Rational Mechanics - a.y. 2016/2017
Period (Year/Semester): II/I
Required/expected prior knowledge: Mathematical Analysis I, Geometry and Algebra
Acquiring concepts and general principles that represent the scientific foundation of several significant mathematical models for engineering. Displaying the ability to apply the previously gained knowledge in order to solve simple evolution and equilibrium problems.
Tables of contents:
Vector theory and tensor calculus. Equivalent systems of applied vectors. Geometry of masses. Kinematics of rigid bodies. Translational and rotational motions. Mozzi - Chasles' theorem and the screw axis. Rigid plane motions and applications to transmission problems. Relative motions and Coriolis theorem. Constraints and their classification with their analytic descriptions. Holonomic systems. Possible and virtual displacements. Degrees of freedom and generalized coordinates. Newton's laws of motion. Work, potential and energy. Constraints reactions and experimental properties. Friction laws. Principles and problems of mechanics of material systems. d’Alembert’s principle. Applications to rigid bodies. Introduction to the Lagrange’s equations. Equations of equilibrium. Principle of virtual works with applications. Equilibrium analysis and computation of constraints reactions. Analysis of Trusses: the method of joints and the method of sections. Beams. Eulerian and Lagrangian descriptions. Elements of continuum mechanics.
Lectures and classroom exercises.
Textbooks and learning aids:
Levi Civita , Amaldi U - Lezioni Di Meccanica Razionale vol I, vol II ,Complementi alle Lezioni (2013) Ed CompoMat.
D’Acunto, Massarotti, “Meccanica razionale per l’ingegneria”, Maggioli Ed. (2016).
Biscari, Ruggeri, Saccomandi, Vianello, “Meccanica razionale per l’ingegneria”, Springer (2016).
Learning aids: notes in the site and class notes
Assessment will be written and oral. Question are: multiple choice tests, open questions, numerical exercises.