Form Invariance and Non-Noether Conserved Quantity for Holonomic Mechanical Systems with Variable Mass

Using a form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the holonomic mechanical systems with variable mass is studied. The differential equations of motion of the systems are established. The definition and criterion of the form invariance of the systems under special infinitesimal transformations are studied. 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 non-Noether conserved quantity and the form of the conserved quantity are obtained.