Programma

Conservative mechanical systems. Qualitative analysis of motion and Lyapunov stability. Planar systems and one-dimensional mechanical systems. Central motions and the two-body problem. Change of frames of reference. Fictitious forces. Constraints. Rigid bodies. Lagrangian mechanics: variational principles, cyclic variables, Routh method, constants of motion and symmetries. Hamiltonian mechanics: Liouville's theorem and Poincaré's recurrence theorem, canonical transformations, generating functions, Hamilton-Jacobi method and action-angle variables.

Testi Adottati

G. Gentile, Introduzione ai sistemi dinamici. 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni, Springer, Milano, 2021.
G. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana, Springer, Milano, 2022.

Modalità Erogazione

Lectures, integrative teaching and assisted study (tutoring).

Modalità Frequenza

Attendance is not compulsory but is strongly recommended.

Modalità Valutazione

The exam consists of a written test, possibly replaced by two tests of exoneration in progress, and/or in a subsequent oral interview, in which the student will have to discuss the topics treated in class, with reference to the texts used and the notes distributed in class.

Programma

Conservative mechanical systems. Qualitative analysis of motion and Lyapunov stability. Planar systems and one-dimensional mechanical systems. Central motions and the two-body problem. Change of frames of reference. Fictitious forces. Constraints. Rigid bodies. Lagrangian mechanics: variational principles, cyclic variables, Routh method, constants of motion and symmetries. Hamiltonian mechanics: Liouville's theorem and Poincaré's recurrence theorem, canonical transformations, generating functions, Hamilton-Jacobi method and action-angle variables.

Testi Adottati

G. Gentile, Introduzione ai sistemi dinamici. 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni
G. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana

Modalità Erogazione

Lectures, integrative teaching and assisted study (tutoring). [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]

Modalità Valutazione

The exam consists of a written test, possibly replaced by two tests of exoneration in progress and in a subsequent oral interview, in which the student will have to discuss the topics treated in class, with reference to the texts used and the notes distributed in class. [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]