A methodology for analyzing the dynamics of hybrid systems

We discuss an algebraic and computational framework for formally analyzing hybrid systems that attempts to avoid numerical integration by resorting to (algebraically) finding primitives, and inverting and (numerically) evaluating functions when needed. The goal of the paper is to start exploring a little bit deeper into this idea to try to find out (a) a methodology, (b) algebraic and computational tools to support it, (c) classes of systems to which we can apply it in principle, and (d) a framework in which we can reasonably apply it in practice (with today´s computational tools).