CONNECTIONS AND GEODESIC CHARACTERISTIC OF EQUATIONSOF MOTION FOR CONSTRAINED MECHANICAL SYSTEMS

The geodesic characteristic of equations of motion for nonautonomous constrainedmechanical systems is studied in the modern setting of global differential geometry . Anecessary and sufficient condition for the dynamical flow of a monautonomous mechanical system with geodesic characteristic was obtained with respect to aconnection on jet bundle . The dynamical flow concerning the non-autonomous casewas always of geodesic characteristic with regard to torsion-free connections. Thus the motion of any nonautonomous mechanical system with constraints can be alwaysrepresented by the motion along the geodesic line of torsion-free connection on 1-jetbundle, which is different from the case in an autonomous mechaincal system.