By means of a tangent space we introduce, a system of Lagrange's equations of the second kind is represented in the vector form. It is shown that the tangential space is partitioned by equations of constraints into the direct sum of two subspaces. In one of them the component of an acceleration vector of system is uniquely determined by the equations of constraints. The notion of ideality of holonomic constraints and nonholonomic constraints of the first and second orders is analyzed. This notion is extended to high-order constraints. The relationship and equivalence of differential variational principles of mechanics are considered. A geometric interpretation of the ideality of constraints is given. Generalized Gaussian principle is formulated. By means of this principle for nonholonomic systems with third-order constraints the equations in Maggi's form and in Appell's form are obtained.