Construction of a functional by a given second-order Ito stochastic equation-Reference-Cited by-同舟云学术

Construction of a functional by a given second-order Ito stochastic equation

Published:2023-01-01 Issue:1 Volume:21 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Tleubergenov Marat¹²,Vassilina Gulmira¹³,Ismailova Shakhmira¹²

Affiliation:

1. Institute of Mathematics and Mathematical Modeling , Almaty , Kazakhstan

2. Al-Farabi Kazakh National University , Almaty , Kazakhstan

3. Almaty University of Power Engineering and Telecommunication named Gumarbek Daukeev , Almaty , Kazakhstan

Abstract

Abstract In this article, we consider the problem of extending Hamilton’s principle to the class of natural mechanical systems with random perturbing forces of white noise type. By the method of moment functions, we construct the functionals taking a stationary value on the solutions of a given stochastic equation of Lagrangian structure.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2023-0148/pdf

Reference31 articles.

1. N. P. Yerugin, Construction of the entire set of systems of differential equations having a given integral curve, Appl. Math. Mech. 10 (1952), no. 6, 659–670. (in Russian)

2. A. S. Galiullin, Methods for Solving Inverse Problems of Dynamics, Nauka, Moscow, 1986. (in Russian)

3. A. S. Galiullin, Selected Works in Two Volumes, V. I. and V. II, People’s Friendship University, Moscow, 2009. (in Russian)

4. I. A. Mukhametzyanov and R. G. Mukharlyamov, Equations of Program Motions, Publishing House of the Peoples’ Friendship University, Moscow, 1986 (in Russian).

5. R. G. Mukharlyamov, Differential-algebraic equations of programmed motions of Lagrangian dynamical systems, Mech. Solids 46 (2011), no. 4, 534–543, DOI: https://doi.org/10.3103/S0025654411040042. (in Russian)