20410085 - COMPLEMENTI DI MECCANICA ANALITICA - MOD. B

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
teacher profile | teaching materials

Programme

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.


Core Documentation

V.I. Arnol’d, Metodi Matematici della Meccanica Classica, Editori
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


Type of delivery of the course

Lectures in the classroom

Type of evaluation

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

teacher profile | teaching materials

Programme

Ergodic, chaotic and mixing systems.
Euler angles.
Analysis of the dynamics for rigid body.
Study of dynamics of the Lagrange spinning top and heavy spinning top.
Gradient systems.


Core Documentation

V.I. Arnol’d, Metodi Matematici della Meccanica Classica, Editori
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

Type of delivery of the course

Lectures in the classroom

Type of evaluation

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