1. To provide a compendium of lagrangian and hamiltonian geometries;

2. To introduce and investigate a new analytical mechanics: finslerian, lagrangian and hamiltonian.

One knows that the geometrical theory of nonconservative mechanical systems cannot be rigourously constructed without the use of the geometry of the tangent bundle of the configuratuion space.

The solution of this problem is based on the lagrangian and hamiltonian geometries. In fact, the construction of these geometries relies on the mechanical principles and on the notion of Legendre transformation.

Contents

Part I lagrange and hamilton spaces

Part II lagrangian and hamiltonian spaces

Part III analytical mechanics of lagrangian and hamiltonian mechanical systems