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

Lectures and exercises.

Written and oral examination.

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

Kinematics of a point.

Dynamics: fundamental principles.

The motion of a free particle.

Constraints.

Multi particles systems.

Constraints. Rigid systems.

Cardinal equations of dynamics.

Lagrange's equations.

Some classical problems: the problem of two bodies.

Equilibrium and stability.

Hamilton's principle.

Hamilton's equations.

Canonical tranformations. Poisson brackets.







Kinematics of a point. Frenet's frame.

Constraints and their classification.

The motion of a free particle.

Degree of freedom. Lagrangian coordinates.

Dynamics: the fundamental principles of mechanics.

Work and energy. Conervatives forces.

The motion of a point under constraint.

Multi particles systems. Cardinal equations of dynamics.

Virtual work's principle. D'Alembert principle. Lagrange's equations. Lagrange's equations for conservative systems. Conservations laws.

Some classical problems: the problem of two bodies. Keplero's equations.

Kinematics of a rigid system: Euler's angles. Angular velocity.

Dynamics of a rigid system: inertia tensor. Euler's equations.

Stability ans small oscillations. Lagrange- Dirichlet theorem.

The Hamiltonian function (via Legendre transformation). Hamilton's equations.

Canonical tranformations. Poisson brackets.

Variational principles of mechanics: Hamilton's principle.

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.