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## MATHEMATICAL PHYSICS 1

CODE 60352 2022/2023 6 cfu during the 2nd year of 10375 INGEGNERIA CHIMICA E DI PROCESSO (L-9) - GENOVA 6 cfu during the 2nd year of 8716 INGEGNERIA ELETTRICA (L-9) - GENOVA MAT/07 GENOVA 1° Semester Prerequisites You can take the exam for this unit if you passed the following exam(s): Electrical Engineering 8716 (coorte 2021/2022) MATHEMATICAL ANALYSIS I 56594 GEOMETRY 56716 FUNDAMENTAL OF PHYSICS 72360 Prerequisites (for future units) This unit is a prerequisite for: Electrical Engineering 8716 (coorte 2021/2022) POWER ELECTRONICS AND ELECTRICAL DRIVES 84373 FUNDAMENTALS OF ELECTRIC POWER SYSTEMS CONTROL 66049 ENVIRONMENT AND WORK SECURITY AND INTERDISCIPLINAR SKILL 84375 MISURE ELETTRICHE 106718 ELECTRICAL MACHINES 66171 ELECTRICAL INSTALLATIONS 66117 ELECTRICAL EQUIPMENT TECHNOLOGIES 86822 This unit is a module of: AULAWEB

## AIMS AND CONTENT

### LEARNING OUTCOMES

Formative aims

A rigorous approach to Newtonian mechanics with applications to the motion of rigid systems. The basic methods of analytical mechanics to solve equilibrium and dynamic problems.

Technical skills

Ability to write potential and kinetic energies of mechanical systems with few degrees of freedom, to  derive the differential equations of motion and the equilibrium conditions.

### 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
• Bampi F., Benati M., Morro A., Problemi di Meccanica Razionale, Ecig (Genova)
• Bampi F. e Zordan C., Lezioni di Meccanica Razionale, Ecig (Genova)
• Goldstein H., Meccanica Classica, Zanichelli (Bologna, 1971)
• Levi M., Classical mechanics with calculus of variations and optimal control - An intuitive introduction. AMS (USA, 2014)

## TEACHERS AND EXAM BOARD

### Exam Board

PIERRE OLIVIER MARTINETTI (President)

LAURA BURLANDO

CRISTINA CAMPI

MAURIZIO CHICCO

MARC ALEXANDRE MUNSCH

SIMONE MURRO (President Substitute)

## LESSONS

### LESSONS START

https://corsi.unige.it/10375/p/studenti-orario

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

A  written test on technical skills  and a successive spoken exam on theoretical issues.

### ASSESSMENT METHODS

The written test consists of a problem on rigid body mechanics where the following results are required: Equilibrium configurations and their stability; Differential equations of motion.

The objective of the spoken exam is to verify the student's knowledge about: Kinematics and dynamics of Newtonian systems; Lagrangian description of mechanical system with finite degrees of freedom.

### Exam schedule

Date Time Location Type Notes
18/01/2023 09:00 GENOVA Scritto + Orale
15/02/2023 09:00 GENOVA Scritto + Orale
23/06/2023 09:00 GENOVA Scritto + Orale
18/07/2023 09:00 GENOVA Scritto + Orale
14/09/2023 09:00 GENOVA Scritto + Orale

### FURTHER INFORMATION

Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.