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## MATHEMATICAL PHYSICS 1

CODE 60352 2017/2018 6 credits during the 2nd year of 10375 INGEGNERIA CHIMICA E DI PROCESSO (L-9) GENOVA 6 credits during the 2nd year of 8716 Electrical Engineering (L-9) GENOVA MAT/07 Italian GENOVA (INGEGNERIA CHIMICA E DI PROCESSO ) 1° Semester Prerequisites You can take the exam for this unit if you passed the following exam(s): Electrical Engineering 8716 (coorte 2016/2017) MATHEMATICAL ANALYSIS I 56594 GEOMETRY 56716 FUNDAMENTAL OF PHYSICS 72360 Prerequisites (for future units) This unit is a prerequisite for: Electrical Engineering 8716 (coorte 2016/2017) ELECTRICAL MACHINES 66171 GENERAL PHYSICS LABORATORY 52449 ELECTRICAL INSTALLATIONS 66117 ELECTRICAL EQUIPMENT TECHNOLOGIES 86822 ELECTRICAL TECHNOLOGIES LABORATORY 84374 POWER ELECTRONICS AND ELECTRICAL DRIVES 84373 ENVIRONMENT AND WORK SECURITY 84375 ELECTRICAL MEASURES 84371 FUNDAMENTALS OF ELECTRIC POWER SYSTEMS CONTROL 66049 This unit is a module of:

## 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.

### TEACHING METHODS

Lectures with applications and exercises.

### SYLLABUS/CONTENT

Vector functions and smooth curves. Kinematics, absolute and relative motions. Dynamics of a material point, equation of motion and equilibrium. Forces and constraints. Systems of bound vectors and mechanics of material systems. Cardinal equations. Center of mass. Rigid motions and mechanics of rigid bodies. Inertial operator. Rigid body with a fixed axis or with a fixed point. Analytical mechanics, ideal constraints, holonomic systems and Lagrange equations. Kinetic moments and first integrals. Equilibrium and stability for holonomic systems.  Harmonic modes near stable equilibrium configurations.

• Lecture notes by the teacher (Italian and English versions on the website AulaWeb)
• 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

DANILO PERCIVALE (President)

MAURIZIO ROMEO (President)

MAURO BENATI

CLAUDIO ESTATICO

ANNA ONETO

## LESSONS

### TEACHING METHODS

Lectures with applications and exercises.

### LESSONS START

September 19, 2017

### 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
09/01/2018 09:00 GENOVA Orale Le prove si svolgeranno in aula B4
17/01/2018 09:00 GENOVA Scritto La prova si svolgerà in aula G1
23/01/2018 09:00 GENOVA Orale Le prove si svolgeranno in aula B4
31/01/2018 09:00 GENOVA Scritto La prova si svolgerà in aula G1
13/02/2018 09:00 GENOVA Orale Le prove si svolgeranno in aula B4
29/05/2018 09:00 GENOVA Orale Le prove si svolgeranno in aula B4
06/06/2018 09:00 GENOVA Scritto La prova si svolgerà in aula G1
12/06/2018 09:00 GENOVA Orale Le prove si svolgeranno in aula B4
20/06/2018 09:00 GENOVA Scritto La prova si svolgerà in aula G1
03/07/2018 09:00 GENOVA Orale Le prove si svolgeranno in aula B4
11/07/2018 09:00 GENOVA Scritto La prova si svolgerà in aula G1
17/07/2018 09:00 GENOVA Orale Le prove si svolgeranno in aula B4
05/09/2018 09:00 GENOVA Scritto La prova si svolgerà in aula G1
11/09/2018 09:00 GENOVA Orale Le prove si svolgeranno in aula B4