Portale di Ateneo - En.Unibs.it

1. Kinematics

Motion, velocity and acceleration of a point particle: central, plane 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.

2. 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.

3. 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.

4. 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.

5. 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.