## 20810127 - THEORETICAL MECHANICS

The primary aim of the course is to provide to the students the skills to formalize a problem of rigid-bodies mechanics using the appropriate mathematical tools. Particular attention is paid on the modeling and analysis of simple engineering problems, in order to provide the cultural background required to cope with engineering analysis and design.
teacher profile | teaching materials

Programme

Vector Space: definition of vectors; scalar and vector product.
Matrix algebra: tensor product and proiector.
Damped harmonic oscillator; study of mechanical power involved; phase plane.
Kinematics of material point.
Geometry of curves; velocity and acceleration in the moving frame.
Kinematics in polar coordinates; rigid motion; spin, angular speed and Poisson formulas.
Study of velocity field for rigid bodies.
Planar motions: center of rotation (CR)
Kinematics of constraints, points system; degrees of freedom.
Theoremes of Galileo and Coriolis
Principles of the mechanics of material point; notion of forces; friction forces.
Dynamics of material point.
Fundamental mechanical quantities.
Cardinal Equations; riduction of system of forces.
Power, Work, Energy, Potential
Kinetic energy theorem; balance of mechanical energy.
Center of mass and its properties.
Moment of inertia and its matrix representation
Momentum and angular momentum for CR
Statics; Euler’s Equations for 3D Rigid Body (cardial equations in Italian).
Statics of suspended cables.
Introduction to Analytics Mechanics;
Principle of Virtual Power
Lagrange equations for conservative system; analysis of stability
Small oscillations.
Elements of impulsive dynamics

Core Documentation

Free pdf notes, comprehensive of exercises .
Reference text: Biscari, Ruggeri, Saccomandi, Vianello, “Meccanica Razionale per l’Ingegneria”, Monduzzi, (seconda edizione).

Type of evaluation

Student performance is evaluated with a written test lasting 1 and ½ hour, and an oral discussion. Only students with sufficient grade are admitted at the oral discussion. During the discussion, the written test will be examined; afterwards, there will be a session with some random questions about the progam.