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

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.