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MATHEMATICAL PHYSICS 1

CODE 60352
ACADEMIC YEAR 2022/2023
CREDITS
  • 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
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/07
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 1° Semester
    PREREQUISITES
    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
    MODULES This unit is a module of:
    TEACHING MATERIALS 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

    RECOMMENDED READING/BIBLIOGRAPHY

    • 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

    ADA ARUFFO (President)

    PIERRE OLIVIER MARTINETTI (President)

    LAURA BURLANDO

    CRISTINA CAMPI

    MAURIZIO CHICCO

    MARC ALEXANDRE MUNSCH

    SIMONE MURRO (President Substitute)

    LESSONS

    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.