## 20810301 - Meccanica razionale

The primary aim of the course is to provide to the students the skills to formalise a problem of rigid-body mechanics using the appropriate mathematical tools. Particular attention is paid on the modelling and analysis of simple engineering problems, in order to provide the cultural background required to approach problems of analysis and design in mechanical engineering.
teacher profile | teaching materials

Programme

Teaching unit I – Fundamental tools and methods
Elements of vector algebra
Rotation matrix
ODE homogeneous and non-homogeneous
Spectral analysis of symmetric matrices
Eigenvalues problem and diagonalization
Conservative, potential and irrotational vector fields
Teaching unit II – Mechanics of a material particle
Fundamental properties of the motion of a particle
Dynamics of free and constrained material elements
Un-damped and damped oscillators
Mechanical work, power and energy
Stabilty of mechanical equilibrium
Teaching unit III – Mechanics of systems of particles
Internal forces
Conservation of momentum
Conservation of angular momentum
Kinetic energy, Koenig’s theorem
Teaching unit IV – Rigid-body motion and Galilean relativity
Two- and Three-dimensional rigid-body motion
Kinematics in non-inertial frames of reference
Dynamics in non-inertial frames of reference, fictitious forces
Derivative of vectors in moving frames of reference
Trasformazioni tra riferimenti in moto relativo
Derivata temporale di R
Teaching unit V – Statics and dynamics of rigid bodies
Dynamics
Conservation of momentum and angular momentum
Inertia tensor
Ellipsoid of inertia
Koenig’s theorem
Euler equations
Gyroscopes and precessions
Statics
Equivalent forces
Central axis of a system of forces
Constraints reactions
Graphic methods for the analysis of equilibrium
Teaching unit VI – Elements of Lagrangean mechanics

Core Documentation

• Lecture notes with solved problems

Reference Bibliography

• Spiegel, Meccanica Razionale, collana Schaum's, McGraw-Hill • Beer, Johnston, "Vector Mechanics for Engineers", McGraw-Hill • Muracchini, Ruggeri, Seccia, "Esercitazioni di Meccanica Razionale con Matlab e Simulink", Progetto Leonardo, Bologna • Levi-Civita, Amaldi, "Lezioni di Meccanica Razionale", Zanichelli, Bologna • Benvenuti, Maschio, “Complementi ed esercizi di Meccanica Razionale”, Ed. Kappa

Type of delivery of the course

The agenda of the course is structured as follows: - three hours/week of frontal teaching on topics related to Teaching Units I to VI - one hours/week of supervised solution of problems The material provided by the teacher includes a set of interactive, dynamic scripts in Wolfram Mathematica language. The interactive material is periodically illustrated during classes. Source code is provided to students upon request, including basic instructions for coding.

Attendance

Although not mandatory, attendance is strongly recommended in consideration of the strong link existing between the theoretical part of the subject matter and the applications.

Type of evaluation

The exam is divided into a written test (90 mins) and a viva voce. A successful test guarantees the access to the oral examination. The latter starts with a critical review of the written test, followed by questions on topics that are part of the syllabus.