Advanced topics in physics

1) Gravitation: Gravitational acceleration and potential; Kepler's laws of planetary motion; Gravitational acceleration and the potential of a solid sphere; Laplace's equation is spherical polar coordinates; MacCullagh's formula for the gravitational potential.

2) Earth's rotation: Motion in a rotating coordinate system; The Coriolis and Eotvos effects; Precession and forced nutation of the Earth's rotation axis; The free Eulerian nutation of a rigid Earth; The Chandler wobble.

3) Gravity: The ellipticity of the Earth's figure; The geopotential; The equipotential surface of gravity; Gravity on the reference spheroid; Geocentric and geographic latitude; The geoid.

4) The tides: Origin of the lunar tide-raising forces; Tidal potential of the Moon; Tidal friction and deceleration of terrestrial and lunar rotations.

5) Seismic waves: Elasticity theory, stress and strain tensors, elasticity modulii and Poisson's ratio. Relations between elastic modulii; Lamé constants; The seismic wave equation; Three-dimensional propagation of P- and S- waves; Superficial waves; Absorption and Q factor of seismic waves; Free oscillations and standing waves. Case of 1D oscillation of a string; Free oscillations of the Earth; radial and toroidal modes. Seismometry and equation of the seismometer.

6) Waves and oscillations: Examples of oscillations in simple systems. Study of the resonance in a damped and forced oscillator. Other examples of wave: string waves, acoustic waves (velocity, brief description of music theory, notes, interval as ratio between different harmonics, etc..); waves in water; beats; transversal oscillations of a continuous string, wave equation, progressive waves, phase velocity, dispersion and group velocity; wave energy and intensity; reflection and transmission of waves. Fourier analysis of a periodic function.

7) Electromagnetic theory: Maxwell's equations in vacuum and in material; General properties, Energy, momentum and angular momentum carried by electromagnetic fields; plane waves; linear and circular polarization; electromagnetic waves in materials of geophysical interest, microscopic model of matter.

8) Geomagnetism: The dipole magnetic field and potential; Potential of the geomagnetic field; The Earth's dipole magnetic field; Secular variation; The origin of the internal field.