During these lectures, the student is introduced to the Lagrangian and Hamiltonian formulation of the classical mechanics.
Furthermore, the lectures contains also some elements of the theory of stability for dynamical systems, variational principles and Hamilton-Jacobi equation.
The teaching aims to make students acquire the ability to solve typical problems in classical physics by means of the tools provided by the formulation of Lagrangian and Hamiltonian mechanics
At the end of the learing path the student will be able to:
- describe the foundations of the Lagrangian and Hamiltonian formulation of classical mechanics
- describe the dynamics of classical systems by means of the Euler-Lagrange equation
- find the equilibrium configurations of Lagrangian systems
- analyze the stability of the equilibrium configurations of these systems
- formulate the equation of motion in the case of Hamiltonian mechanics
- know and use the canonical transforamtions
- know some advanced techniques to solve some motion equations like those furnished by the Hamilton-Jacobi equation
- characterize the studied equation of motion by means of some variational principles
The course are organized in lectures given by the teachers where the theoretical part it will be presented and where its application to the resulutions of some exercises will be discussed.
Introduction and some basic concepts
Analytical mechanics of holonomic systems
Introduction to stability of dynamical systems
Hamiltonian mechanics
Variational principles
The notes of the course will be made available within aul@web.
Further deeper suggested readings:
1) H. Goldstein, C. Poole, J. Safko, “Classical Mechanics”, 3rd edn. Addison-Wesley, San Francisco, (2002).
2) V. I. Arnold “Metodi Matematici della Meccanica Classica” Editori Riuniti University Press, (2010).
Ricevimento: By appointment.
NICOLA PINAMONTI (President)
SIMONE MURRO
MARCO BENINI (President Substitute)
PIERRE OLIVIER MARTINETTI (Substitute)
The exam is usually formed by a written and by an oral part.
Students with learning disorders ("disturbi specifici di apprendimento", DSA) will be allowed to use specific modalities and supports that will be determined on a case-by-case basis in agreement with the Lecturers.
The written exams verifies the ability of the student to solve some exercises by means of the tecniques studied during the lectures.
The oral part is about the teoretical arguments presented during the lectures.
Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.
