Lecturer: Riccardo Rosso  

Course name: Fisica matematica
Course code: 500474
Degree course: Ingegneria Industriale
Disciplinary field of science: MAT/07
L'insegnamento costituisce attività di base per: Ingegneria Industriale
University credits: CFU 6
Course website: http://smmm.unipv.it/rossoall.html

Specific course objectives

The course aims at giving an overwiev of classical mechanics stressing the importance of an adequate mathematical formulation of the problems.

Course programme

Vector and tensor algebra
Scalar and vector products; mixed product and double vector product. Distributions of vectors. Diadic product; Symmetric tensors: spectral theorem. Skew tensors: spin axis. Orthogonal tensors: Euler angles.

Relative and rigid Kinematics
Absolute and relative time derivative of vectors. Fundamental formulae of relative kinematics. Fundamental formula of rigid kinematics. Screw axis and Chasles' theorem.

Momentum, moment of momentum, and kinetic energy
Center of mass of a material system. Momentum and moment of momentum. Trasnport theorem for moment of momentum. Kinetic energy: Koenig theorem..

Inertia tensor
Basic properties of the inertia tensor. Moment of inertia. Huygens-Steiner theorem. Perpendicular axes. Composition theorem. Material symmetry.

Fundamentals of dynamics
Basic laws of dynamics. Kinetic energy theorem. Conservation laws. Power expended in a rigid motion.

Lagrangian dynamics
Derivation of Lagrange's equations

Rigid body dynamics
Euler's equations. Motion a` la Poinsot. Lagrange's top.

Stability of motion
Stability according to Ljapunov. Dirichlet-Lagrange theorem. First Liapunov's instability criterion. Stability of permanent rotation in rigid body dynamics

Normal modes
Linearization of Lagrange equations; normal coordinates. Oscillating, linear, and hyperbolic modes.

Course entry requirements

Course structure and teaching

Lectures (hours/year in lecture theatre): 30
Practical class (hours/year in lecture theatre): 30
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

Lecture notes are available at the web address of the course

P. Biscari, C. Poggi, E.G. Virga. Mechanics Notebook. Liguori.

R. Rosso. Esercizi e Complementi di Meccanica Razionale. Cusl.

Testing and exams

A written exam based on exercises, and an oral exam based on theoretical topics should be passed at the end of the course.