New Conserved Quantity Constructed upon Form Invariance for Holonomic Systems

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