  Differential analysis aims at inferring global properties of nonlinear
behaviors from the local analysis of the linearized dynamics. The paper
motivates and illustrates the use of differential analysis on the nonlinear
pendulum model, an archetype example of nonlinear behavior. Special emphasis is
put on recent work by the authors in this area, which includes a differential
Lyapunov framework for contraction analysis and the concept of differential
positivity.
