Introduction to the Geometry of Classical Dynamics

The aim of this introduction to the geometry of Classical Dynamics is to lead postgraduate students of Mathematics or Physics from the historical Newtonian-d’Alembertian dynamics up to the border with the modern (geo metrical) Lagrangian-Hamiltonian dynamics, without making any direct use of the traditional (analytical) formulation of the latter. The purpose is to cover the big gap existing in literature between the (empirical) elementary presentation of historical dynamics and the (abstract) differential-geometric formulation of analytical dynamics. The method is the pedagogical principle of working from bottom up, in order to highlight roots, motivations and inductive proceedings of the modern differential-geometrical developments in such an ancient physical area.