Representing a second-order Ito equation as an equation with a given force structure
Екiншi реттi Ито теңдеуiн берiлген құрылымы бар күштердiң теңдеуi түрiнде кұру
Представление уравнения Ито второго порядка в виде уравнения с заданной структурой сил
Tleubergenov M.I. Vassilina G.K. Abdrakhmanova A.A.
2023E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2023#112Issue 4119 - 129 pp.
The problem of constructing equivalent equations with a given structure of forces by the given system of stochastic equations is considered. The equivalence of equations in the sense of almost surely is investigated. The paper determines the conditions under which a given system of second-order Ito stochastic differential equations is represented in the form of stochastic Lagrange equations with non-potential forces of a certain structure. Necessary and sufficient conditions for the representability of stochastic equations in the form of stochastic equations with non-potential forces admitting the Rayleigh function are obtained. The obtained results are illustrated by an example of motion of a symmetric satellite in a circular orbit, assuming a change in pitch under the action of gravitational and aerodynamic forces.
equivalence almost surely , Stochastic differential equation , stochastic equations with non-potential forces , stochastic Lagrange equation
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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 Telecommunication named Gumarbek Daukeev, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University
Almaty University of Power Engineering and Telecommunication named Gumarbek Daukeev
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026