To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
Curriculum
teacher profile teaching materials
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
Fruizione: 20410085 COMPLEMENTI DI MECCANICA ANALITICA - MOD. B in Fisica L-30 MARCELLI GIOVANNA, GENTILE GUIDO
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, 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
Type of delivery of the course
Lectures in the classroomType 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
Fruizione: 20410085 COMPLEMENTI DI MECCANICA ANALITICA - MOD. B in Fisica L-30 MARCELLI GIOVANNA, GENTILE GUIDO
Programme
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).Core Documentation
G. Gentile, Introduzione ai sistemi dinamici. 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni, Springer, Milano, 2021Attendance
Attendance is not compulsory but is strongly recommended.Type of evaluation
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. teacher profile teaching materials
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
Fruizione: 20410085 COMPLEMENTI DI MECCANICA ANALITICA - MOD. B in Fisica L-30 MARCELLI GIOVANNA, GENTILE GUIDO
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, 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
Type of delivery of the course
Lectures in the classroomType 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
Fruizione: 20410085 COMPLEMENTI DI MECCANICA ANALITICA - MOD. B in Fisica L-30 MARCELLI GIOVANNA, GENTILE GUIDO
Programme
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).Core Documentation
G. Gentile, Introduzione ai sistemi dinamici. 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni, Springer, Milano, 2021Attendance
Attendance is not compulsory but is strongly recommended.Type of evaluation
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. teacher profile teaching materials
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
Fruizione: 20410085 COMPLEMENTI DI MECCANICA ANALITICA - MOD. B in Fisica L-30 MARCELLI GIOVANNA, GENTILE GUIDO
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, 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
Type of delivery of the course
Lectures in the classroomType 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
Fruizione: 20410085 COMPLEMENTI DI MECCANICA ANALITICA - MOD. B in Fisica L-30 MARCELLI GIOVANNA, GENTILE GUIDO
Programme
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).Core Documentation
G. Gentile, Introduzione ai sistemi dinamici. 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni, Springer, Milano, 2021Attendance
Attendance is not compulsory but is strongly recommended.Type of evaluation
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.