1. Special form of the equations of motion

Motivation

To better grasp the developments that follow and their order, it is necessary to have an overview of the general form that is most often given to the equations of motion of a system for their numerical resolution in simulation software. A priori, the method that seems best suited to the algorithmic treatment that, of course, interests us here, is Lagrange's method. We'll now take a look at this method, so that we can clearly see all the elements that need to be developed.