To deepen the study of dynamical systems both with more advanced methods, in the context of Lagrangian and Hamiltonian theory and providing applications also in other fields
scheda docente
materiale didattico
Euler's equations for rigid body dynamics.
Integrability of the rigid body with a point not subjected to forces.
Lagrange spinning top.
Ergodic, chaotic and mixing systems.
Action angle variables: the theorem of
Arnold-Liouville.
Perturbation theory in classical mechanics:
precession of the perihelion of Mercury and hints at the KAM theory.
Riuniti, Roma, 1979 G. Gallavotti, Meccanica Elementare, ed. P.
Boringhieri, Torino, 1986 G. Gentile, Introduzione ai sistemi
dinamici, 1 (Equazioni differenziali ordinarie, analisi qualitativa e
alcune applicazioni) e
2 (Meccanica lagrangiana e hamiltoniana) L.D. Landau, E.M. Lifshitz,
Meccanica, Editori Riuniti, Roma, 1976
Programma
Euler angles.Euler's equations for rigid body dynamics.
Integrability of the rigid body with a point not subjected to forces.
Lagrange spinning top.
Ergodic, chaotic and mixing systems.
Action angle variables: the theorem of
Arnold-Liouville.
Perturbation theory in classical mechanics:
precession of the perihelion of Mercury and hints at the KAM theory.
Testi Adottati
V.I. Arnol’d, Metodi Matematici della Meccanica Classica, EditoriRiuniti, Roma, 1979 G. Gallavotti, Meccanica Elementare, ed. P.
Boringhieri, Torino, 1986 G. Gentile, Introduzione ai sistemi
dinamici, 1 (Equazioni differenziali ordinarie, analisi qualitativa e
alcune applicazioni) e
2 (Meccanica lagrangiana e hamiltoniana) L.D. Landau, E.M. Lifshitz,
Meccanica, Editori Riuniti, Roma, 1976
Modalità Erogazione
Lectures in the classroomModalità Valutazione
The exam consists in the solution of a sheet of exercises assigned to lesson, to be returned resolved within the oral exam, and in an interview oral on a selection of the topics covered, to be agreed with the teacher
scheda docente
materiale didattico
Programma
Some examples of dynamical systems with application to the physical world: gradient systems, ecosystems, electric circuits and epidemiologic systems. Microcanonical ensemble, quasi-periodic motions and introduction to ergodi theory (ergodic, mixing and chaotic systems)Testi Adottati
G. Gentile, Introduzione ai sistemi dinamici. 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni, Springer, Milano, 2021Modalità Frequenza
Attendance is not compulsory but is strongly recommended.Modalità Valutazione
The exam consists of an oral interview, in which the student will have to discuss the topics treated in class, with reference to the texts used in class.