3. The example of the simple pendulum

In this section, we'll introduce a system approximating an elementary physical system. After modeling this system, we'll note that its evolution obeys an autonomous differential equation of order 2, i.e. an autonomous differential system of size 2. We will then study the solutions, with the aim of using the tools introduced in 2 , drawing the phase portrait and illustrating the language of autonomous systems. We will also deliberately demonstrate...