### Technology

## Subject: CLASSICAL MECHANICS (A.A. 2019/2020)

### degree course in AUTOMOTIVE ENGINEERING

Course year | 2 |
---|---|

CFU | 9 |

Teaching units |
Unit meccanica razionale
Related or Additional Studies (lesson)
- TAF: Supplementary compulsory subjects SSD: MAT/07 CFU: 9
Cecilia VERNIA |

Mandatory prerequisites |
Analisi Matematica I |

Exam type | written |

Evaluation | final vote |

Teaching language | Italiano |

### Teachers

### Overview

The purpose is to provide both the basic concepts of Classical Mechanics and the mathematical tools with the aim to model some simple mechanical systems.

### Admission requirements

Analytic geometry, elementary functions, differential and integral calculus of multi variable functions.

### Course contents

Vector Algebra: definition of a vector; the scalar product; the vector product; the triple products;

differentiation of a vector with respect to a scalar parameter.

Mass Geometry: mass; centre of mass; moments of inertia; momental ellipsoid; principal axes of inertia.

Kinematics: velocity and acceleration of a particle; harmonic motion; circular motion; the rigid body; eulerian angles; Poisson formulas; velocity of a particle of a rigid body; kinetic states; kinematics of a particle with respect to non fixed orthogonal axes; rigid motion in the plane.

Fundamental units and notion: forces; laws of motion; lagrangian coordinates; real and virtual displacements; constraints; active forces and reactions; systems of forces and characteristic vectors; equivalence theorem for force systems; elementary operations with forces; parallel force systems; weight force; work; conservative forces; conservative systems.

Particle mechanics: Newton law; equilibrium and motion of a particle; friction; linear momentum, angular momentum and kinetic energy; kinetic energy theorem; energy conservation theorem; pendulum; harmonic oscillator; relative equilibrium and motion; centrifugal force.

Mechanics of systems of particles: equilibrium of particle systems; principle of virtual works; equilibrium of rigid body; equilibrium of conservative systems; stability of equilibrium; linear momentum, angular momentum and kinetic energy; energy theorems; theorem of motion of the centre of mass and theorem of angular momentum; first integrals; lagrange equations. constants of motion and lagrangian formalism.

### Teaching methods

Course teaching consists of theoretical lectures on the topics described in the section "Contents" and of solution of exercises on simple classical mechanics models.

### Assessment methods

Learning assessment is based on: - Two written (mid-term and final) tests with theory and exercises. Or, alternatively, - Oral final exam on the topics of the section “Contents”.

### Learning outcomes

Knowledge and understanding

Knowledge of Vector Algebra; knowledge of mass geometry; knowledge of kinematics of a particle and of a rigid body; knowledge of basic classical mechanics notions (forces; laws of motion; lagrangian coordinates); knowledge of particle mechanics; knowledge of mechanics of particle systems.

Applying knowledge and understanding

Solution of problem of classical mechanics: computation of center of mass and of moment of inertia; equilibrium and motion of a particle and of a rigid body; lagrange equations.

Making judgements

Skills of decideng when and how to apply classical mechanics models and understanding the results.

Comunication skills

Skills to communicate in a clear and rigorous way the methods of classical mechanics.

### Readings

V. Franceschini, C. Vernia, Meccanica Razionale per Ingegneria, Pitagora Editrice, Bologna.