Mathematical models have been very successful in the study of the physical world. Galilei and Newton introduced point particles moving without friction under the action of simple forces as the basis for the description of concrete motions like the ones of the planets. This approach was sustained by appro priate mathematical methods, namely infinitesimal calculus, which was being developed at that time. In this way classical analytical mechanics was able to establish some general results, gaining insight through explicit solution of some simple cases and developing various methods of...