We construct a geometric setup based on the theory of left and right jet bundles of a fiber bundle over IR appropriate to model the presence of constraints for a time-dependent impulsive mechanical system. A detailed classification of constraints is presented and all types of constraints are proved to be naturally flamed in the setup. The concepts of reactive impulse and constitutive characterization of constraints can be defined very naturally according to the nature of the constraint. A minimum principle strongly related to Gauss's principle of minimal constraint is introduced to propose an ideality criterion suitable for all the classified constraints.
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