CODE 60352 2023/2024 6 cfu anno 2 INGEGNERIA ELETTRICA 8716 (L-9) - GENOVA MAT/07 Italian GENOVA 1° Semester Per sostenere l'esame di questo insegnamento è necessario aver sostenuto i seguenti esami: Electrical Engineering 8716 (coorte 2022/2023) MATHEMATICAL ANALYSIS I 56594 2022 GEOMETRY 56716 2022 FUNDAMENTAL OF PHYSICS 72360 2022 Questo insegnamento è propedeutico per gli insegnamenti: Electrical Engineering 8716 (coorte 2022/2023) MATHEMATICAL PHYSICS 1 60352 2022 Electrical Engineering 8716 (coorte 2022/2023) MATHEMATICAL PHYSICS 1 60352 2022 Electrical Engineering 8716 (coorte 2022/2023) MATHEMATICAL PHYSICS 1 60352 2022 Electrical Engineering 8716 (coorte 2022/2023) MATHEMATICAL PHYSICS 1 60352 2022 Electrical Engineering 8716 (coorte 2022/2023) MATHEMATICAL PHYSICS 1 60352 2022 Electrical Engineering 8716 (coorte 2022/2023) MATHEMATICAL PHYSICS 1 60352 2022 Electrical Engineering 8716 (coorte 2022/2023) MATHEMATICAL PHYSICS 1 60352 2022 Questo insegnamento è un modulo di: AULAWEB

## AIMS AND CONTENT

### AIMS AND LEARNING OUTCOMES

The main objective of this module is a rational approach to the following issues:

1) Kinematics of matererial point by a geometrical description of spatial curves.

2) Equilibrium and dynamics of discrete or continuum material systems using cardinal equations of mechanics

3) Inertial èproperties of material systems

4) A Lagrangian description by the introduction of free coordinates for system subject to constraints and the role of first integrals.

5) Equilibrium and stability by analytical approaches.

The module aims to give some technical skills on the following problems:

1) KInematical and dynamical description of a system subject to constraints

2) Computation of kynetic anf potential enrgies by the Lagrangian formalism and the derivation of differential equations of motion

3) Computation of equilibrium configurations of a mechanical system and a discussion on their stability.

At the end of the course the student can arrive at the following results:

1) The knowledge of the algebraic and analytical tools necessary to the description of motion.

2) Understanding the main mathematical techniques relating linear momentum, angular momentum and energy to the inertial and dynamical properties of a mechnical system.

3) The ability to analize a mechanical systems subject to given loads and constraints, achieving results on the equilibrium conditions and obtaining the differential equations of motion, also recognizing possible first integrals.

### TEACHING METHODS

Lectures on the theoretical contents with applications and exercises.

### SYLLABUS/CONTENT

INTRODUCTION

MASSIVE POINT

• Kinematics of the massive point
• Mechanics of the free and constrained point

RELATIVE MECHANICS

•     Derivation and observer, Poisson formula
•     Relative kinematics
•     Relative mechanics

DISCRETE SYSTEMS

•   Newton third principle and internal forces
•   Equation for the cinetic and angolar momenta
•   Center of mass

RIGID BODY

•     RIgidity constraints and the law of distribution of velocities
•     Kinematics
•     Operator of inertia
•     Mechanics of the rigid body
•     Constrained rigid body

ANALITICAL MECHANICS

•     Olonomous systems
•     D'Alembert principle
•     Euler-Lagrange equation
•     Eulero-Lagrange equation and cardinal equations.

INTRODUCTION TO STABILITY THEORY

•    Equilibrium and stability for mechanical systems
•    Small oscillations

• Lecture notes by the teacher
• Valter Moretti: "Meccanica Analitica: Classical, Lagrangian and Hamiltonian Mechanics, Stability Theory, Special Relativity"

## TEACHERS AND EXAM BOARD

### Exam Board

EDOARDO MAININI (President)

SIMONE MURRO (President)

LAURA BURLANDO (President Substitute)

PIERRE OLIVIER MARTINETTI (President Substitute)

## LESSONS

### Class schedule

L'orario di tutti gli insegnamenti è consultabile all'indirizzo EasyAcademy.

## EXAMS

### Exam schedule

Data Ora Luogo Degree type Note
19/01/2024 09:00 GENOVA Scritto + Orale
22/01/2024 09:00 GENOVA Scritto
13/02/2024 09:00 GENOVA Scritto
15/02/2024 09:00 GENOVA Scritto + Orale
24/06/2024 09:00 GENOVA Scritto + Orale
26/06/2024 09:00 GENOVA Scritto
16/07/2024 09:00 GENOVA Scritto
18/07/2024 09:00 GENOVA Scritto + Orale
30/08/2024 09:00 GENOVA Scritto
13/09/2024 09:00 GENOVA Scritto + Orale