Classical Mechanics
A.Y. 2018/2019
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
Expected learning outcomes
Undefined
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
CORSO A
Responsible
Lesson period
First semester
Course 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.
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.
MAT/07 - MATHEMATICAL PHYSICS - University credits: 7
Practicals: 20 hours
Lessons: 40 hours
Lessons: 40 hours
Professors:
Bambusi Dario Paolo, Montalto Riccardo
CORSO B
Responsible
Lesson period
First semester
Course 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.
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.
MAT/07 - MATHEMATICAL PHYSICS - University credits: 7
Practicals: 20 hours
Lessons: 40 hours
Lessons: 40 hours
Professors:
Carati Andrea, Fermi Davide
Professor(s)
Reception:
Wednesday, 13.30-17.30
Room 1005, Department of Mathematics, Via Saldini 50, 20133, Milan