DYNAMIC CONNECTIONS AND HIGHER-ORDER LAGRANGIAN SYSTEMS

We show that if xi is a (2r)-order differential equation (semispray) on the (2r - 1)-jet bundle T2r-1Q whose paths are solutions of the non-autonomous Lagrange equations, then there is a connection GAMMA on T2r-1Q whose paths are also solutions of the same equations. Moreover, GAMMA is a connection whose associated semispray is precisely xi. This is an extension to higher-order Lagrangian dynamics of a previous result given by M. DE LEON and P. RODRIGUES [3].