A New Conserved Quantity Constructed by Form Invariance for Holonomic Systems with Redundant Coordinates

A new conserved quantity constructed directly by using the form invariance for a holonomic system with redundant coordinates was presented. The definition and the criterion of the form invariance of the system were obtained by relying on the fact that the differential equations of motion and the constrained equations of the bilateral ideal holonomic mechanical system with redundant coordinates preserve an invariance under the infinitesimal transformations. The condition under which the form invariance can lead to a conserved quantity and the form of the conserved quantity were deduced, and three corollaries in special cases were given. Two examples are finally given to illustrate the application of the results.