2017
Том 69
№ 9

All Issues

On the construction of a set of stochastic differential equations on the basis of a given integral manifold independent of velocities

Azhymbaev D. T., Tleubergenov M. I.

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Abstract

We construct the Lagrange equation, Hamilton equation, and Birkhoff equation on the basis of given properties of motion under random perturbations. It is assumed that random perturbation forces belong to the class of Wiener processes and that given properties of motion are independent of velocities. The obtained results are illustrated by an example of motion of an Earth satellite under the action of gravitational and aerodynamic forces.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 7, pp 1163-1173.

Citation Example: Azhymbaev D. T., Tleubergenov M. I. On the construction of a set of stochastic differential equations on the basis of a given integral manifold independent of velocities // Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 1002–1008.

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