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

The geodesic characteristic of equations of motion for nonautonomous constrained mechanical systems is studied in the modern setting of global differential geometry. A necessary and sufficient condition for the dynamical flow of a nonautonomous mechanical system with geodesic characteristic was obtained with respect to a connection of 1-jet bundle. The dynamical flow concerning 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 the case in an autonomous mechanical system.