1 - Small oscillations of systems with N degrees of freedom. Normal modes of oscillation; the system of principal axes and normal coordinates. Forced and damped oscillations of systems. Resonance.
2 - Covariant formulation of special relativity: the Einstein's postulates, covariant formulation of the theory, invariance and conservation, center of mass system, threshold energy, elastic and inelastic collisions.
3 - Elements of tensor calculus: general transformations, tensors, the fundamental metric tensor.
4 - Deformable bodies/elasticity: tensor fields of deformations and stresses, the Cauchy equation, elastic energy and elastic hysteresis; observables of the theory of elasticity; the Navier equation, propagation of elastic waves , s and p waves.
5 - Deformable bodies/fluid mechanics: ideal fluids, the Euler and Bernoulli equations; real fluids, the Navier-Stokes equation, vorticity, the Reynolds number, boundary layer of Prandt; drag force, lift force, the D' Alembert paradox.
Bibliography of reference
GOLDSTEIN, H. (1980). Classical Mechanics. 2. ed. Addison-Wesley.
LANDAU & LIFSHITZ. Mechanics.
LANDAU & LIFSHITZ. Elasticity.
BHATIA A. B.; & SINGH, R. N. (1986). Mechanics of Deformable Media. Adam Hilger.
FEYNMAN, R. P.; SANDS, R. B. Leightonm M. (1977). The Feynmann Lectures on Physics. Addison-Wesley. vol. II.
JACKSON, J. D.. Classical Electrodynamics.
MATHEWS & WALKER. Mathematical Methods of Physics
MARION, J. B. & THORNTON, S. T. (1995). Classical Dynamics of Particles and Systems. 4. ed. Academic Press.
FRENCH, A. P. (1968). Special Relativity. W. W. Norton.
Mecânica clássica II, textos letivos (2013), J. Pinto da Cunha.