# MATHEMATICAL PHYSICS 1

_
iten
Code
60352
2019/2020
CREDITS
6 credits during the 2nd year of 10375 CHEMICAL AND PROCESSES ENGINEERING (L-9) GENOVA

6 credits during the 2nd year of 8716 Electrical Engineering (L-9) GENOVA

SCIENTIFIC DISCIPLINARY SECTOR
MAT/07
TEACHING LOCATION
GENOVA (CHEMICAL AND PROCESSES ENGINEERING)
semester
1° Semester
Prerequisites
modules
This unit is a module of:
Teaching materials

## 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

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

Ricevimento: By appointment

Exam Board

MAURIZIO ROMEO (President)

MICHELE PIANA (President)

RICCARDO CAMERLO (President)

## LESSONS

Teaching methods

Lectures on the theoretical contents with applications and exercises.

LESSONS START

September 23, 2019

## 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
26/10/2020 09:00 GENOVA Scritto La prova scritta si svolgerà online sul canale Teams che verrà comunicato dal docente a fine iscrizione
28/10/2020 09:00 GENOVA Orale La prova orale si svolgerà online sul canale Teams che verrà comunicato dal docente a fine iscrizione