• 应用研究 •

### 再论实位移与虚位移——从“无功约束”概念谈起

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

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