in analytical mechanics and in the work-energy theorem in theoretic mechanics. The possible misunderstanding due to the use of the same term with different connotations is illustrated. In this setting, a new technical term "null-work constraint" is suggested instead in the work-energy theorem for the sake of the uniqueness and consistency of terminology in mechanics. Then the differential form of the work-energy theorem is transformed into a sum form indexed by the generalized coordinates, and the reason why the general dynamic equations of the system cannot be obtained from this sum form as in the general equation of dynamics is analyzed and illustrated by a comparison with the Lagrange equation method. The arguments for the two problems both involve the concepts of real displacement and virtual displacement, accordingly, they may serve as a way to understand and distinguish the concepts of displacement and virtual displacement.

Key words:

real displacement|virtual displacement|null-work constraint|ideal constraint|kinetic energy theorem|Lagrange equation

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