Portale di Ateneo - En.Unibs.it

1. Kinematics. Motion, velocity and acceleration of a point particle: central, plane, circular, harmonic and helical motions. Holonomic constraints and systems of particles. Kinematics of rigid bodies: Poisson's formula and Mozzi's theorem. Relative motions. Plane rigid motions and centrodes. Rigid motion around a fixed point.

2. Dynamics of unconstrained material particles and bodies. Mass, force, and Newton's laws. Inertial frames and Galilei transformations. Typical force fields: constitutive, impressed, and reference-induced forces. Gravitational force and weight. Dynamics of a single mass point. The two-body system. The kinetic energy balance. The principle of mechanical energy conservation. Conservative force fields and potentials.

3. Dynamics of constrained material bodies. The principle of virtual work for reactions of constraints. Properties of the center-of-mass. Moment of inertia. The balance principles of linear and angular momentum. Koenig's theorems for kinetic energy and angular momentum. Kinetic energy and angular momentum of a rigid body. Properties of the inertia tensor. Huygens-Steiner theorem. Statics of constrained rigid bodies. Motion of a rigid body spinning around a fixed axis. Rigid body dynamics with a fixed point.

4. Lagrangian mechanics. D'Alembert's principle. The principle of virtual works. Statics and dynamics of holonomic systems. Lagrange's equations. Lagrangian functions. First-order integrals of motion.