1. Covariant formulation of restricted relativity: Newton and Maxwell laws and the principle of relativity; Einstein’s postulates; three-dimensional space covariant formulation; tensors in Minkowski space; conservation of the linear momentum tetravector; total inelastic collision; particle with null mass; centre-of-mass system; collision of two particles; some tetravectors in Physics.
2. Small oscillations of many-particle systems: single degree-of-freedom system; multiple degree-of-freedom systems; the double plane pendulum; vibrations of a linear triatomic molecule.
3. Elasticity theory: second order tensor and orthogonal transformations.
3.1- Deformations tensor: unidimensional and three-dimensional deformations, the deformation tensor; incompatibility relations.
3.2- Tension tensor: tension force per unit volume; balance conditions.
3.3- Hooke’s law: work done by tension forces; elastic bodies; Young’s modulus and Poisson’s ration; the tension graphic versus deformation; theory of rupture and tensile strength.
3.4- Applications to elastic and isotropic materials: traction of a bar; tension in a hollow cylindrical tube; torsion of a bar; flexion of a beam.
3.5- Wave propagation in an infinite and homogeneous medium: flow speed; motion equation; linear approximation for solids; wave propagation in infinite isotropic media: waves and P-waves.
4. Constitutive equations for fluids: fluids in balance, Euler equation; fluids with viscosity; Navier-Stokes equation.
Bibliography of reference
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.
GOLDSTEIN, H. (1980). Classical Mechanics. 2. ed. Addison-Wesley.
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.