Construction of the differential equations system of the program motion in Lagrangian variables in the presence of random perturbations
Кездейсоқ түрткiлер болғанда Лагранждың айнымалыларындағы бағдарламалық қозғалыстың дифференциалдық теңдеулер жүйесiн құру
Построение системы дифференциальных уравнений программного движения в лагранжевых переменных при наличии случайных возмущений
Tleubergenov M.I. Vassilina G.K. Azhymbaev D.T.
2022E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2022#105Issue 1118 - 126 pp.
The classification of inverse problems of dynamics in the class of ordinary differential equations is given in the Galiullins monograph. The problem studied in this paper belongs to the main inverse problem of dynamics, but already in the class of second-order stochastic differential equations of the Ito type. Stochastic equations of the Lagrangian structure are constructed according to the given properties of motion under the assumption that the random perturbing forces belong to the class of processes with independent increments. The problem is solved as follows: First, a second-order Ito differential equation is constructed so that the properties of motion are the integral manifold of the constructed stochastic equation. At this stage, the quasi-inversion method, Erugins method and Itos rule of stochastic differentiation of a complex function are used. Then, by applying the constructed Ito equation, an equivalent stochastic equation of the Lagrangian structure is constructed. The necessary and sufficient conditions for the solvability of the problem of constructing the stochastic equation of the Lagrangian structure are illustrated by the example of the problem of constructing the Lagrange function from a motion property of an artificial Earth satellite under the action of gravitational forces and aerodynamic forces.
integral manifold , quasi-inversion method , stochastic basic inverse problem , stochastic differential equation , stochastic equation of Lagrangian structure
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Almaty University of Power Engineering and Telecommunications named after G.Daukeev, Almaty, Kazakhstan
K.Zhubanov Aktobe Regional University, Aktobe, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University
Almaty University of Power Engineering and Telecommunications named after G.Daukeev
K.Zhubanov Aktobe Regional University
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