Time-dependent kinetic energy metrics for Lagrangians of electromagnetic   type
  We extend the results obtained in a previous paper about a class of Lagrangian systems which admit alternative kinetic energy metrics to second-order mechanical systems with explicit time-dependence. The main results are that a time-dependent alternative metric will have constant eigenvalues, and will give rise to a time-dependent coordinate transformation which partially decouples the system. 
W. Sarlet, G. Prince, T. Mestdag, O. Krupkova
math-ph math.DS math.MP