CODE  60504 

ACADEMIC YEAR  2023/2024 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/07 
LANGUAGE  Italian 
TEACHING LOCATION 

SEMESTER  2° Semester 
PREREQUISITES 
Propedeuticità in ingresso
Per sostenere l'esame di questo insegnamento è necessario aver sostenuto i seguenti esami:

MODULES  Questo insegnamento è un modulo di: 
TEACHING MATERIALS  AULAWEB 
AIMS AND CONTENT
LEARNING OUTCOMES
The module aims to provide knowledge of mechanics of multi degree of freedom systems . The case of the rigid body e'trattato in detail .
AIMS AND LEARNING OUTCOMES
After the course completion the student should be familiar with the statics and the dynamics of mechanical systems with finite degrees of freedom (particles systems and systems composed by rigid bodies)
TEACHING METHODS
60 standard teaching hours in attendance
SYLLABUS/CONTENT
Elements of Vector Algebra:
Free and applied vectors. Vector quantities. Geometric representation of vector quantities. Vector structure of the space of free vectors. Scalar product of vectors. Orthonormal bases. Vector, triple scalar and triple vector product of vectors and their component representations. Orthogonal matrices. Change of orthonormal bases. Euler angles. Linear operators. Linear symmetric and skewsymmetric operators. Vector functions. Elements of geometric theory of a curve.
Absolute Kinematics:
Observer. Absolute Space and time. Frame of reference. Velocity, acceleration and their Cartesian and intrinsic representations. Rectilinear, uniform and uniformly accelerated motion. Circular motion. Harmonic motion. Ballistics problems. Central motions and Binet’s formula. Polar, cylindrical and spherical coordinates.
Relative kinematics:
Relative motion of frames of reference. Angular velocity. Poisson formulae. Theorem on composition of angular velocities. Transportation motion. Theorems on composition of velocities and accelerations.
Dynamics:
Newton’s first law. Inertial mass. Momentum of a particle. Momentum conservation for isolated systems. Newton’s second and third laws. Kinetic energy. Work and power of a force. Theorem of energy. Conservative forces. Potential of a conservative force. Theorem on conservation of energy.
Relative Dynamics:
Transportation inertial force. Coriolis inertial force. Earth Mechanics.
Mechanics of a particle:
Motion of a free particle. Friction laws. Motion of a particle along a curve. Motion of a particle on a surface.
Mechanics of systems:
Systems of applied vectors. Resultant and resultant moment of a system of vectors. Scalar invariant. Central axis. Reducible and irreducible systems of vectors. Centre of parallel vectors and centre of gravity. Mechanical quantities of a system. Konig’s theorem. Momentum and angular momentum theorems. Theorem of energy for systems. Conservation laws for systems.
Mechanics of a rigid body:
The bodyfixed reference frame of a rigid body. Rigid motion. Velocities and accelerations of the particles of a rigid body. Translational and rotational motions of a rigid body. Composition of rigid motions. Mechanical quantities of a rigid body. Inertia Tensor and its properties. Moment of a rigid body with respect to an Axis. Moments and products of Inertia. Inertia matrices. Huygens and parallel axes theorems. Momentum and angular momentum theorems for a rigid body. Power of a system of forces acting on a rigid body. Energy theorem for a rigid body. Motion of a free rigid body. Ideal constraints applied to a rigid body. Rotational motion of a rigid body about a fixed axis. Rotational motion of a rigid body about a fixed point. Poinsot motions. Elementary theory of a gyroscope and its application to the gyroscopic compass.
Outlines of Lagrangian Mechanics:
Principle of the stationary potential for the equilibrium of a conservative holonomic system (without proof). Lagrange equations for a conservative holonomic system (without proof) .
RECOMMENDED READING/BIBLIOGRAPHY
Enrico Massa, Elementi di Meccanica Razionale, dispense Università di Genova.
T. LeviCivita and U. Amaldi, Lezioni di Meccanica Razionale, Zanichelli, Bologna (1984).
B. Finzi, Meccanica Razionale, Vol. II, Zanichelli, Bologna, (1965).
G. Grioli, Lezioni di Meccanica Razionale, Edizioni Libreria Cortina, Padova, (1985).
P. Biscari, T. Ruggeri. G. Saccomandi and M. Vianello, Meccanica Razionale per l'Ingegneria, Monduzzi Editore S.p.A., Bologna, (2008)..
TEACHERS AND EXAM BOARD
Ricevimento: Thursday from 14,30 to 16,30, in the teacher's office (Via all'Opera Pia 15).
Exam Board
STEFANO VIGNOLO (President)
VALENTINA BERTELLA (President Substitute)
ROBERTUS VAN DER PUTTEN (President Substitute)
LESSONS
LESSONS START
Class schedule
The timetable for this course is available here: Portale EasyAcademy
EXAMS
EXAM DESCRIPTION
A written and an oral test, after passing the written test with a mark greater then or egual to 16.
ASSESSMENT METHODS
The assignment of the exam grade will take into account: knowledge and understanding of the covered topics, ability and clarity of exposition, ability to solve problems related to the covered topics
Exam schedule
Data  Ora  Luogo  Degree type  Note 

12/01/2024  10:00  LA SPEZIA  Orale  
09/02/2024  10:00  LA SPEZIA  Orale  
10/06/2024  14:30  LA SPEZIA  Scritto  
14/06/2024  10:00  LA SPEZIA  Orale  
28/06/2024  14:30  LA SPEZIA  Scritto  
02/09/2024  14:30  LA SPEZIA  Scritto 