Scheda programma d'esame
ISTITUZIONI DI FISICA MATEMATICA
GIOVANNI FEDERICO GRONCHI
Anno accademico2016/17
CdSMATEMATICA
Codice137AA
CFU9
PeriodoPrimo semestre
LinguaItaliano

ModuliSettoreTipoOreDocente/i
ISTITUZIONI DI FISICA MATEMATICAMAT/07LEZIONI63
GIOVANNI FEDERICO GRONCHI unimap
Programma non disponibile nella lingua selezionata
Learning outcomes
Knowledge
The student who completes the course successfully will be able to demonstrate a solid knowledge of the main topics in Classical Mechanics, in its Newtonian, Lagrangian and Hamiltonian formulation. He/she will be able to model by differential equations the problem of the motion of systems constituted by material points and rigid bodies, possibly with constraints. He/she will also be able to discuss some qualitative aspects of the motion of such systems, like stability and small oscillations around equilibria.
Assessment criteria of knowledge
In the written exam (3 hours), the student must demonstrate his/her knowledge of the course material by solving some exercises concerning the different formulations of Mechanics. During the oral exam the student must be able to demonstrate his/her knowledge of the results and the related proofs explained in this course.

Methods:

  • Final oral exam
  • Final written exam

Teaching methods

Delivery: face to face

Learning activities:

  • attending lectures

Attendance: Advised

Teaching methods:

  • Lectures

Syllabus
Newtonian Mechanics: mechanical systems, basic dynamical quantities, cardinal equations, relative motions, angular velocity. Constrained systems: holonomic and nonholonomic constraints, ideal constraints. The rigid body: kinematics, inertia operator, principal axes and momenta of inertia, Euler's equations for a rigid body with a fixed point and Poinsot's description of the motion. Lagrangian Mechanics: Euler-Lagrange equations, invariance by coordinate change, first integrals and symmetries, Noether's theorem, Routh's reduction. Equilibria and stability, Lagrange-Dirichlet's theorem, small oscillations. Euler's angles and Lagrange's top. Variational principles by Hamilton and Maupertuis. Hamiltonian Mechanics: Legendre's transform, Hamilton's equations di Hamilton, canonical transformations. Hamilton-Jacobi equations and Liouville-Arnold's theorem.
Bibliography
Recommended reading includes the following works; further bibliography will be indicated. V. I. Arnold: Mathematical Methods of Classical Mechanics, Springer G. Benettin, L. Galgani, A. Giorgilli: Appunti di Meccanica Razionale G. F. Gronchi: note del Corso di Istituzioni di Fisica Matematica (in preparation, only partly available)
Work placement
Yes
Ultimo aggiornamento 14/11/2016 17:27