Variational Formulation of Linear Time-Dependent Invariants
  It is shown that linear time-dependent invariants for arbitrary multi\-dimensional quadratic systems can be obtained from the Lagrangian and Hamiltonian formulation procedures by considering a variation of coordinates and momenta that follows the classical trajectory and defines a noetherian symmetry transformation. 
O. Casta\~nos, R. L\'opez-Pe\~na and V.I. Man'ko