Subject: CLASSICAL MECHANICS (A.A. 2019/2020)
Unit meccanica razionale
Related or Additional Studies (lesson)
Analisi Matematica I
The purpose is to provide both the basic concepts of Classical Mechanics and the mathematical tools with the aim to model some simple mechanical systems.
Analytic geometry, elementary functions, differential and integral calculus of multi variable functions.
Vector Algebra: definition of a vector; the scalar product; the vector product; the triple products;
differentiation of a vector with respect to a scalar parameter.
Mass Geometry: mass; centre of mass; moments of inertia; momental ellipsoid; principal axes of inertia.
Kinematics: velocity and acceleration of a particle; harmonic motion; circular motion; the rigid body; eulerian angles; Poisson formulas; velocity of a particle of a rigid body; kinetic states; kinematics of a particle with respect to non fixed orthogonal axes; rigid motion in the plane.
Fundamental units and notion: forces; laws of motion; lagrangian coordinates; real and virtual displacements; constraints; active forces and reactions; systems of forces and characteristic vectors; equivalence theorem for force systems; elementary operations with forces; parallel force systems; weight force; work; conservative forces; conservative systems.
Particle mechanics: Newton law; equilibrium and motion of a particle; friction; linear momentum, angular momentum and kinetic energy; kinetic energy theorem; energy conservation theorem; pendulum; harmonic oscillator; relative equilibrium and motion; centrifugal force.
Mechanics of systems of particles: equilibrium of particle systems; principle of virtual works; equilibrium of rigid body; equilibrium of conservative systems; stability of equilibrium; linear momentum, angular momentum and kinetic energy; energy theorems; theorem of motion of the centre of mass and theorem of angular momentum; first integrals; lagrange equations. constants of motion and lagrangian formalism.
Course teaching consists of theoretical lectures on the topics described in the section "Contents" and of solution of exercises on simple classical mechanics models.
Learning assessment is based on: - Two written (mid-term and final) tests with theory and exercises. Or, alternatively, - Oral final exam on the topics of the section “Contents”.
Knowledge and understanding
Knowledge of Vector Algebra; knowledge of mass geometry; knowledge of kinematics of a particle and of a rigid body; knowledge of basic classical mechanics notions (forces; laws of motion; lagrangian coordinates); knowledge of particle mechanics; knowledge of mechanics of particle systems.
Applying knowledge and understanding
Solution of problem of classical mechanics: computation of center of mass and of moment of inertia; equilibrium and motion of a particle and of a rigid body; lagrange equations.
Skills of decideng when and how to apply classical mechanics models and understanding the results.
Skills to communicate in a clear and rigorous way the methods of classical mechanics.
V. Franceschini, C. Vernia, Meccanica Razionale per Ingegneria, Pitagora Editrice, Bologna.