Non Noether conserved quantity of the holonomic mechanical systems in terms of quasi-coordinates - An extension of Hojman theorem

Using the Lie symmetry under infinitesimal transformations in which the time in not variable, a new conserved quantity of holonomic mechanical systems in terms of quasi-coordinates is studied. The differential equations of motion of the systems are established. Determining equations of Lie symmetry under infinitesimal transformations are given. The Hojman theorem is generalized. Finally, an example is given to illustrate the application of the results.