Classical mechanics
A.Y. 2018/2019
Lesson for
Learning objectives
 Imparare a scrivere le equazioni di moto in coordinate qualunque
ed anche in presenza di vincoli ideali.
 Conoscenza di base della dinamica Hamiltoniana.
 Conoscenza dei principi base della Relativita' Ristretta
ed anche in presenza di vincoli ideali.
 Conoscenza di base della dinamica Hamiltoniana.
 Conoscenza dei principi base della Relativita' Ristretta
Course structure and Syllabus
CORSO A
Active edition
Yes
Responsible
MAT/07  MATHEMATICAL PHYSICS  University credits: 7
Practicals: 20 hours
Lessons: 40 hours
Professors:
Bambusi Dario Paolo, Montalto Riccardo
Syllabus
 Lagrange equation: deduction starting from Newton equation, in the case of a point on a smooth surface; deduction in the general case of holonomic constraint. Jacobi energy. The case of keplerian potential: bounded and scattering motions, scattering cross section.
Equilibrium points and normal modes of oscillations.  Hamilton Equation: deduction of the equation; phase space and Liouville theorem; Poisson brackets and first integrals; canonical transformation. Relation between simmetries and conserved quantities.  Variational principles: Hamilton principle of least action for both Lagrange and Hamilton equation. Application to the canonical transformation (Lie theorem and generating functions). Principle of Mapertius. Hamilton principle for the vibrating string.  Relativity: spacetime, inertial systems and the the principle of invariant light speed. Deduction of the Lorentz transformations and comparison with Galileo transformations. Some applications: bound on the speed of particles, addition of velocities, Lorentz contraction and time dilation. Geometrical interpretation in spacetime: pseudometric and proper time. Twin paradox. Lagrangian of the free particle, momentum, energy and rest energy. Four velocity and four momentum. Relativistic invariance of Maxwell's equations, and the lagrangian of a particle interacting with the electromagnetic field. Lesson period
First semester

CORSO B
Active edition
Yes
Responsible
MAT/07  MATHEMATICAL PHYSICS  University credits: 7
Practicals: 20 hours
Lessons: 40 hours
Professors:
Carati Andrea, Fermi Davide
Syllabus
 Lagrange equation: deduction starting from Newton equation, in the case of a point on a smooth surface; deduction in the general case of holonomic constraint. Jacobi energy. The case of keplerian potential: bounded and scattering motions, scattering cross section.
Equilibrium points and normal modes of oscillations.  Hamilton Equation: deduction of the equation; phase space and Liouville theorem; Poisson brackets and first integrals; canonical transformation. Relation between simmetries and conserved quantities.  Variational principles: Hamilton principle of least action for both Lagrange and Hamilton equation. Application to the canonical transformation (Lie theorem and generating functions). Principle of Mapertius. Hamilton principle for the vibrating string.  Relativity: spacetime, inertial systems and the the principle of invariant light speed. Deduction of the Lorentz transformations and comparison with Galileo transformations. Some applications: bound on the speed of particles, addition of velocities, Lorentz contraction and time dilation. Geometrical interpretation in spacetime: pseudometric and proper time. Twin paradox. Lagrangian of the free particle, momentum, energy and rest energy. Four velocity and four momentum. Relativistic invariance of Maxwell's equations, and the lagrangian of a particle interacting with the electromagnetic field. Lesson period
First semester

Lesson period
First semester