Variational Method of Auxiliary Equations in Nonlinear Systems Analysis and Synthesis Problems

To avoid the operation of differentiating the original equations matrix of coefficients, and find a parametric sensitivity matrix, we propose a method for constructing auxiliary first variation differential equations of nonlinear system state equations, written in coordinates and velocities. Auxiliary equations of the first variation are written in impulses. This allows you reduce the monodromy matrix to the multiplication of two matrices (the coefficients matrix and the auxiliary sensitivity to the initial conditions matrix), instead the operation of differentiating the original equations matrix of coefficients by argument that is almost impossible. The Cauchy problem and the boundary value problem for ordinary nonlinear differential equations of state and their first variation differential equations are solved. As an example, the results of transient and stable processes computer simulation of computerized control system executive object are given.