Subject: ANALYTICAL MECHANICS (A.A. 2021/2022)
Unit Meccanica analitica
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.
Basic elements of Mechanics and Calculus.
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.
Standard lectures and exercise sessions
Written examination (3 h).
- 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.
Notes of the course (in italian).
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]