RATIONAL MECHANICS
Academic Year 2025/2026 - Teacher: RITA TRACINA'Expected Learning Outcomes
The course aims to provide foundational knowledge of vector calculus, statics, and dynamics of material systems and rigid bodies, enabling the determination of equilibrium configurations and the associated constraint reactions of material systems with a finite number of degrees of freedom. These objectives are aligned with Goals 4, 9, and 11 of the 2030 Agenda, as they promote the technical training necessary for the sustainable development of infrastructure and communities.
The students will be able to find the center of gravity, and the equilibrium configurations for a mechanical system with a finite number of freedom degrees and to compute the constraint reactions.
Course Structure
Lectures and exercises in the classroom.
Required Prerequisites
Required background: analytic geometry and linear algebra, differential calculus of single- and multivariable functions, integral calculus of single- and multivariable functions, and fundamentals of general physics. Prerequisites: Physics, Mathematical Analysis I, Linear Algebra and Geometry.
Attendance of Lessons
Detailed Course Content
Vector fields
Free and applied vectors. Systems of applied vectors. Equivalent systems of vectors and their reduction. Intrinsic trihedron.
Kinematics
Particle kinematics. Rigid motions for systems. Analysis of a rigid motion. Relative kinematics. Some special rigid motions. Constrained systems. Holonomic and anholonomic constraints. Degrees of freedom and free coordinates. Displacements, virtual displacements.
Mechanics.
Dynamics and statics of a particle (free and constrained). Centre of mass. Inertia matrices. Cardinal equations of mechanics. Balance theorem of kinetic energy. Conservative forces and conservation of energy. Virtual work principle and its applications. Equilibrium of a holonomic system. Principle of stationary potential energy. Statics of constrained rigid body. Determinations of constraint reactions
Textbook Information
1) E. OLIVERI, Lezioni di Meccanica Razionale. Ed. CULC, Catania.
2) G. GRIOLI, Lezioni di Meccanica Razionale. Ed. Libreria Cortina, Padova.
3) M. FABRIZIO, Elementi di Meccanica Classica. Ed. Zanichelli Bologna.
4) S. BRESSAN, G. GRIOLI, Esercizi di Meccanica Razionale. Ed. Libreria Cortina, Padova.
5) A. GRASSO – A. RIGANO, Esercizi di Meccanica Razionale. Ed. CULC, Catania.
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Calcolo vettoriale | 3, 1 |
| 2 | Cinematica | 1, 2 |
| 3 | Moti rigidi | 1, 2 |
| 4 | Cinematica delle masse | 1,2 |
| 5 | Meccanica del punto | 1,2,3 |
| 6 | Meccanica dei sistemi | 1,3 |
| 7 | Statica dei rigidi | 1,2,3 |
Learning Assessment
Learning Assessment Procedures
The examination consists of a written test and an oral test.
Assessment of learning may also be conducted remotely, if circumstances require.
To take the exam, students must register by the deadlines established for each exam session exclusively online through the student portal, and must have completed the required prerequisites.
The written test consists of solving exercises with justification and is divided into two parts: Part A and Part B. Part A covers topics in kinematics and mass kinematics (e.g., calculation of centers of mass and moments of inertia). Part B covers topics in statics and dynamics (e.g., calculation of equilibrium configurations and constraint reactions).
The oral test covers the theory in its entirety.
Passing the written test (both parts) is required to take the oral test. A student passes the written test by achieving a minimum score of 7.5/15 in each of the two parts (even if obtained in different exam sessions).
A student who passes the written test with a score of at least 18/30 (always with a minimum of 7.5/15 in each of the two parts) may choose not to take the oral test. If the student decides not to proceed with the oral test, the final grade will be at most 22/30, assigned according to the following table:
Written score between 18/30 and 19/30 → final grade 18/30;
Written score between 20/30 and 22/30 → final grade 19/30;
Written score between 23/30 and 25/30 → final grade 20/30;
Written score between 26/30 and 28/30 → final grade 21/30;
Written score between 29/30 and 30/30 → final grade 22/30.
The written test score serves two distinct functions:
1) Threshold for admission to the oral exam: the written test is considered passed only if the student obtains at least 7.5/15 in both parts A and B (even if obtained in different exam sessions). Only in this case can the student access the oral exam.
2) Determination of the final grade (without oral exam): if the total written score is at least 18/30 (with at least 7.5/15 in each part), the student may choose not to take the oral exam. In this case, the final grade is assigned according to the previous conversion table, with a maximum of 22/30.
The final grade in the case of the oral exam is determined by an overall assessment of both tests. The written test serves as the basis for access and the verification of applied skills. In particular, a modest but sufficient written test does not preclude achieving a high final grade, provided that the oral exam clearly demonstrates a level of preparation such that the written test can be considered an isolated, non-representative episode. In any case, the final evaluation is not a mathematical average of the written and oral exams, but the result of a comprehensive consideration of knowledge, application, connections, and clarity of exposition. The oral exam allows the assessment to be integrated and deepened, making it possible to achieve honors in the presence of excellent preparation.
The assignment of the final grade will take into account the following parameters:
Qualitative description of the oral exam (in addition to a sufficient written test) | |
Not passed | Lacks minimum knowledge of the main contents and has very poor or no ability to use the specific terminology. Unable to independently apply acquired knowledge. |
18–21 | Essential but fragmented knowledge. Mechanical application and limited connections. Comprehensible expression but poor command of language. |
22-24 | Fair knowledge, limited to main topics. Correct applications to standard cases with few connections. Expression fairly clear, though language not always correct. |
25–26 | Good knowledge, not in depth. Correct application of methods in familiar contexts; connections only between closely related topics. Clear expression with satisfactory language skills. |
27–28 | Confident and well-structured knowledge. Correct application even in non-standard contexts. Well-managed connections. Clear and fluent expression. |
29–30 | Complete, in-depth, and well-structured knowledge. Excellent ability to apply concepts and make connections. Rigorous and effective expression. |
30 cum laude | Excellence in all aspects. High level of abstraction, personal insights, and flawless, independent presentation. |
Information for students with disabilities and/or specific learning disorders (SLD):
In order to ensure equal opportunities and in compliance with current legislation, interested students may request a personal meeting to plan possible compensatory and/or exemption measures, based on the learning objectives and their specific needs.
Students may also contact the CInAP (Center for Active and Participatory Integration – Services for Disabilities and/or SLD) representative of the Department.