Newtonian and canonical analysis of the motion of a rope falling from a table

Abstract

One of the few examples of variable mass systems treated in textbooks is the movement of a rope lying on a table, with a part y(t) hanging and falling. In solving this problem what is usually obtained is v(y), but not y(t). In this work, first we obtain y(t) and then show that it is possible to make a canonical formulation of the problem, which in this case also permits an expedite approximation to y(t).