Programme

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.

Core Documentation

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.

Type of delivery of the course

Lectures, integrative teaching and assisted study (tutoring).

Attendance

Attendance is not compulsory but is strongly recommended.

Type of evaluation

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.

Programme

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.

Core Documentation

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

Type of delivery of the course

Lectures, integrative teaching and assisted study (tutoring).

Attendance

Attendance is not compulsory but is strongly recommended.

Type of evaluation

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.