RATIONAL MECHANICS

Course objectives

The course is a logical-deductive rational treatment of the phenomena of mechanics,thus propaedeutic to the professional courses of the following years. The course yes aims to introduce the student to mechanics, understood as that part of physics which,through the constitution of logical schemes based on mathematics, formulates and analyzes models that identify the state of rest and describe the motion of rigid systems and systems with a finite number of degrees of freedom. At the end of the course, the student knows the results of classical mechanics and the basic notions of analytical mechanics. He is able to use this knowledge to study the motion and equilibrium of systems of rigid bodies.

Channel 1
ADRIANO BARRA Lecturers' profile

Program - Frequency - Exams

Course program
Introduction to Analytical Mechanics Kinematics of points and systems of points Dynamics of rigid motion, Poisson formulas, CIR and its usage Constraint's classification, rigid body kinematics Principles of the Mechanics for both points and systems of points Cardinal equations of Mechanics Energy, work and conservation theorems Center of gravity and moment of inertia Momentum and angular momentum for the rigid body Statics and dynamics of rigid bodies Principle of Virtual Jobs Lagrangian Formulation of Mechanics First integrals and Noether symmetries Hamiltonian Formulation of Mechanics Legendre transforms Small oscillations theory Stability of perturbations and qualitative analysis of motions
Prerequisites
A basic knowledge of Classical Physics (in particular of Mechanics taught during the first academic year) is welcome while a thorough knowledge of Mathematics, with particular attention to Mathematical Analysis and Geometry is mandatory. Specifically, in order to understand the contents of the teaching and achieve the learning objectives, it is essential that the student has: 1. thorough knowledge of elementary algebra and affine and analytical geometry; 2. thorough knowledge of mathematical analysis (calculus); 3. rudimentary knowledge of mechanics.
Books
1. Meccanica Razionale. Biscari, P., Ruggeri, T., Saccomandi, G., Vianello, M. Springer (2016) 2. Appunti di Meccanica Razionale. Turzi S. (free download from the webpage of the Author)
Frequency
In person. Yet attending classes is voluntary and takes place in the classrooms and according to the schedule published by the Dean office. Attending classes, although warmly encouraged, does not contribute to the final mark.
Exam mode
The examination consists of the analytical solution of an exercise and, once this first written test has been passed, a short oral interview to also verify knowledge of the theory (oral test).
Lesson mode
Lessons will be given using a blackboard or a beamer.
ADRIANO BARRA Lecturers' profile

Program - Frequency - Exams

Course program
Introduction to Analytical Mechanics Kinematics of points and systems of points Dynamics of rigid motion, Poisson formulas, CIR and its usage Constraint's classification, rigid body kinematics Principles of the Mechanics for both points and systems of points Cardinal equations of Mechanics Energy, work and conservation theorems Center of gravity and moment of inertia Momentum and angular momentum for the rigid body Statics and dynamics of rigid bodies Principle of Virtual Jobs Lagrangian Formulation of Mechanics First integrals and Noether symmetries Hamiltonian Formulation of Mechanics Legendre transforms Small oscillations theory Stability of perturbations and qualitative analysis of motions
Prerequisites
Knowledge of standard Classical Physics (in particular of Mechanics, as taught during the first academic year) and a basic knowledge of Mathematics, with particular emphasis on Analysis (and, eventually, also rudiments of Algebra and Geometry). To be sharper, in order to understand the topics of the Meccanica Razional lectures, the students must have a good knowledge of the following topics: 1. elementary algebra; 2. trigonometry; 3. mathematical analysis; 4. linear algebra; 5. geometry of Euclidean spaces; 6. mechanics of point particle.
Books
1. Meccanica Razionale. Biscari, P., Ruggeri, T., Saccomandi, G., Vianello, M. Springer (2016) 2. Appunti di Meccanica Razionale per l'Ingegneria. S. Turzi (2013)
Frequency
In person. Yet attending classes is voluntary and takes place in the classrooms and according to the schedule published by the Dean office. Attending classes, although warmly encouraged, does not contribute to the final mark.
Exam mode
The examination consists of the analytical solution of an exercise and, once this first written test has been passed, a short oral interview to also verify knowledge of the theory (oral test).
Bibliography
Further integrative bibliography 3. Appunti delle Lezioni di Meccanica Razionale per l'Ingegneria, E.M. Cirillo, Edizioni CompoMat (2018). 4. Metodi Matematici della Meccanica Classica, V.I. Arnold, Editori Riuniti (1986). 5. Meccanica Classica, H. Goldstein, C. Poole, J. Safko, Zanichelli, (2005).
Lesson mode
Lessons will be given using a blackboard and via a beamer.
  • Lesson code1003305
  • Academic year2024/2025
  • CourseGreen Transition Mechanical Engineering
  • CurriculumSingle curriculum
  • Year2nd year
  • Semester1st semester
  • SSDMAT/07
  • CFU6
  • Subject areaMatematica, informatica e statistica