Form Invariance and Non-Noether Conserved Quantity of Holonomic Mechanical System

Non Noether conserved quantity led by form invariance for holonomic systems is studied. Equations of motion and criterion equations of the form invariance are established. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the result.