Form invariance and non-Noether conserved quantity for holonomic mechanical systems with remainder coordinates

This paper studies the form invariance and the non-Noether conserved quantity of the holonomic mechanical systems with remainder coordinates. Firstly, the differential equations of motion of the systems are established. The definitions and criterions of the form invariance and the Lie symmetry of the systems under the infinitesimal transformations which only depend upon the generalized coordinates are given, and the relation between the form invariance and the Lie symmetry is discussed. Secondly, the condition under which the form invariance can lead up to a non-Noether conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.