Symmetry and conserved quantity of Tzenoff equations for holonomic systems with redundant coordinates

A holonomic system with redundant coordinates can be expressed in Tzenoff equations. We concentrate on the symmetry for these Tzenoff equations under the infinitesimal transformations of groups. The notions are given for both Mei symmetry and Lie symmetry of the Tzenoff equations for holonomic system with redundant coordinates. The determination equations of symmetries for these systems have been obtained and the sufficient and necessary conditions for deriving Lie symmetries from Mei symmetries are proposed. It is shown that Hojman conserved quantities can be found from a special Lie symmetry or a Lie symmetry derived from Mei symmetry for the Tzenoff equations of holonomic systems with redundant coordinates.