The primary aim of the course is to provide to the students the skills to formalize a problem of rigid-bodies mechanics using the appropriate mathematical tools. Particular attention is paid on the modeling and analysis of simple engineering problems, in order to provide the cultural background required to cope with engineering analysis and design.
teacher profile teaching materials
ODE homogeneous and non-homogeneous
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
-Mechanics of systems of particles
Internal forces
Conservation of momentum
Conservation of angular momentum
Kinetic energy, Koenig’s theorem
-Kinematics of rigid-body motion
Two-dimensional rigid-body motion
Instant centre of rotation
Three-dimensional rigid-body motion
-Galilean relativity
Kinematics in non-inertial frames of reference
Dynamics in non-inertial frames of reference, fictitious forces
Classes of frames of reference
Derivative of vectors in moving frames of reference
-Dynamics of rigid bodies
Dynamics
Conservation of momentum and angular momentumInertia tensor
Ellipsoid of inertia
Koenig’s theorem
Euler equations
Rotation about central axes
-Elements of Lagrangean mechanics
Virtual displacements
Virtual work
Lagrange-Euler equations
-Beer, Johnston, "Vector Mechanics for Engineers", McGraw-Hill
-Benvenuti, Maschio, “Complementi ed esercizi di Meccanica Razionale", Ed. Kappa
Programme
-Mechanics of a material particleODE homogeneous and non-homogeneous
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
-Mechanics of systems of particles
Internal forces
Conservation of momentum
Conservation of angular momentum
Kinetic energy, Koenig’s theorem
-Kinematics of rigid-body motion
Two-dimensional rigid-body motion
Instant centre of rotation
Three-dimensional rigid-body motion
-Galilean relativity
Kinematics in non-inertial frames of reference
Dynamics in non-inertial frames of reference, fictitious forces
Classes of frames of reference
Derivative of vectors in moving frames of reference
-Dynamics of rigid bodies
Dynamics
Conservation of momentum and angular momentumInertia tensor
Ellipsoid of inertia
Koenig’s theorem
Euler equations
Rotation about central axes
-Elements of Lagrangean mechanics
Virtual displacements
Virtual work
Lagrange-Euler equations
Core Documentation
-Lecture notes with solved problems-Beer, Johnston, "Vector Mechanics for Engineers", McGraw-Hill
-Benvenuti, Maschio, “Complementi ed esercizi di Meccanica Razionale", Ed. Kappa
Reference Bibliography
-Levi-Civita, Amaldi, "Lezioni di Meccanica Razionale", Zanichelli, Bologna -Spiegel, Meccanica Razionale, collana Schaum's, McGraw-HillType of delivery of the course
The course consists of frontal teaching lectures concerning both theoretical aspects and exercises on material point and rigid body mechanics. In case of extension of the COVID-19 health emergency, all the provisions that regulate teaching activities will be implemented.Attendance
The course consists of frontal teaching lectures concerning both theoretical aspects and exercises on material point and rigid body mechanics.Type of evaluation
The exam is divided into a written test (90 mins) and an oral test. A successful written 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. In case of extension of the COVID-19 health emergency, all the provisions that regulate the methods of carrying out exams will be implemented. In particular, the exam will consist exclusively on an oral test.