29690 - Rational Mechanics T

Academic Year 2018/2019

  • Docente: Barbara Lazzari
  • Credits: 6
  • SSD: MAT/07
  • Language: Italian
  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Chemical and Biochemical Engineering (cod. 8887)

Learning outcomes

Notions of kinematics, statics and dynamics of material systems. Motions of rigid bodies. An introduction to analytical mechanics.

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.

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.

Analytical Mechanics. Symbolic equations of Dynamics: D'Alembert's principle. Lagrange's equations. Lagrangian systems and their first integrals. Symbolic equations of statics: Principle of Virtual Work and its applications. Equilibrium conditions for a holonomic system. Stability of equilibrium. Nonlinear oscillations: Weierstrass method. Small oscillations around a position of stable equilibrium.

Readings/Bibliography

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

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

Teaching methods

The basic theory is explained in standard lessons and illustrated with several examples and exercises.

Assessment methods

Achievements will be assessed by the means of a final exam. This is based on an analytical assessment of the "expected learning outcomes" described above. In order to properly assess such achievement the examination is composed of two different sections: written session and theoretical (written or oral) exam. The written session consists of a simple problem with multiple questions, and its possible scores are "sufficiente", "quasi sufficiente" or "insufficiente". To be eligible to take the theoretical exam the student must score in the written test "sufficiente" or "quasi sufficiente".

The oral session, consists of two or three theoretical questions.

Higher grades will be awarded to students who demonstrate an organic understanding of the subject, a high ability for critical application, and a clear and concise presentation of the contents.

To obtain a passing grade, students are required to at least demonstrate a knowledge of the key concepts of the subject, some ability for critical application, and a comprehensible use of technical language.

Teaching tools

Blackboard, transparencies and projector.

Office hours

See the website of Barbara Lazzari