On nonholonomic dynamics of any orders

The extension of a classical dynamics (ECD) at systems with arbitrary nonholonomic constraints is offered. The motion of such a system is featured as a motion of its constrained figuring particle (FP) with mass, equal mass of system, in R_s-space. The theorem of structure of an r-derivative of a FP constraint force is demonstrated. On its basis the FP motion equations and series of their covariant forms are output: in "generalized forces" (GF), similar the LaGrange and Appell equations, in "generalized forces factors" (GFF) and others. For this purpose the generalized measures of a motion and action at system are introduced: kineta (K_S) as the generalization of a kinetic energy and Appell\´s function, GFF of external forces and inertial forces