Complements of Classical Mechanics and Thermodynamics
Prerequisiti
General physics course for first-year students in Chemistry, Physics, and Mathematics.
Programma
- Units of measurement and dimensional analysis.
- Reference frames. Vectors. Kinematics of a point particle and rigid body.
- Newton's laws. Forces and moments. Equations of motion.
- Energy conservation in one dimension. The phase space.
- Oscillations: harmonic oscillator, driven oscillator, damped oscillator.
- Energy conservation in three dimensions, work, and potential energy.
- Central forces. Angular momentum. Effective potential.
- Momentum conservation. Center of mass. The two-body problem.
- Gravity. Kepler's laws. Multipole expansion.
- The Lagrangian formalism. Euler-Lagrange equation. The Noether theorem
- Coupled oscillators: normal modes.
- Moment of inertia. Torque. Fixed-direction angular momentum.
- The General case of angular momentum. Angular velocity. Inertia tensor. Principal axes.
- Euler's equations. Spinning tops and gyroscopes.
- Tidal forces.
- Kinetic theory of gases. Pressure, temperature, and kinetic energy. Ideal gas law, Boltzmann law, specific heat.
- Temperature and heat. First and second laws of thermodynamics. Entropy.
Obiettivi formativi
Develop the skills to tackle and solve medium- to high-difficulty problems in classical mechanics, using advanced mathematical techniques beyond those typically covered in a first-year university general physics course.
Riferimenti bibliografici
Landau Lev D., Lifšits Evgenij M, Fisica Teorica 1 Meccanica.
Goldstein H., Poole C.P., Safko J.L., Classical Mechanics, 3rd edition.
Morin D., Introduction to Classical Mechanics.
Fermi E., Thermodynamics.