Kinematics
Motion, velocity and acceleration of a point particle: central, plane. Holonomic constraints and systems of particles. Kinematics of rigid
bodies: Poisson's formula and Mozzi's theorem. Relative motions. Plane
rigid motions. Rigid motion around a fixed point. Poinsot’s cones and
regular precession.
Principles and fundamental laws
Mass, force, and Newton's laws. Inertial frames and Galilei
transformations. Typical force fields: constitutive, impressed, and
reference-induced forces. Gravitational force and weight. The principle
of virtual work for reactions of constraints. The principle of mechanical
energy conservation. Conservative force fields and potentials.
Geometry of masses
Properties of applied vectors. Properties of the center-of-mass. Moment
of inertia. The balance principles of linear and angular momentum. The
Kinetic energy balance. Koenig's theorems for kinetic energy and
angular momentum. Kinetic energy and angular momentum of a rigid
body. Properties of the inertia tensor. Huygens and Steiner's theorems.
Statics and Dynamics of constrained material bodies
Statics of constrained rigid bodies. Dynamics of constrained material
bodies. Equations of motion of a rigid body spinning around a fixed axis. Rigid body dynamics with a fixed point.
Canonical mechanics and qualitative dynamics
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.