MATHEMATICAL PHYSICS
Stampa
Enrollment year
2021/2022
Academic year
2021/2022
Regulations
DM270
Academic discipline
MAT/07 (MATHEMATICAL PHYSICS)
Department
DEPARTMENT OF CIVIL ENGINEERING AND ARCHITECTURE
Course
CIVIL AND ENVIRONMENTAL ENGINEERING
Curriculum
PERCORSO COMUNE
Year of study
Period
2nd semester (07/03/2022 - 17/06/2022)
ECTS
6
Lesson hours
60 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
BISI FULVIO (titolare) - 6 ECTS
Prerequisites
Notions given in basic courses in Calculus Analisi Matematica), Linear Algebra, Geometry (Geometria e Algebra), and Physics (Fisica).
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. 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.

General kinematics
Center of mass of a system of material points; Momentum, moment of momentum, and kinetic energy. Transport theorem for moment of momentum. K├Ânig'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's equations of motion

Stability of motion
Stability of motion according to Ljapunov. Dirichlet-Lagrange theorem. First Ljapunov's instability criterion.

Normal modes
Linearization of Lagrange's equations; normal co-ordinates. Oscillating, linear, and hyperbolic normal modes.

One-dimensional Continuum mechanics
Basic properties of curves. Unit tangent and unit normal vector to a plane curve; curvature of a curve. Intrinsic trihedron. Equilibrium equations for one-dimensional continuum bodies. Constitutive hypothesis: flexible and inextensible threads. Conservative active forces. Equilibriun profile of a homogeneous catenary. Suspended bridges.
Teaching methods
Lectures (hours/year in lecture theatre): 22.5
Practical class (hours/year in lecture theatre): 37.5
Practicals / Workshops (hours/year in lecture theatre): 0
Reccomended or required readings
F. Bisi, R. Rosso: Introduzione alla meccanica teorica (La Dotta, Bologna).

P. Biscari, C. Poggi, E.G. Virga, Mechanics Notebook (Liguori, Napoli).
Assessment methods
Written test and oral exam (this latter is optional, and can be requested by the student or by the examiner). The student has to pass the test with 18/30 at least, and then, a few days later, he may take an oral test on theoretical topics. The final grade (including non-pass grade)
depends on the outcome of both tests.
Further information
Written test and oral exam (this latter is optional, and can be requested by the student or by the examiner). The student has to pass the test with 18/30 at least, and then, a few days later, he may take an oral test on theoretical topics. The final grade (including non-pass grade)
depends on the outcome of both tests.
Sustainable development goals - Agenda 2030