Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics

The purpose of the book is a short presentation of the geometrical theory of Lagrange and Hamilton spaces of order 1 or of order k ≥1, as well as the definition and investigation of some new Analytical Mechanics of Lagrangian and Hamiltonian type of order k ≥1.

The aim of the present monograph is twofold: 
1.  to provide a Compendium of Lagrangian and Hamiltonian geometries;
2. to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian.

The book is divided in three parts: 
I. Lagrange and Hamilton spaces; 
II. Lagrange and Hamilton spaces of higher-order; 
III. Analytical Mechanics of Lagrangian and Hamiltonian mechanical systems.

For short, in this monograph we aim to solve some difficult problems:
   - the problem of geometrization of classical nonconservative mechanical systems;
   - the foundations of geometrical theory of new mechanics: Finslerian, Lagrangian and Hamiltonian;
 - to determine the evolution equations of the classical mechanical systems for whose external forces depend on the higher-order accelerations.