Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree: 
Academic year in which the course will be held: 
Course type: 
Supplementary compulsory subjects
First Semester
Standard lectures hours: 
Detail of lecture’s hours: 
Lesson (64 hours)

Knowledge of newtonian mechanics of a single particle and systems of particles, calculus for functions of one and several variables, linear algebra.

Final Examination: 

The final examination consists in a written test (2h), where the student is required to prove a methodological rigor as well as the ability to apply the techniques of analytic mechanics to specific systems.

Voto Finale

The goal is to provide a detailed knowledge of the foundations of lagrangian and hamiltonian mechanics, to discuss physically relevant applications and to introduce the fundamental principles on integrable and chaotic systems.
In the structure of first level degree, analytic mechanics, besides its intrinsic importance, plays also an essential role in the subsequent introduction to quantum mechanics.
We expect that the student ripen a quantitative understanding and be able to deal with exercises and insights in this area.

Review of fundamental concepts and Lagrangian form of the equations of motion. [15h]
Central forces. Kinematics and dynamics of rigid bodies. Oscillations. [18h]
Hamiltonian mechanics, canonical transformations. [15h]
Hamilton-Jacobi theory. Integrable systems. [10h]
An introduction to Hamiltonian chaos and perturbation theory. [6h]

L.D. Landau and E.M. Lifshits, Mechanics; H. Goldstein, C. Poole and J. Safko, Classical Mechanics; J.H. Lowenstein, Essentials of hamiltonian dynamics.

The course include both theory lectures and recitation sessions, where we will discuss further theoretical developments as well as applications of the theory.

More detailed informations can be obtained from my web page, including a pdf copy and recordings of the lectures.

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