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### Fundamentals of Mechanics

Professors:
Year:
2015/2016
Course code:
502218
ECTS:
9
SSD:
MAT/07
DM:
270/04
Lessons:
84
Period:
II semester
Language:
Italian

#### Objectives

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

#### Teaching methods

Lectures and exercises.

#### Examination

Written and oral examination.

#### Prerequisites

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

#### Syllabus

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.

#### Bibliography

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.

Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602