00537 - Fundamentals of Mathematical Physics

Learning outcomes

At the end of the course the students master some important models of Mathematical Physics in the framework of classical Newtonian Mechanics (in the formalism of dynamical systems), of Analytical Mechanics and of Continuum Mechanics. Moreover they learn techniques and tools to solve the integrability problem of the mentioned systems.

Course contents

Elements of tensor analysis and differential geometry - Kinematics of discrete systems and continuum media: characterization of rigid motions - Newtonian mechanics in the formalism of dynamical systems -  Qualitative analysis of one dimensional motion and stability of equilibrium - Linear oscillator (dumped and forced) - The central force problem and the two body problem - Dynamics of rigid body with a fixed point - Euler's equations and their integrability - Analytical mechanics: the variational formalism from the Lagrangian and Hamiltonian point of view for holonomous systems with ideal constraints. Examples of integrable systems - The normal modes theorem and Liouville's theorem - Symplectic matrices - Canonical transformations and generating functions - Poisson brackets and their properties -  Introduction to the Hamilton-Jacobi theory.

Readings/Bibliography

Fasano-Marmi: Meccanica Analitica, Boringhieri
T. Ruggeri: Introduzione alla Termomeccanica dei continui, Monduzzi 2007
Lecture notes of the teacher

Teaching methods

Lectures

Assessment methods

Written and oral examination

Office hours

See the website of Franca Franchi