Programme

Euler-Lagrange equations. Solving mechanics problems using the Lagrangian formalism. Central motions and the two-body problem. Constraints and rigid systems. D’Alembert’s principle and Lagrangian mechanics: variational principle, cyclic variables, conserved momenta, and symmetries.

Reference Bibliography

- H. Goldstein, Classical Mechanics, Pearson, 2013 - L.D. Landau, E.M. Lifšits, Mechanics: Volume 1 (Course of Theoretical Physics), Butterworth Heinemann, 1976 - G. Gentile, Introduzione ai sistemi dinamici - Volume 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni, Springer, 2021 - G. Gentile, Introduzione ai sistemi dinamici - Volume 2. Formalismo lagrangiano e hamiltoniano, Springer, 2022 - V.I. Arnol'd, Mathematical Methods of Classical Mechanics, Springer 1989 - D. Morin, Introduction to Classical Mechanics: With Problems and Solutions, Cambridge University Press, 2008

Attendance

Optional

Type of evaluation

The written exams consists in solving problems similar to those shown in the exercise classes. The oral exam consists in the presentation of theoretical topics taught in the course, and their connection to the applications discussed during the lectures.