We study the inverse dynamics problem: for a given manifold restore a force field, which lies in the tangent subspace to manifold. This inverse problem is very important for a variety of mathematical models mechanics. We solve the problem of construction of differential equations' system by given program manifold. This problem is reduced to investigation of quality properties of program manifold. The conditions of instability of the control systems with non-stationer nonlinearities are considered in the neighborhood of a program manifold. Nonlinearity satisfies conditions of local quadratic relations. The sufficient conditions of instability of the program manifold have been obtained relatively to a given vector-function by means of construction of Lyapunov function in the class of continuously-differentiable at time and bounded on a norm matrices.
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