# RATIONAL MECHANICS

## Learning outcomes of the course unit

The student independently should be able to understand and to schematize by means of mathematical models the phisical phenomena, and acquire the aptitude to learn, with critical mind, the courses that characterize the Civil and Ambient Engineering degree.

The student independently should be able to understand and to schematize by means of mathematical models the phisical phenomena, and acquire the aptitude to learn, with critical mind, the courses that characterize the Civil and Ambient Engineering degree.

## Course contents summary

The Theoretical Mechanics course is an applied mathematics course, the link between the pure mathematics courses (Mathematical Analisys and Geometry) and of engineering contents (expecially Structural Mechanics). The course is structured in two parts. In the first one we furnish the basis of the kinematics of the element and of the rigid body. In the second one, we apply the laws of the classical mechanics to the mechanical systems. In particular,we emphasize the statics of the articulate systems subjected to the ideal constraints.

The Theoretical Mechanics course is an applied mathematics course, the link between the pure mathematics courses (Mathematical Analisys and Geometry) and of engineering contents (expecially Structural Mechanics). The course is structured in two parts. In the first one we furnish the basis of the kinematics of the element and of the rigid body. In the second one, we apply the laws of the classical mechanics to the mechanical systems. In particular,we emphasize the statics of the articulate systems subjected to the ideal constraints.

## Course contents

Theory of free vectors - geometry of plane curves - kinematics of the element and of the rigid body - rigid motions acts - relative kinematics - plane rigid motions - statics and dynamics of the element - cardinal equations - theory of the applied vectors - statics and dynamics of the rigid body - statics and dynamics of the articulate systems - virtual works principle

Theory of free vectors - geometry of plane curves - kinematics of the element and of the rigid body - rigid motions acts - relative kinematics - plane rigid motions - statics and dynamics of the element - cardinal equations - theory of the applied vectors - statics and dynamics of the rigid body - statics and dynamics of the articulate systems - virtual works principle

## Recommended readings

As well the duplicate lecture notes provided by the lecturer, the following texts are reccomended: P.G. Bordoni "Lezioni di Meccanica Razionale" - P.Biscari, T.Ruggeri, G.Saccomandi, M.Vianello "Meccanica Razionale per l'ingegneria" - G.Frosali, E.Minguzzzi "Meccanica Razionale per l'ingegneria" - P.Benvenuti, G.Maschio "Complementi ed esercizi di Meccanica Razionale".

As well the duplicate lecture notes provided by the lecturer, the following texts are reccomended: P.G. Bordoni "Lezioni di Meccanica Razionale" - P.Biscari, T.Ruggeri, G.Saccomandi, M.Vianello "Meccanica Razionale per l'ingegneria" - G.Frosali, E.Minguzzzi "Meccanica Razionale per l'ingegneria" - P.Benvenuti, G.Maschio "Complementi ed esercizi di Meccanica Razionale".

## Teaching methods

The course consists of lectures, of which a significant proportion (almost half) will be devoted to pratical work. This consists of mechanical examples and exercises that are designed to illustrate and apply the concepts presented in the theoretical part of the course. The same type of exercises are proposed in the first written examination.

The course consists of lectures, of which a significant proportion (almost half) will be devoted to pratical work. This consists of mechanical examples and exercises that are designed to illustrate and apply the concepts presented in the theoretical part of the course. The same type of exercises are proposed in the first written examination.

## Assessment methods and criteria

The exam consists of two written tests and one possible oral test. The first written test (of about three hours) contains one or more exercises. The second written test (of about one hour) is a theoretical one. Before the second written test the student must communicate if he would take alse the oral test. The oral test can be requested by the professor in case the first written test is unsatisfactory. The mark "cum laude" can get only with the oral test.

The exam consists of two written tests and one possible oral test. The first written test (of about three hours) contains one or more exercises. The second written test (of about one hour) is a theoretical one. Before the second written test the student must communicate if he would take alse the oral test. The oral test can be requested by the professor in case the first written test is unsatisfactory. The mark "cum laude" can get only with the oral test.