20410339 - FM210 - Analytical Mechanics

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

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, Routh method, 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 online
G. 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). [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]

Attendance

Attending the course is strongly 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 discuss the topics treated in class, with reference to the texts used and/or the notes distributed in class. [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]

teacher profile | teaching materials

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, Routh method, 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
G. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana

Type of delivery of the course

Lectures, integrative teaching and assisted study (tutoring). [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]

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. [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]

teacher profile | teaching materials

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, Routh method, 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 online
G. 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). [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]

Attendance

Attending the course is strongly 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 discuss the topics treated in class, with reference to the texts used and/or the notes distributed in class. [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]

teacher profile | teaching materials

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, Routh method, 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
G. Gentile, Introduzione ai sistemi dinamici. 2. Meccanica lagrangiana e hamiltoniana

Type of delivery of the course

Lectures, integrative teaching and assisted study (tutoring). [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]

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. [In the event of an extension of the health emergency from COVID-19, all provisions that regulate the methods of carrying out both teaching activities and student assessment will be implemented.]