# Variations of tractrix: Accelerated rolling object chases another object

## Abstract

We investigated conditions for meeting or non-meeting of two objects with one of them on a tractrix and another on the same curve or in the x-axis. In the first case, a body that starts from rest on a tractrix at a certain height and acted upon by constant gravitational force, chases another body on the x-axis moving with constant speed. We found out that there is a limiting speed that should be imposed on the body on the x-axis for which the two could define a straight line parallel to the y-axis. In the second case, two objects are released on a tractrix but with a time difference of release. It was found out that as long as the initial body has a greater moment of inertia than the second body, the two would always meet independent of the time difference of release. On the other hand, in the third case we found out that for the two objects described in the first case, there exists a gravitational potential function for which the two bodies could always be constantly separated.

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## How to Cite

*Proceedings of the Samahang Pisika ng Pilipinas*

**21**, SPP-2003-PB-20 (2003). URL: https://proceedings.spp-online.org/article/view/SPP-2003-PB-20.