A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations

For the relativistic holonomic nonconservative system, a new Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the theory of invariance of differential equations of motion under infinitesimal transformations for t and q_s, we construct the relativistic Lie symmetrical determining equations and obtain directly a new relativistic Lie symmetrical non-Noether conserved quantity of the system, which only depend on the variables t, q_s and \dotq_s. An example is given to illustrate the application of the results.