One dimensional systems. Lagrange equations. Variational principles. Simmetries and constants of motions Hamilton equations. Integrability, canonical transformations, Hamilton-Jacobi equations.
The course provides a solid knowledge of the foundaments ao analytical mechanics, in the two formulations, lagrangian and hamiltonian. The curse presents also the idea that mathematics is particularly fit in the description of the natural systems.
During the course, beside theoretical lessons and exercises, some important problems (e.g. relativistic precession, restricted three body problem, dipole scattering) are presented.
KNOWLEDGE AND UNDERSTANDING:
The students have to acquire a basic knowledge about analytical mechanics; they have to acquire a certain familiarity with the scientific method; they have to have clear the concept of mathematical model of a physical system.
The leaning is verified by written tests, both during the course and at the end of it, and an oral exam.
APPLYING KNOWLEDGE AND UNDERSTANDING:
One of the most important concepts that has to be clear in the end of the course regarding the application is the fact that the choice of the better coordinates is crucial to solve the problems.
The students have to be able also to find the analytical techniques more suitable to describe the properties of the system studied.