Learning outcomes of the course unit
Classical mechanics topics are presented following the hypothetical-deductive method typical of mathematics. The course also introduces the Lagrangian and Hamiltonian formulations of motion problems in mechanical systems.
Students are required to be familiar with the main topics of the 1st year Mathematical Analysis (Calculus) and Geometry courses.
Course contents summary
Review of vector calculus and kinematics. Central motions. Classification of orbits. Constrained systems. Lagrangian coordinates. Degrees of freedom. Cardinal theorems. First integrals of motion. Lagrange’s equations. Hamilton’s equations. Stability of motion and equilibrium. Small motions about a stable equilibrium configuration. Normal coordinates and normal modes.
A.FASANO - S.MARMI, Meccanica analitica, Bollati-Boringhieri.
H.GOLDSTEIN, Meccanica classica, Zanichelli.
L.D.LANDAU - E.M.LIFSCHITZ, Meccanica, Ed. Riuniti
Classroom lectures, with exercises. Oral exam, preceded by discussion of a proposed exercise.