AIMS AND CONTENT

LEARNING OUTCOMES

The aim of the module is to introduce and deepen techniques and methods of Mathematical Physics for the construction of mathematical models and the solution of mechanical problems in Naval Engineering.

AIMS AND LEARNING OUTCOMES

The course aims to provide students with the fundamental concepts of Lagrangian mechanics, with a particular focus on its applications to rigid body dynamics and hydrodynamics.

At the end of the course, the student will be able to:

      1    analytically represent constraints in mechanical systems with a finite number of degrees of freedom;

    2    describe the Kinematics of such systems through the introduction of a corresponding configuration space-time and of a space of kinetic states;

    4    use the Lagrangian formalism to analyse the Dynamics and Statics of systems with a finite number of degrees of freedom subject to ideal constraints;

    5    analyse equilibrium stability and small oscillations for such systems; 

    6    use the Lagrangian formalism to analytically represent the hydrostatic and hydrodynamic stresses and analyse the Dynamics of the ship.

TEACHING METHODS

Frontal lectures.

Students with valid certifications for Specific Learning Disorders (SLDs), disabilities or other educational needs are invited to contact the teacher and the School's disability liaison at the beginning of teaching to agree on possible teaching arrangements that, while respecting the teaching objectives, take into account individual learning patterns

SYLLABUS/CONTENT

Recapitulation of fundamental concepts of Kinematics and Dynamics. Transformations between orthonormal bases Tait-Bryan angles. Singularities of Tait-Bryan angles. Concept of time. Reference systems. Temporal derivation of vectors. Poisson formulas. Act of dragging motion. Drag acceleration. Particular drag motions. Addition laws of velocity and acceleration. Mechanics of the free point. Equilibrium as a particular case of motion. Energy concepts. Conservative forces. Potential. Energy theorem.

Mechanics of the constrained point. Constraints and constraint reactions. Constitutive characterization of constraints. Friction. Material point constrained to a smooth, fixed line. Material point constrained to a smooth, mobile line. Point constrained to a smooth surface. Free material point.

Holonomic systems. Space–time of configurations. Space of acts of motion. Postulate of constraint reactions. Lagrange equations. Translational and rotational coordinates. Kinetic energy. Normality of Lagrange equations.

Lagrangian formalism. Conservative stresses. Lagrangian. Generalized potential. Lagrange equations in the general case. First integrals. Lagrange equations and relative mechanics. Scleronomous systems. Generalized velocities. Kirchhoff equations.

Complements of Rigid Body Mechanics. Recall of Rigid Body Kinematics. Mechanical quantities for the rigid body. Cardinal equations. Kirchhoff equations. Lagrangian formalism.

Lagrangian statics. Statics of holonomic systems. Stability and pseudo-stability of equilibrium. Theory of small oscillations.

Elements of fluid mechanics. Fundamental integral identities. Transport theorem. Evolution equations of a fluid. Bernoulli equations.

Hydrostatic and hydrodynamic stresses. Archimedean potential. Statics of the ship at anchor. Pseudo-stability of the equilibrium configuration. Small motions around the equilibrium configuration. Hydrodynamic actions. Theory of added masses.

RECOMMENDED READING/BIBLIOGRAPHY

1. Lecture notes by the teacher;
2. Goldstein H., Pool C., Safko J. "Meccanica Classica". Zanichelli (2005);
3. Lewandowski E.M. “The dynamics of marine craft”;
4. Newman J.N. ”Marine hydrodynamics”

TEACHERS AND EXAM BOARD

Exam Board

PATRIZIA BAGNERINI (President)

ANGELO ALESSANDRI (President Substitute)

SANTE CARLONI (President Substitute)

ENRICO MASSA (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/8738/p/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of an oral test divided into two parts. In the first (50% of the final grade), an overview of the Lagrangian formalism is required. In the second (50% of the final grade), the student is required to apply the cardinal equations and the tools of the Lagrangian formalism to topics related to the study of fluid mechanics and ship dynamics.

ASSESSMENT METHODS

The first part of the test assesses the students' ability to apply the concepts acquired during the course. Given a mechanical system, the student must demonstrate that he or she is able to perform one or more of the following tasks: correctly identify the constraints, build a representation of the kinetic states of the system, determine the Lagrangian of the system, derive the pure equations of motion. In this way, the deductive and analytical skills necessary for the application of the techniques presented in the course are assessed. The second part assesses the students' understanding of the basic theoretical concepts they have acquired. The ability to present a demonstration with proper language and to argue the conclusions and the meaning of the logical steps is assessed.

Exam schedule

FURTHER INFORMATION

Ask the professor for any additional information not included in this course presentation form.