- Docente: Marco Lenci
- Credits: 8
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Physics (cod. 9244)
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from Nov 03, 2023 to May 30, 2024
Learning outcomes
At the end of the course, the student possesses a basic knowledge of Lagrangian and Hamiltonian mechanics and their integrable models. In particular, the student is able to write the Lagrangian and Hamiltonian functions of a mechanical system; describe the phase space of one-dimensional systems; determine the existence of constants of motion related to symmetries; study the stability of equilibria and find the laws of motion in the approximation of small oscillations; describe the laws of motion for central fields and spinning tops; use variational principles to write the equations of motion and apply perturbative methods.
Course contents
Tentative syllabus:
Recap of Newtonian Mechanics: one-particle and many-particle systems, conservation principles. Integration of motion: systems with one degree of freedom. Central fields. Kepler's laws. Two-body problems. Lagrangian formulations of the equation of motion. Least Action Principle. Hamiltonian formulation. Lagrangian Mechanincs of constrained systems. Noether's Theorem. D'Alembert's Principle. Small oscillations. The rigid body. Mobile systems of coordinate. Elements of canonical formalism and integrable systems.
Readings/Bibliography
The reference textbook for the course is:
- V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag
This is a rather advanced textbook, which will be covered at a suitable pace for students of this class, simplifying and integrating the various topics. Other reference textbooks (in order of importance for this course) are:
- H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 3rd ed., Pearson
- L. D. Landau, E. M. Lifshits, Mechanics (Course of Theoretical Physics Volume 1), 3rd ed., Butterworth-Heinemann
Teaching methods
Classroom lectures
Assessment methods
Written and oral exams
Teaching tools
Teacher's notes and printed companion notes of Arnold's textbook by Profs. Degli Esposti, Graffi, Isola.
Office hours
See the website of Marco Lenci