advanced analytical mechanics
Lecturer: L. Secco

Variational Principles which ground the physical description of nature: of D'Alembert, Hamilton, Maupertuis. Lagrange- and Hamilton- equations. The equation of Eulero-Lagrange in the continuum.

Structural analogies between Mechanics and Optics: eiconal equations. Relationship between Fermat's and Maupertuis' Principle.

Contact canonical transformations: the principal Jacobi function, the characteristic Hamilton-Jacobi function and their related equations. On real and apparent dynamics.

The Noether's theorem: application to the mechanical symmetries.

The E-H field; the Maxwell's equations as the solutions of Eulero-Lagrange equation for the field. The Jordan's demonstration for QED.

The Klein-Gordon field.

Forces as symmetries in the field theory.

Unifications and symmetry breakings during the very early phases of cosmological evolution (some outlines).