Università degli Studi di Perugia


Course name Mechanical engineering
Study-unit Code 70047510
Curriculum Gestionale
Lecturer Maria Cesarina Salvatori
CFU 10
Course Regulation Coorte 2016
Supplied 2017/18
Supplied other course regulation
Type of study-unit Obbligatorio (Required)
Type of learning activities Attività formativa integrata


Code 70A00505
Lecturer Maria Cristina Valigi
  • Maria Cristina Valigi - Didattica Ufficiale
  • 45 Hours - Didattica Ufficiale - Maria Cristina Valigi
Learning activities Caratterizzante
Area Ingegneria meccanica
Sector ING-IND/13
Type of study-unit Obbligatorio (Required)


Code 70A00605
Lecturer Maria Cesarina Salvatori
  • Maria Cesarina Salvatori - Didattica Ufficiale
  • 45 Hours - Didattica Ufficiale - Maria Cesarina Salvatori
Learning activities Base
Area Matematica, informatica e statistica
Sector MAT/07
Type of study-unit Obbligatorio (Required)
Language of instruction Italian
Contents Vectorial Calculus.

The Kinematic of Rigid Body

Relative Kinematics.

Constrained Systems.

Centre of Mass. Moment of Inertia.

Force, Work, Potential.

Laws of Mechanics.

Lagrange Equations.
Reference texts T. Ruggeri: Richiami di Calcolo Vettoriale e Matriciale. - Pitagora Editrice Bologna.

P. Biscari, T. Ruggeri, G. Saccomandi, M.Vianello : Meccanica Razionale. - Spinger.
Educational objectives The goal of this course is to provide the students with an introduction to the statics and the dynamics of the rigid body as well as of the holonomic systems using the principle of virtual work and the Lagrange Equations respectively .
Prerequisites Calculus level I and II, geometry I.
Teaching methods Lectures on all subjects of the course and Exercices in the classroom.
Other information Yor are recommanded to attend the lectures.

The lectures will be held at the department at
in Via Goffredo Duranti
06125 Perugia.

A tutor is available by appointment at mariacesarina.salvatori@unipg.it
Learning verification modality The oral examination consists on an interview about 2/3 arguments treated during the course. This allows to verify the ability of knowledge and understanding, the ability to apply the acquired skills, the ability to display and learn. Operating time up to 30-40 minutes.
Extended program Vectorial Calculus: dot product, cross product, scalar triple product, vectorial triple product. Applied vectors. Moment of a vector about a point. Moment of a vector about an axis. Couples. Equivalence of systems of vectors.

The Kinematic of the Rigid Body: rigid configurations. Euler angles. Angular velocity. Poisson's formulas. Rigid motion. Mozzi's Theorem.

Relative Kinematics: Galileo's Theorem. Coriolis Theorem.

Constrained Systems: virtual constraints, virtual displacement and virtual velocity. Rigid virtual displacement. Holonomic constraints. Degrres of freedom. Configurations space.

Centre of Mass. Moment of Inertia.

Force, Work, Potential: elementary work. Work of a force moving along a curve. Work of a system of forces acting on a rigid body. Conservative forces.

Laws of Mechanics: Princilples of Mechanics.

Statics: Equation of statics, Equilibrium positions of a rigid body and of an holonomic system. The priciple of virtual works.
The dynamics of the rigid body. Lagrange Equations.