Università degli Studi di Pavia

Dipartimento di Matematica ''F. Casorati''

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Fundamentals of Mechanics

Professors:
Pulvirenti Ada
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