s-equivalent Lagrangians in generalized mechanics

The problem of s-equivalent Lagrangians is discussed in generalized mechanics. Some results known from ordinary (nongeneralized) mechanics are extended to the generalized case. A theorem allowing the reduction of the higher-order Lagrangian description to the usual order is derived. The theorem is found to be useful in the analysis of generalized mechanical systems, and it leads to a new type of equivalence between Lagrangian functions. Some new perspectives are pointed out.