  An account of the transversality conditions of variational problems gives
rise to essential results in the analysis of different physical phenomena. This
powerful and elegant approach has proven to be fruitful in a diversity of
variational problems with free endpoints, when the endpoints are free to slip
along preset curves. We illustrate the transversality condition by the study of
a heavy inextensible rope sagging both symmetrically and asymmetrically between
two steering variously-shaped guide wires without friction. In this case, the
transversality conditions lead to the orthogonality of the rope to the wires at
endpoints of the rope, which is confirmed experimentally. Freeing the endpoints
of the rope yields exact and simple analytical equations predicting the tension
of the rope. Heavy ropes whose endpoints are free to slip between
variously-shaped wires are discussed.
