- Docente: Barbara Lazzari
- Credits: 6
- SSD: MAT/07
- Language: Italian
- Moduli: Barbara Lazzari (Modulo 1) Roberta Nibbi (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- 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
See the website of Roberta Nibbi