Model of Sensitivity to the Initial Conditions of the Equations of Motion in the Electric Fieldn

Abstract

A numerical method for calculating steady periodic processes of nonlinear differential equations of motion in an electric field is proposed based on their integration under initial conditions that exclude transient reaction. The calculation of such initial conditions is based on Newton's iterative formula. At each iteration, together with the basic equations of motion, the corresponding equations of the first variation are integrated over the periodicity time interval, which represent a model of sensitivity to the initial conditions, In addition, the number of unknown variational equations has been reduced, which makes it possible to lower their order, and, at the same time, the order of the monodromy matrix. All this contributes to the simplification of the relevant computational algorithms and computer programs. The method takes into account the finite rate of electric field propagation.