M. Fabbrichesi , SISSA

In this lesson the professor solve the problems of homework number 5. Then he continues with the canonical transformation and introduces the infinitesimal contact transformations. In the second part of the lecture the professor introduce the Hamilton–Jacobi theory by deriving the Hamilton–Jacobi equation for the Hamilton's principal function?. Then he solves the harmonic oscillator problem as an example of the Hamilton–Jacobi method solving this problem he obtain the Hamilton’s characteristic function.

Lecture 6/9 | Modern Physics: Classical Mechanics (Stanford)

In this lesson the profesor focused in the Hamiltonian formulation of classical mechanics and its physical consequences, the relation between the Hamiltonian and the Lagrangian. The functional form of Hamilton's equations and the Poisson bracket and their properties were introduced.

Lecture 7/9 | Modern Physics: Classical Mechanics (Stanford) This lesson continues with the study of Hamiltonian and the Lagrangian formulation of classical mechanics. The lecture starts with the introduction of the Liouville's theorem and was demostrated that the Hamiltonian flow in phase space is incompressible. Some concepts were introduced as the information conservation, friction and chaos. It was also shown that the area in phase space is always the same, a result that is related with the Uncertainty principle. Finally the motion of a particle in a magnetic field was studied