Scheda programma d'esame
ISTITUZIONI DI FISICA MATEMATICA
GIOVANNI FEDERICO GRONCHI
|ISTITUZIONI DI FISICA MATEMATICA||MAT/07||LEZIONI||63|
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KnowledgeThe 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 knowledgeIn 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.
- Final oral exam
- Final written exam
Delivery: face to face
- attending lectures
SyllabusNewtonian 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.
BibliographyRecommended 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)
Ultimo aggiornamento 14/11/2016 17:27