Knowledge and understanding: fundamentals of analytical mechanics and mathematical modelling of rigid bodies

Applying knowledge and understanding: being able to use abstract techniques for the resolution of concrete problems with many degrees of freedom

Autonomous judgment: being able to determine independently which element of the abstract formalism can be applied to various problems of physical origin

Communication skills: being able to explain the basic ideas of the mathematical formalism, describe physical systems in abstract terms

Learning skills: creative application of the formalism to complex systems, such as those encountered in Engineering, and understanding of advanced texts.

Newtonian Mechanics, Linear Algebra, Multivariables Calculus

The course develops the mathematical methods for modeling complex mechanical systems. Kinematics of rigid bodies: rigid bodies, rigid motions, Euler angles, Poisson formulas, and motion acts. General principles of the mechanics of systems: material systems, forces, cardinal equations. Mechanics of holonomic systems: constraints, virtual work, Lagrange equations, mechanical quantities for the rigid body, inertia tensor, structure of the Lagrange equations, conservation laws, statics and equilibrium, approximation methods. Dynamics of the rigid body: special motions, Euler's equations, Poinsot-type motions, gyroscopes.

Lecture notes which cover all the theory and several exercises. Examples of written exams.

Auxiliary books:
G. Borgioli: "Modelli Matematici di Evoluzione ed Equazioni Differenziali", Celid (Torino)
A. Fasano, S. Marmi: "Meccanica Analitica", Bollati Boringheri (Torino)
A. Fasano, V. de Rienzo, A. Messina: "Corso di Meccanica Razionale", Laterza (Bari)
H. Goldstein: "Meccanica Classica", Zanichelli (Bologna)
T. Levi-Civita, U. Amaldi: "Compendio di Meccanica razionale", Zanichelli (Bologna)

The course develops the mathematical methods used to model complex mechanical systems. Kinematics of rigid bodies: rigid bodies, rigid motions, Euler angles, Poisson formulas, and the motion act. In this part, we will develop the geometric tools needed to describe the configuration of a rigid body in space and its motion. General principles of system mechanics: material systems, forces, cardinal equations. In this part, we will study the equations that govern the dynamics of rigid bodies. Mechanics of holonomic systems: constraints, virtual work, Lagrange equations, mechanical quantities for rigid bodies, inertia tensor, structure of the Lagrange equations, conservation laws, statics and equilibrium, approximation methods. In this section, we will encounter constrained and articulated rigid bodies and develop the general formalism to describe their dynamics and statics. We will introduce approximation methods to solve the equations of motion. Dynamics of rigid bodies: special motions, Euler's equations, Poinsot-type motions, gyroscopes. In this part, we will explore specific aspects of rigid body dynamics in detail.

Theoretical lessons and plenty of exercises

The course will be supported by Moodle and MSTeams

All the course material will be available on the Moodle platform.

Exam Format The exam consists of a mandatory written test and an optional oral exam. Students may take the oral exam only after passing the written test with a score of at least 18/30. Written Exam (mandatory) The written exam lasts 3 hours and focuses on the exercises covered during the course. It may also include theoretical questions. The maximum score achievable on the written test is 27/30. Students who choose not to take the oral exam will have their written exam score confirmed as their final grade. Oral Exam (optional) The oral exam consists of a brief discussion on the topics covered in class, including: The main concepts, their applications, and their physical significance; The techniques used to solve problems and their theoretical foundations; The key theorems and their proofs. The oral exam results in a score adjustment ranging from –5 to +5 points, to be added to the written exam score.

The course will cover the fundamentals of mechanics applied to engineering and the study of infrastructurs.