Symmetry and Conserved Quantity of Tzénoff Equations for Holonomic Systems with Redundant Coordinates

A holonomic system with redundant coordinates can be expressed in Tzénoff equations. We concentrate on the symmetry for these Tzénoff equations under the infinitesimal transformations of groups. The notions are given for both Mei symmetry and Lie symmetry of the Tzénoff 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 Tzénoff equations of holonomic systems with redundant coordinates.