20410770 - FM410-Complements of Analytical Mechanics – Moldule B

To deepen the study of dynamical systems, with more advanced methods, in the context of Lagrangian and Hamiltonian theory.
teacher profile | teaching materials

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 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 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

Fruizione: 20410085 COMPLEMENTI DI MECCANICA ANALITICA - MOD. B in Fisica L-30 REUVERS Robin Johannes Petrus , MARCELLI GIOVANNA

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.