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
> 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
Programme
Euler angles. Euler's equations for body dynamics> 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.
Core Documentation
V.I. Arnol'd, Mathematical Methods of Classical Mechanics, Editors> 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
Type of delivery of the course
lectures in the classroomAttendance
Attendance is strongly recommended but not mandatoryType 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
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 classroomAttendance
Attendance is strongly recommended but not mandatoryType 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