Connections and geodesic characteristic of equations of motion for constrained mechanical systems

The geodesic characteristic of equations of motion for nonautonomous constr ained mechanical systems is studied in the modern setting of global differe ntial geometry. A necessary and sufficient condition for the dynamical flow of a nonautonomous mechanical system with geodesic characteristic was obta ined with respect to a connection of 1-jet bundle. The dynamical flow conce rning the non-autonomous case motion of an nonautonomous mechanical system with constraints can be always represented by the motion along the geodesic line of torsion-free connection on 1-jet bundle, which is different from t he case in an autonomous mechanical system.