Università Roma Tre

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

Free pdf notes, comprehensive of exercises .

Reference text: Biscari, Ruggeri, Saccomandi, Vianello, “Meccanica Razionale per l’Ingegneria”, Monduzzi, (seconda edizione).