Analysis of Nonlinear Systems by Using a Modified Matching Method.

In analyzing the dynamics of nonlinear systems by the matching method, ″matching″ of solutions is effected at the boundaries of the linearity sectors. The paper shows that matchng procedures can be eliminated, thus resulting in considerable reduction of computations. This is achieved by using the proposed writing of the equations of the system dynamics in combination with the use of the operator method. Solution of the system for each of the successive sectors of linearity is obtained in analytical form as a general recurrent formula. Thus, the solution of the problem becomes considerably simplified and is reduced in the main to the construction of the unknown time functions - coordinates of the system.