Applications of approximate Lagrangians to linear dissipative nonreciprocal circuits. IV. Sufficient conditions for equivalence of L/sub c/ and L/sub r/

In applications of the method of approximate Lagrangians, the classical Lagrangian L/sub c/ and the reverse-time Lagrangian L/sub r/ of linear time-invariant systems are equivalent, i.e., they produce identical approximate solutions with the same test-functions if they belong to a certain class of functions. Sufficient conditions for equivalence of L/sub c/ and L/sub r/ are derived and illustrated by examples of test-functions which do and do not satisfy these conditions, and generate the same or different approximations with L/sub c/ and L/sub r/.