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  3. Volume 14, Number 1, 2024
  4. Model of sensitivity to the initial conditions of the equations of motion in the electric fieldn

Model of sensitivity to the initial conditions of the equations of motion in the electric fieldn

JCPEE.
2024;
Volume 14, Number 1
: pp. 36-41
https://doi.org/10.23939/jcpee2024.01.036
Authors:
  1. Vasyl Tchaban
1
Lviv Polytechnic National University

. 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.

electric field
nonlinear differential equations of motion
periodic solutions
model of sensitivity to initial conditions
reduction of order of variational equations and monodromy matrix
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  11. V. Сhaban, Theoretical substantiation of the results of the laser location of the trajectory of the Moon moving away from the Earth.
  12. V. Tchaban, Radial Componet of Vortex Ektctric Field Force. – Computational Problems of Electrical Engineering, vol. 11, No 1, 2021, pp. 32–35. ttps://doi.org/10.23939/jcpee2021.01.032
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