On stability and some remarks about positional systems - Caetano, Marcelo Farias (2018)
In this thesis, we study problems concerns to planar force fields, that is, second degree ordinary differential systems x¨ = f(x; y); y¨ = g(x; y); f; g are Ck: Our focus is on the stability of equilibrium in the sense of Lyapunov. We give a special attention for the existence of auxiliary functions, obtained from first integral which is known. In the end we study a particular case when the force is analytic, i. e. f(x; y) = g(x; y) = f(x) is analytic.