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

### 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.
Published

25.07.2010

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 62, no. 7, July 2010, pp. 1002–1008, https://umj.imath.kiev.ua/index.php/umj/article/view/2932.

Issue

Section

Short communications