  In this paper we discuss how the gauge principle can be applied to
classical-mechanics models with finite degrees of freedom. The local invariance
of a model is understood as its invariance under the action of a matrix Lie
group of transformations parametrized by arbitrary functions. It is formally
presented how this property can be introduced in such systems, followed by
modern applications. Furthermore, Lagrangians describing classical-mechanics
systems with local invariance are separated in equivalence classes according to
their local structures.
