F. talamucci,
"Manuale di meccanica analitica", Aracne 2017
Exercise Book:
F. Talamucci, "Esercizi svolti sul formalismo lagrangiano e hamiltoniano", Edizioni Nuova Cultura
Learning Objectives
Knolewdge acquired: the main aspects of the lagrangian and of the hamiltonian formulation of
analytical mechanics.
Competence acquired: geometrical and analytical overview of discrete systems motion, sketch of some classical problems
Skills acquired (at the end of the course): make use of geometry and calculus for getting the idea of Lagrange and Hamilton mathematical formulation of motion. Put into practice the results of understanding for the study of some specific problems.
Prerequisites
Courses required: Mathematical analysis I, Geometry
Teaching Methods
Number of credits: 6
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations,etc...): 150
Contact hours for: Lectures (hours): 52
Further information
Office hours: every day, Appointment needed, phone or email
Exam modality:
Written and oral tests.
Written test is also valid for any following oral dates.
At the end of each part of the Course (lagrangian and hamiltonian formalism) a written partial test is scheduled: if both are passed, the student is dispensed with the written test.
If just one partial test is passed, the student has to complete the written exam by carrying out only the complementary part.
Course program
Course Contents (detailed programme):
I part: Lagrangian formalism.
Constrained systems, Lagrangian coordinates, Riemannian manifolds, geodesics. Kinematics and dynamics of holonomic systems. Lagrange equations. Equilibrium and stability. Noether's theorem.
II Part: Hamiltonian formalism.
Legendre's transform and Hamilton canonical equations. Liouville's and Poincare's theorems. Variational principles. Hamiltonian systems. Canonical transformations. Integral invariant of Poincaré-Cartan.Poisson's brackets. Poincare-Cartan form. Symmetries of the Hamiltonian. Hamilton-Jacobi equation.