# COMPLEMENTS OF RATIONAL MECHANICS cod. 1005640

3° year of course - First semester
Professor
- Giancarlo CANTARELLI
Fisica matematica (MAT/07)
Field
A scelta dello studente
Type of training activity
Student's choice
48 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in ITALIAN

## Learning objectives

At the end of the course the student should know very well the mechanics of the rigid body, should be able to relate the experimental results with the theoretical ones, and should be able to apply their theoretical knowledge to the concrete applications. But, above all, the student should be able to schematize and to formulate self-evaluations about rather complex phisical phenomena.

## Prerequisites

There are not mandatory propedeuticities, but the Rational Mechanics course is strongly recommended.

## Course unit content

Rational Mechanics is the science that studies the general laws of mechanical motion of material bodies, and establishes general procedures and methods for solving problems involving such motions. Also this second course of Rational Mechanics can be divided into three parts: Statics, Kinematics and Dynamics.

In Statics we introduce the principle of the virtual work, and we show as it is possible to apply this principle also to articulate mechanical systems subjected to non ideal costraints. In Kinematics and in Dynamics we complete the study of the rigid body mechanics
that in the Rational Mechanics course includes only plane motions. Moreover, we provide the basic concepts of Analytycal Mechanics, by introducing the Lagrange equations and the first integral of the motion. Finally, we shortly illustrate stability theory of the equilibrium.

## Full programme

Plane motions - Kinematics of the rigid body - finite rigid displacements - principal axis of inertia - momentum and kinetic energy: Konig's theorems - conservation of the mechanical energy - mechanics of the constrained element - mechanics of the free and constrained rigid body - motion of a rigid body about a fixed point - mechanical holonomic systems - principle of virtual work - Lagrange's equations - - first integrals of the motion - Lyapunov stability.

## Bibliography

All the lectures are avilable to students and shared on Elly platform. Moreover, on the Libreria Universitaria Santa Croce the duplicate lecture notes provided by the lecturer are avilable. In addition, to this material, the student can personally study some of the topics discussed during the course in the following books: G.Ferrarese, L.Stazi "Lezioni di Meccanica Razionale" -
P.Biscari,T.Ruggeri,G.Saccomandi,M.Vianello "Meccanica Razionale per l'ingegneria" - G.Frosali, E.Minguzzi "Meccanica Razionale per l'ingegneria" - G.Andreassi "Introduzione alla meccanica del corpo rigido" - N.Rouche, P.Habets, M.Laloy "Stability Theory by Liapunov's direct Method".

## Teaching methods

The course counts 6 CFTs (one CFU , University Credits equals one ECTS credit and represents the workload of a student during educational activities aimed at passing the exams), that corresponds to 48 hours of lectures. The didactic activities are composed of frontal lessons. Almost half of such lessons will be dedicated to examples and phisical concrete applications, that aim to illustrate the concepts presented in the theoretical part of the course.

## Assessment methods and criteria

The exam consists of one oral test: usually questions that may relate to theoretical content, demonstations,applications and exercises that have been done during the course.

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