To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
Curriculum
teacher profile teaching materials
rigid. Integrability of the rigid body with a point not subjected to
strength. Lagrange spinning top. Arnold–Liouville theorem. Variables
action-angle for the harmonic oscillator and for the problem of the two
bodies. Formulation in action-angle variables of the 3 problem
bodies restricted.
Calculation of the precession of Mercury's perihelion.
Notes on the KAM theory on the convergence of the theory of
classic perturbations. Notes on the statistical theory of motion:
integrable, quasi-integrable and chaotic systems. Demonstration of the
dense and uniform filling of the torus by the flow
quasi-periodic irrational. Visiting frequencies.
Riuniti, Rome, 1979 G. Gallavotti, Meccanica Elementare, ed. P.
Boringhieri, Turin, 1986 G. Gentile, Introduction to systems
dynamics, 1 (Ordinary differential equations, qualitative analysis and
some applications) and
2 (Lagrangian and Hamiltonian mechanics) L.D. Landau, E.M. Lifshitz,
Meccanica, Editori Riuniti, Rome, 1976
Fruizione: 20410085 COMPLEMENTI DI MECCANICA ANALITICA - MOD. B in Fisica L-30 REUVERS Robin Johannes Petrus , MARCELLI GIOVANNA
Programme
Euler angles. Euler's equations for body dynamicsrigid. Integrability of the rigid body with a point not subjected to
strength. Lagrange spinning top. Arnold–Liouville theorem. Variables
action-angle for the harmonic oscillator and for the problem of the two
bodies. Formulation in action-angle variables of the 3 problem
bodies restricted.
Calculation of the precession of Mercury's perihelion.
Notes on the KAM theory on the convergence of the theory of
classic perturbations. Notes on the statistical theory of motion:
integrable, quasi-integrable and chaotic systems. Demonstration of the
dense and uniform filling of the torus by the flow
quasi-periodic irrational. Visiting frequencies.
Core Documentation
V.I. Arnol'd, Mathematical Methods of Classical Mechanics, EditorsRiuniti, Rome, 1979 G. Gallavotti, Meccanica Elementare, ed. P.
Boringhieri, Turin, 1986 G. Gentile, Introduction to systems
dynamics, 1 (Ordinary differential equations, qualitative analysis and
some applications) and
2 (Lagrangian and Hamiltonian mechanics) L.D. Landau, E.M. Lifshitz,
Meccanica, Editori Riuniti, Rome, 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
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 REUVERS Robin Johannes Petrus , MARCELLI GIOVANNA
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
rigid. Integrability of the rigid body with a point not subjected to
strength. Lagrange spinning top. Arnold–Liouville theorem. Variables
action-angle for the harmonic oscillator and for the problem of the two
bodies. Formulation in action-angle variables of the 3 problem
bodies restricted.
Calculation of the precession of Mercury's perihelion.
Notes on the KAM theory on the convergence of the theory of
classic perturbations. Notes on the statistical theory of motion:
integrable, quasi-integrable and chaotic systems. Demonstration of the
dense and uniform filling of the torus by the flow
quasi-periodic irrational. Visiting frequencies.
Riuniti, Rome, 1979 G. Gallavotti, Meccanica Elementare, ed. P.
Boringhieri, Turin, 1986 G. Gentile, Introduction to systems
dynamics, 1 (Ordinary differential equations, qualitative analysis and
some applications) and
2 (Lagrangian and Hamiltonian mechanics) L.D. Landau, E.M. Lifshitz,
Meccanica, Editori Riuniti, Rome, 1976
Fruizione: 20410085 COMPLEMENTI DI MECCANICA ANALITICA - MOD. B in Fisica L-30 REUVERS Robin Johannes Petrus , MARCELLI GIOVANNA
Programme
Euler angles. Euler's equations for body dynamicsrigid. Integrability of the rigid body with a point not subjected to
strength. Lagrange spinning top. Arnold–Liouville theorem. Variables
action-angle for the harmonic oscillator and for the problem of the two
bodies. Formulation in action-angle variables of the 3 problem
bodies restricted.
Calculation of the precession of Mercury's perihelion.
Notes on the KAM theory on the convergence of the theory of
classic perturbations. Notes on the statistical theory of motion:
integrable, quasi-integrable and chaotic systems. Demonstration of the
dense and uniform filling of the torus by the flow
quasi-periodic irrational. Visiting frequencies.
Core Documentation
V.I. Arnol'd, Mathematical Methods of Classical Mechanics, EditorsRiuniti, Rome, 1979 G. Gallavotti, Meccanica Elementare, ed. P.
Boringhieri, Turin, 1986 G. Gentile, Introduction to systems
dynamics, 1 (Ordinary differential equations, qualitative analysis and
some applications) and
2 (Lagrangian and Hamiltonian mechanics) L.D. Landau, E.M. Lifshitz,
Meccanica, Editori Riuniti, Rome, 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
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 REUVERS Robin Johannes Petrus , MARCELLI GIOVANNA
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
rigid. Integrability of the rigid body with a point not subjected to
strength. Lagrange spinning top. Arnold–Liouville theorem. Variables
action-angle for the harmonic oscillator and for the problem of the two
bodies. Formulation in action-angle variables of the 3 problem
bodies restricted.
Calculation of the precession of Mercury's perihelion.
Notes on the KAM theory on the convergence of the theory of
classic perturbations. Notes on the statistical theory of motion:
integrable, quasi-integrable and chaotic systems. Demonstration of the
dense and uniform filling of the torus by the flow
quasi-periodic irrational. Visiting frequencies.
Riuniti, Rome, 1979 G. Gallavotti, Meccanica Elementare, ed. P.
Boringhieri, Turin, 1986 G. Gentile, Introduction to systems
dynamics, 1 (Ordinary differential equations, qualitative analysis and
some applications) and
2 (Lagrangian and Hamiltonian mechanics) L.D. Landau, E.M. Lifshitz,
Meccanica, Editori Riuniti, Rome, 1976
Fruizione: 20410085 COMPLEMENTI DI MECCANICA ANALITICA - MOD. B in Fisica L-30 REUVERS Robin Johannes Petrus , MARCELLI GIOVANNA
Programme
Euler angles. Euler's equations for body dynamicsrigid. Integrability of the rigid body with a point not subjected to
strength. Lagrange spinning top. Arnold–Liouville theorem. Variables
action-angle for the harmonic oscillator and for the problem of the two
bodies. Formulation in action-angle variables of the 3 problem
bodies restricted.
Calculation of the precession of Mercury's perihelion.
Notes on the KAM theory on the convergence of the theory of
classic perturbations. Notes on the statistical theory of motion:
integrable, quasi-integrable and chaotic systems. Demonstration of the
dense and uniform filling of the torus by the flow
quasi-periodic irrational. Visiting frequencies.
Core Documentation
V.I. Arnol'd, Mathematical Methods of Classical Mechanics, EditorsRiuniti, Rome, 1979 G. Gallavotti, Meccanica Elementare, ed. P.
Boringhieri, Turin, 1986 G. Gentile, Introduction to systems
dynamics, 1 (Ordinary differential equations, qualitative analysis and
some applications) and
2 (Lagrangian and Hamiltonian mechanics) L.D. Landau, E.M. Lifshitz,
Meccanica, Editori Riuniti, Rome, 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
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 REUVERS Robin Johannes Petrus , MARCELLI GIOVANNA
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