Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics

Understand

The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian.

• The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus applied to the integral of action and these can be studied by using the methods of Lagrangian or Hamiltonian geometries.
• More general, the notions of higher order Lagrange or Hamilton spaces have been introduced and developed by the present author.
• The applications led to the notions of Lagrangian or Hamiltonian Analytical Mechanics of higher order.