29690 - Rational Mechanics T

Academic Year 2012/2013

  • Docente: Barbara Lazzari
  • Credits: 6
  • SSD: MAT/07
  • Language: Italian
  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Mechanical Engineering (cod. 0927)

Learning outcomes


Course contents

Localized vectors
Resultant force and resultant moment, equivalent system of localized vectors, plane and parallel systems of vectors.
Kinematics of material points and rigid bodies
Constrain and holonymic systems.
Kinematics of a point
Plane motions, circular and uniform motions, harmonic motions.

Kinematics of rigid systems

Particular rigid motions, the Eulerian angles, state of motion, Poisson¹s formulae, and Mozzi¹s theorem.

Kinematics of relative motions

Special transport motions, plane rigid motions, polar paths.



Dynamics of the systems

Mass, force, Newton laws, weight force, theorem of work for a free material system, conservation of mechanical energy.

Statics and dynamics of a free material point

The differential equations of the motion of a free material point, first integral. Statics of a free material point. Motion of a heavy point in vacuum, harmonic oscillator, damped harmonic oscillator, resonance phenomena.

Statics and dynamics of a constrained material point

Principe of virtual work on the constrains, statics of a constrained material point, dynamics of a point constrained on a surface, motion of a point constrained on a curve, simple pendulum, nonlinear oscillations, Weierstrass method, phase diagrams, stability of equilibrium.

Geometry of masses for material systems

Definition and properties of center of mass, inertia matrix, principal axes of inertia, the Huyghens theorem.

General theorem for material systems

Linear and angular momentum, momentum of momentum, kinetic energy, cardinal equations, theorem of work and kinetic energy for a constrained material system, first integrals.

Material rigid systems

Cardinal equations of statics and dynamics and applications, systems of rigid bodies, motion of a rigid wit a fixed axis and kinetic constrains, motion of a rigid body with a fixed point and Poinsot¹s motion, motion of a free rigid body.

Readings/Bibliography

M. FABRIZIO, Elementi di Meccanica Classica, Zanichelli. Bologna

A.MURACCHINI, T.RUGGERI, L.SECCIA, Laboratorio di Meccanica Razionale, Esculapio, Bologna

Teaching methods


Assessment methods

Preliminary written examination and oral examination.

Teaching tools

Blackboard, transparencies and projector.

Office hours

See the website of Barbara Lazzari