MATHEMATICAL PHYSICS
Stampa
Enrollment year
2018/2019
Academic year
2018/2019
Regulations
DM270
Academic discipline
MAT/07 (MATHEMATICAL PHYSICS)
Department
DEPARTMENT OF ELECTRICAL,COMPUTER AND BIOMEDICAL ENGINEERING
Course
ELECTRICAL ENGINEERING
Curriculum
PERCORSO COMUNE
Year of study
Period
1st semester (01/10/2018 - 18/01/2019)
ECTS
6
Lesson hours
60 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
ROSSO RICCARDO (titolare) - 6 ECTS
Prerequisites
Notions given in standard courses in Calculus (Analisi A and B) and Geometry.
Learning outcomes
The course aims at giving an overwiev of classical mechanics to show that an adequate mathematical formulation can give a deep insight into the problems of this discipline.
Course contents
Vector and tensor algebra
Scalar and vector product; mixed product and repeated vector product; Diadics; symmetric tensors: spectral theorem. Skew-symmetric tensors: spin axis. Orthogonal tensors: Euler's angles. Systems of vectors

Relative and rigid-body kinematics
Poisson formulae; Time derivatives of vectors in different frames. Basic formulae in relative kinematics. Fundamental formula in rigid kinematics; Planar rigid motion: Chasles theorem.

General kinematics
Center of mass of a system of mateiral points; Momentum, moment of momentum, and kinetic energy. Transport theorem for moment of momentum. König's theorem.

Inertia tensor
Definition and main properties of the inertia tensor. Moments of inertia. Huygens-Steiner theorem. Theorem of perpendicular axes. Composition theorem. Material symmetry.

General dynamics
Balance equations. Kinetic energy theorem. Conservation laws. Power expanded in a rigid motion.

Lagrangian dynamics
Lagrange equations. Cyclic coordinates and conservation laws.

Rigid body dynamics
Euler's equations. Poinsot case. Lagrange's top.

Stability of motion
Stability of motion according to Ljapunov. Dirichlet-Lagrange theorem. First Ljapunov's instability criterion. Stability of steady rotations in Poinsot motions.

Normal modes
Linearization of Lagrange's equations; normal co-ordinates. Oscillating, linear, and hyperbolic normal modes.
Teaching methods
Lectures (hours/year in lecture theatre): 60
Practical class (hours/year in lecture theatre): 0
Practicals / Workshops (hours/year in lecture theatre): 0
Reccomended or required readings
Lecture notes available at the course website.

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

P. Biscari, C. Poggi, E.G. Virga. Mechanics Notebook. Liguori.
Assessment methods
Written test and oral exam. The student has to pass the test with 18/30 at least, and then, a few days later, he will take an oral exam on theoretical topics. If a student passes the written test, he can decide to avoid the subsequent oral test. In that case, however, he will obtain 18/30, regardless of the effective judgment of his written test
Further information
Written test and oral exam. The student has to pass the test with 18/30 at least, and then, a few days later, he will take an oral exam on theoretical topics. If a student passes the written test, he can decide to avoid the subsequent oral test. In that case, however, he will obtain 18/30, regardless of the effective judgment of his written test
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