Faster or slower? Body constrained traveling along vertical curved path

In this paper, we consider a body motion in the presence of both external gravity force and the holonomic constraint. We find that in the case of vertical curved path in the form of a “slide”, the total travel time is always greater than the corresponding travel time along the horizontal section of the track. In the case of “valley”, this time can be either more or less than the travel time along the horizontal section. This topic allows the reader to test the free particle model applying simple numerical calculations.

Keywords
Free particle; holonomic constraint; gravity force; numerical analysis