The aim of the course is to present the basic mathematical models of classical mechanics, in their theoretical aspects and in their applications.

Lectures and exercises.

Written and oral examination.

Analysis 1, Analysis 2, Geometry 1 and Linear Algebra.

Kinematics of a point. Frenet's frame.
Constraints and their classification.
The motion of a free particle.
Lagrangian coordinates.
Dynamics: the fundamental principles of mechanics.
Work and energy. Conservatives forces.
The motion of a point under constraint.
Discrete systems. Cardinal equations of dynamics. Non dissipative constraints.
Lagrange's equations. Lagrange's equations for conservative systems. Conservations laws.
One-dimensional motions. Qualitative analysis.
Some classical problems: the problem of two bodies. Keplero's equations.
Rigid body: Euler's angles. Angular velocity. Relative motions.
Rigid body dynamics: inertia ellipsoid. Euler's equations. Lagrange's gyroscope.
Equilibrium and stability: Lagrange-Dirichlet theorem. Instability criteria. Small oscillations.
Variational principles of mechanics: Hamilton's principle.
The Hamiltonian function (via Legendre transformation). Hamilton's equations.
Canonical tranformations. Poisson brackets.

1.Fasano A., Marmi S.,: "Meccanica Analitica", Bollati Boringhieri.
2.Goldstein H., Poole C., Safko J.: "Meccanica Classica", Zanichelli.
3.Gantmacher F.R.: "Lezioni di Meccanica Analitica", Editori Riuniti.
4.Lanczos C., : "The variational principles of Mechanics, Dover.