Constitutive Characterizations of Non-Ideal Constraints in Classical Mechanics

The theory of two-sided, positional constraints with friction acting on a material point in Classical Mechanics is presented in the geometrical context of the jet-extensions of an affine bundle. This context allows one to study both rigid and non-rigid constraints. We prove that the geometry of the system and the forces acting on the point determine in a natural way the direction of the friction reaction. This allows one to introduce a wide class of constitutive characterizations of constraints with friction, that includes the most common ones.