00686 - Analytical Mechanics

Academic Year 2011/2012

  • Docente: Giorgio Turchetti
  • Credits: 8
  • SSD: MAT/07
  • Language: Italian
  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Physics (cod. 8007)

Course contents

 Dynamical systems: phase space, evolution equations, group properties, fisrt integrals, one dimensional problems, phase portraits,  time law. Lagrangian mechanics: constraints and their realization, forces of constraint , geometry of curves and surfaces, D'Alembert's principle, generalized potentials, Lagrange and Hamilton's equations. Symmetries: Noether's theorem, scale and Galileo transformations. Mechanical models: harmonic and anharmonic oscillators,   pendulum, central field with equation of orbits  and Kepler laws,  two body problem, Rotations and  rigid body: Euler angles, velocity field, inertia matrix, principal axis,  free motion and Poinsot cones, Lagrange top.  Dynamics in a rotating frame. Equilibrium and its stability; small oscillations around a stable equilibrium. Hamiltonian mechanics: variational principles, canonical transformations, generating functions, Poisson brackets and Lie series, Maupertui's principle, Hamilton Jacobi equation and elements of  canonical perturbation theory.

 

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Readings/Bibliography

G. Turchetti Meccanica Classica dei Sistemi Fisici Ed. Zanichelli , Bologna.

Additional reading

Landau L. D. Lifshitz  Meccanica Ed. Boringhieri, Torino

Assessment methods

Written and oral examination on the topics treated in the course 

The texts of the written examination and the correspong solutions can be found in teh web site

http://www.physycom.unibo.it/MeccanicaAnalitica1.html

Office hours

See the website of Giorgio Turchetti