Portale di Ateneo - En.Unibs.it

Classical Mechanics

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. 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. Friction Coulomb's laws. The
principle of mechanical energy conservation. Conservative force fields
and potentials.

Geometry of masses

Properties of applied vectors. Properties of the center-of-mass. 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-Steiner's theorem.

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,
or a fixed point. Poinsot's motion.

Canonical mechanics and qualitative dynamics

D'Alembert's principle. Statics and dynamics of holonomic systems.
Lagrange equations. Lyapunov stability and instability of equilibrium
positions. The Lyapunov function method. Lagrange-Dirichlet theorem.
Linearization in the neighborhood of a stable equilibrium position.