To acquire a basic knowledge of the theory of conservative mechanical systems and of the elements of analytical mechanics, in particular of Lagrangian and Hamiltonian mechanics.
Curriculum
teacher profile teaching materials
Planar systems and one-dimensional mechanical systems. Central motions and the two-body problem.
Change of frames of reference. Fictitious forces. Constraints. Rigid bodies. Lagrangian mechanics.
Variational principles. Cyclic variables, constants of motion and symmetries. Hamiltonian mechanics.
Liouville's theorem and Poincaré's recurrence theorem. Canonical transformations. Generating functions.
Hamilton-Jacobi method and action-angle variables.
G. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana, available online
Programme
Conservative mechanical systems. Qualitative analysis of motion and Lyapunov stability.Planar systems and one-dimensional mechanical systems. Central motions and the two-body problem.
Change of frames of reference. Fictitious forces. Constraints. Rigid bodies. Lagrangian mechanics.
Variational principles. Cyclic variables, constants of motion and symmetries. Hamiltonian mechanics.
Liouville's theorem and Poincaré's recurrence theorem. Canonical transformations. Generating functions.
Hamilton-Jacobi method and action-angle variables.
Core Documentation
G. Gentile, Introduzione ai sistemi dinamici. 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni, available onlineG. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana, available online
Reference Bibliography
V.I. Arnol’d, Mathematical Methods of Classical Mechanics, Springer (1989). A. Fasano & S. Marmi, Analytical Mechanics, Oxford University Press (2006). G. Gallavotti, The Elements of Mechanics, Springer (1983). L.D. Landau & E.M. Lifshitz, Mechanics, Pergamon Press (1960).Type of delivery of the course
Lectures, integrative teaching and assisted study (tutoring).Attendance
Attending the course is recommended but not mandatory.Type of evaluation
The exam consists of a written test, possibly replaced by two tests of exoneration in progress and in a subsequent oral interview, in which the student will have to discuss the topics treated in class, with reference to the texts used and the notes distributed in class. teacher profile teaching materials
Planar systems and one-dimensional mechanical systems. Central motions and the two-body problem.
Change of frames of reference. Fictitious forces. Constraints. Rigid bodies. Lagrangian mechanics.
Variational principles. Cyclic variables, constants of motion and symmetries. Hamiltonian mechanics.
Liouville's theorem and Poincaré's recurrence theorem. Canonical transformations. Generating functions.
Hamilton-Jacobi method and action-angle variables.
G. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana, available online
Programme
Conservative mechanical systems. Qualitative analysis of motion and Lyapunov stability.Planar systems and one-dimensional mechanical systems. Central motions and the two-body problem.
Change of frames of reference. Fictitious forces. Constraints. Rigid bodies. Lagrangian mechanics.
Variational principles. Cyclic variables, constants of motion and symmetries. Hamiltonian mechanics.
Liouville's theorem and Poincaré's recurrence theorem. Canonical transformations. Generating functions.
Hamilton-Jacobi method and action-angle variables.
Core Documentation
G. Gentile, Introduzione ai sistemi dinamici. 1. Equazioni differenziali ordinarie, analisi qualitativa e alcune applicazioni, available onlineG. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana, available online
Reference Bibliography
V.I. Arnol’d, Mathematical Methods of Classical Mechanics, Springer (1989). A. Fasano & S. Marmi, Analytical Mechanics, Oxford University Press (2006). G. Gallavotti, The Elements of Mechanics, Springer (1983). L.D. Landau & E.M. Lifshitz, Mechanics, Pergamon Press (1960).Type of delivery of the course
Lectures, integrative teaching and assisted study (tutoring).Attendance
Attending the course is recommended but not mandatory.Type of evaluation
The exam consists of a written test, possibly replaced by two tests of exoneration in progress and in a subsequent oral interview, in which the student will have to discuss the topics treated in class, with reference to the texts used and the notes distributed in class.