A study on the Lagrangian image of the Birkhoffian representations
关于Birkhoff表示的Lagrange像的研究

The Lagrangian image of the Birkhoffian representations is studied. The conditions that the second-order Lagrangians should satisfy are obtained, under which the generalized Lagrange equations are second-order differential equations. A new way for solving the inverse problem in Lagrange mechanics is presented. An error made in the study by some author is pointed out. Two examples are given to illustrate the application of the result.