Form Invariance of Lagrange System Forced by Holonomic Constraints

Deals with the form invariance and the conserved quantities of a Lagrange system forced by holonomic constraints. It obtains the definition and the criterion for the form invariance of the system relying on the fact that the form of Lagrange equations and that of constrained equations with ideal bilateral holonomic constraints preserve an invariance under the infinitesimal transformations. In this case, it is shown that the form invariance of the system usually changes, and the condition under which the form invariance and the corresponding Noether conserved quantity hold is given. Two examples are finally given to illustrate the application of the results.