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Subject: ANALYTICAL MECHANICS (A.A. 2021/2022)

degree course in PHYSICS

Course year 2
CFU 6
Teaching units Unit Meccanica analitica
A12 (lesson)
  • TAF: Supplementary compulsory subjects SSD: MAT/07 CFU: 6
Teachers: Andrea SACCHETTI
Exam type oral
Evaluation final vote
Teaching language Italiano
Contents download pdf download

Teachers

Andrea SACCHETTI

Overview

This course in aimed at second year undergraduate students who have completed first courses in Calculus and Mechanics. Our pourpose it to show the main tools for the study of Lagrangian and Hamiltonian systems, our approach is to use examples to illustrate the significance of the results presented.

Admission requirements

Basic elements of Mechanics and Calculus.

Course contents

Dynamics of a single point. Weierstass'a analysis. Pendulum. Relative dynamics. Lagrange's equations, Hamilton's equations and Hamiltonian flow, Hamilton's Variational principle, Poisson braket, canonical transformation, Hamilton-Jacobi equations. Elements of perturbation theory. Complements: Fourier's series.

Teaching methods

Standard lectures and exercise sessions

Assessment methods

Written examination (3 h).

Learning outcomes

Training Goals

- Knowledge and understanding: at the end of the course the student should have acquired the elements of Analytic Mechanics

- Applying knowledge and understanding: the student at the end of the course should be able to apply the knowledge acquired to simple problems of analytic mechanics, as well as in other fields (e.g. in Quantum Mechanics).

- Making judgements: the student at the end of the course should be able to recognize by himself the appropriate approaches and calculation methods in analytic mechanics.

- Communicating skills: the student at the end of the course should be able to describe with appropriate technical language and mathematical formalism the subjects presented in the course.

- Learning skills: The lectures should stimulate the learning skills and to go deep in subjects connected with the ones presented in the lessons.

Readings

Notes of the course (in italian).

Altri riferimenti:
V.I.Arnold, Metodi Matematici della Meccanica Classica, Editori Riuniti, 1986. [BSI: M.01/ 150];
A.Fasano, S.Marmi, Meccanica Analitica, Boringhieri, 1994. [BSI: M.01/ 212];
G.Gallavotti, Meccanica Elementare, Boringhieri, 1986. [BSI: M.01/ 108];
H.Goldstein, Meccanica Classica, Zanichelli, 1971. [BSI: M.01/ 96];
L.D.Landau, E.M.Lifsic, Corso di Fisica Teorica, Vol.1, Meccanica, Editori Riuniti, 1979. [BSI: M.07/ 084-1]