sentences:  As of 2006, there is no general theorem to circumvent this difficulty in arbitrary dimension, although certain special cases have been resolved.A second avenue of attack is to see whether the system (E) admits a submersion onto a lower-dimensional system and to try to "lift" a Lagrangian for the lower-dimensional system up to the higher-dimensional one.This is not really an attempt to solve the Helmholtz conditions so much as it is an attempt to construct a Lagrangian and then show that its Euler–Lagrange equations are indeed the system (E).