RATIONAL MECHANICS

Academic Year 2022-2023

Teachers

Sebastiano Sonego

Course Year

Unit Credits

Teaching Period

Annuity

Course Type

Supplementary

Prerequisites. Basic knowledge of mechanics (non-relativistic and relativistic), electromagnetism, and linear algebra. Good knowledge of calculus.

Teaching Methods. Lectures, mainly theoretical. Discussion of simple exercises.

Verification of Learning. Two written exams, three hours each. The first contains a multiple choice test and simple exercises. In the second, the student must discuss three theoretical topics. At the end, there will be a short interview.

More Information. If required, the course may be taught in English.

Objectives

The student will develop a detailed knowledge of the conceptual and mathematical foundations of several formulations of dynamics. Mechanics will be presented within the wider context of physical theories. The importance of applying many different mathematical techniques will be stressed. The course has thus an interdisciplinary character, which allows the student to connect topics seen in previous classes.

Foundations and mathematical methods of Newtonian, Lagrangian, and Hamiltonian dynamics of systems with a finite number of degrees of freedom.

Contents:

Foundations of kinematics. Principles of dynamics. Newtonian dynamics of particles and systems. Lagrangian dynamics. Hamiltonian dynamics. Variational principles. Hamilton-Jacobi theory. Canonical formalism.

Texts

Lecture notes, that can be downloaded from the website of the university.

V. I. Arnold, Mathematical Methods of Classical Mechanics, second edition (Springer, New York, 1989).

Academic Year 2022-2023