The paper introduces the author's idea of the system of differential variation principles and equations of mechanics in the systems with arbitrary differential constraints. It is based on the classical mechanics extension variant which describes the dynamics of any orders holonomic and nonholonomic systems. For the constrained system its Affix is introduced. It moves in E3N space on the multifold Rm, restrained by the differential constraints as well. Based on the motion equations the author introduces the covariant forms of mechanics equations and principles of highest order nonholonomic systems.