Abstract: Compared with scleronomic constraint, rheonomic constraint brings more complication, however, it can be dealed with by more means. Through transforming the reference frame, and selecting smartly the proper form of Lagrange equation or energy integral, we can solve the rheonomic constraint problem by various ways. From the comparison among different perspectives, we can verify some results that often neglected by textbooks, such as the ideal constraint does not depend on the reference frame, and the ideal constraint force has no influence on the application conditions of the Lagrange equation for conservative system, even if it does the real work. Through analyzing the rheonomic constraint problem from various perspectives, we can promote efficiently the ability of students to comprehend and apply the important knowledge of analytical mechanics.

Key words:  rheonomic constraint, Lagrange equation, energy integral, differential equation of motion