Classical mechanics

A.Y. 2018/2019
Lesson for
7
Max ECTS
60
Overall hours
SSD
MAT/07
Language
Italian
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

Course structure and Syllabus

CORSO A
Active edition
Yes
Responsible
MAT/07 - MATHEMATICAL PHYSICS - University credits: 7
Practicals: 20 hours
Lessons: 40 hours
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: space-time, 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 space-time: 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
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: space-time, 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 space-time: 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
Assessment methods
Esame
Assessment result
voto verbalizzato in trentesimi