Lecturer: M. Fabbrichesi , SISSA

In this lesson the professor finish the solution of the heavy symmetrical top with one point fixed problem, he find the **cyclic coordinates** and the first integrals of the Lagrangian formulation. Then he start the study of the **Hamiltonian** approach to classical mechanics and introduce the **Legendre transformation **and the **Hamilton's equations** of motion. Finally he obtain the Hamiltonian for three examples, the free particle, the motion of a particle in a central force and the motion of the pendulum.

As a complementary material we suggest in the fallowing lessons a **course in Classical Mechanics given by professor Leonard Susskind at Stanford University **. These lessons, 9 in total, are very interesting and the way of approaching the topics of classical mechanics is different from the present course that is the main reason we find it interesting.

In this first lesson the professor give an introduction to the laws of motion and in particular to the **Newton's laws of motion**.